Panoptic segmentation assigns semantic and instance ID labels to every pixel of an image. As permutations of instance IDs are also valid solutions, the task requires learning of high-dimensional one-to-many mapping. As a result, state-of-the-art approaches use customized architectures and task-specific loss functions. We formulate panoptic segmentation as a discrete data generation problem, without relying on inductive bias of the task. A diffusion model is proposed to model panoptic masks, with a simple architecture and generic loss function. By simply adding past predictions as a conditioning signal, our method is capable of modeling video (in a streaming setting) and thereby learns to track object instances automatically. With extensive experiments, we demonstrate that our simple approach can perform competitively to state-of-the-art specialist methods in similar settings.1

This article does not describe a working system. Instead, it presents a single idea about representation that allows advances made by several different groups to be combined into an imaginary system called GLOM.1 The advances include transformers, neural fields, contrastive representation learning, distillation, and capsules. GLOM answers the question: How can a neural network with a fixed architecture parse an image into a part-whole hierarchy that has a different structure for each image? The idea is simply to use islands of identical vectors to represent the nodes in the parse tree. If GLOM can be made to work, it should significantly improve the interpretability of the representations produced by transformer-like systems when applied to vision or language.

Dynamic evaluation of language models (LMs) adapts model parameters at test time using gradient information from previous tokens and substantially improves LM performance.However, it requires over 3x more compute than standard inference.We present Fast Weight Layers (FWLs), a neural component that provides the benefits of dynamic evaluation much more efficiently by expressing gradient updates as linear attention.A key improvement over dynamic evaluation is that FWLs can also be applied at training time so the model learns to make good use of gradient updates.FWLs can easily be added on top of existing transformer models, require relatively little extra compute or memory to run, and significantly improve language modeling perplexity.

While language tasks are naturally expressed in a single, unified, modeling framework, i.e., generating sequences of tokens, this has not been the case in computer vision. As a result, there is a proliferation of distinct architectures and loss functions for different vision tasks. In this work we show that a diverse set of "core" computer vision tasks can also be unified if formulated in terms of a shared pixel-to-sequence interface. We focus on four tasks, namely, object detection, instance segmentation, keypoint detection, and image captioning, all with diverse types of outputs, e.g., bounding boxes or dense masks. Despite that, by formulating the output of each task as a sequence of discrete tokens with a unified interface, we show that one can train a neural network with a single model architecture and loss function on all these tasks, with no task-specific customization. To solve a specific task, we use a short prompt as task description, and the sequence output adapts to the prompt so it can produce task-specific output. We show that such a model can achieve competitive performance compared to well-established task-specific models.

Capsule networks aim to parse images into a hierarchy of objects, parts and relations. While promising, they remain limited by an inability to learn effective low level part descriptions. To address this issue we propose a way to learn primary capsule encoders that detect atomic parts from a single image. During training we exploit motion as a powerful perceptual cue for part definition, with an expressive decoder for part generation within a layered image model with occlusion. Experiments demonstrate robust part discovery in the presence of multiple objects, cluttered backgrounds, and occlusion. The learned part decoder is shown to infer the underlying shape masks, effectively filling in occluded regions of the detected shapes. We evaluate FlowCapsules on unsupervised part segmentation and unsupervised image classification.

Deep neural networks (DNNs) are powerful black-box predictors that have achieved impressive performance on a wide variety of tasks. However, their accuracy comes at the cost of intelligibility: it is usually unclear how they make their decisions. This hinders their applicability to high stakes decision-making domains such as healthcare. We propose Neural Additive Models (NAMs) which combine some of the expressivity of DNNs with the inherent intelligibility of generalized additive models. NAMs learn a linear combination of neural networks that each attend to a single input feature. These networks are trained jointly and can learn arbitrarily complex relationships between their input feature and the output. Our experiments on regression and classification datasets show that NAMs are more accurate than widely used intelligible models such as logistic regression and shallow decision trees. They perform similarly to existing state-of-the-art generalized additive models in accuracy, but are more flexible because they are based on neural nets instead of boosted trees. To demonstrate this, we show how NAMs can be used for multitask learning on synthetic data and on the COMPAS recidivism data due to their composability, and demonstrate that the differentiability of NAMs allows them to train more complex interpretable models for COVID-19.

We propose a self-supervised capsule architecture for 3D point clouds. We compute capsule decompositions of objects through permutation-equivariant attention, and self-supervise the process by training with pairs of randomly rotated objects. Our key idea is to aggregate the attention masks into semantic keypoints, and use these to supervise a decomposition that satisfies the capsule invariance/equivariance properties. This not only enables the training of a semantically consistent decomposition, but also allows us to learn a canonicalization operation that enables object-centric reasoning. To train our neural network we require neither classification labels nor manually-aligned training datasets. Yet, by learning an object-centric representation in a self-supervised manner, our method outperforms the state-of-the-art on 3D point cloud reconstruction, canonicalization, and unsupervised classification.

Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This decomposition is fundamental in computer graphics, where it provides one of the most common ways to approximate geometry, for example, in real-time physics simulation. A convex object also has the property of being simultaneously an explicit and implicit representation: one can interpret it explicitly as a mesh derived by computing the vertices of a convex hull, or implicitly as the collection of half-space constraints or support functions. Their implicit representation makes them particularly well suited for neural network training, as they abstract away from the topology of the geometry they need to represent. However, at testing time, convexes can also generate explicit representations - polygonal meshes - which can then be used in any downstream application. We introduce a network architecture to represent a low dimensional family of convexes. This family is automatically derived via an auto-encoding process. We investigate the applications of this architecture including automatic convex decomposition, image to 3D reconstruction, and part-based shape retrieval.

This paper presents the Imputer, a neural sequence model that generates output sequences iteratively via imputations. The Imputer is an iterative generation model, requiring only a constant number of generation steps independent of the number of input or output tokens. The Imputer can be trained to approximately marginalize over all possible alignments between the input and output sequences, and all possible generation orders. We present a tractable dynamic programming training algorithm, which yields a lower bound on the log marginal likelihood. When applied to end-to-end speech recognition, the Imputer outperforms prior non-autoregressive models and achieves competitive results to autoregressive models. On LibriSpeech test-other, the Imputer achieves 11.1 WER, outperforming CTC at 13.0 WER and seq2seq at 12.5 WER.

This paper presents SimCLR: a simple framework for contrastive learning of visual representations. We simplify recently proposed contrastive self-supervised learning algorithms without requiring specialized architectures or a memory bank. In order to understand what enables the contrastive prediction tasks to learn useful representations, we systematically study the major components of our framework. We show that (1) composition of data augmentations plays a critical role in defining effective predictive tasks, (2) introducing a learnable nonlinear transformation between the representation and the contrastive loss substantially improves the quality of the learned representations, and (3) contrastive learning benefits from larger batch sizes and more training steps compared to supervised learning. By combining these findings, we are able to considerably outperform previous methods for self-supervised and semi-supervised learning on ImageNet. A linear classifier trained on self-supervised representations learned by SimCLR achieves 76.5% top-1 accuracy, which is a 7% relative improvement over previous state-of-the-art, matching the performance of a supervised ResNet-50. When fine-tuned on only 1% of the labels, we achieve 85.8% top-5 accuracy, outperforming AlexNet with 100X fewer labels.

One paradigm for learning from few labeled examples while making best use of a large amount of unlabeled data is unsupervised pretraining followed by supervised fine-tuning. Although this paradigm uses unlabeled data in a task-agnostic way, in contrast to common approaches to semi-supervised learning for computer vision, we show that it is surprisingly effective for semi-supervised learning on ImageNet. A key ingredient of our approach is the use of big (deep and wide) networks during pretraining and fine-tuning. We find that, the fewer the labels, the more this approach (task-agnostic use of unlabeled data) benefits from a bigger network. After fine-tuning, the big network can be further improved and distilled into a much smaller one with little loss in classification accuracy by using the unlabeled examples for a second time, but in a task-specific way. The proposed semi-supervised learning algorithm can be summarized in three steps: unsupervised pretraining of a big ResNet model using SimCLRv2, supervised fine-tuning on a few labeled examples, and distillation with unlabeled examples for refining and transferring the task-specific knowledge. This procedure achieves 73.9% ImageNet top-1 accuracy with just 1% of the labels ($\le$13 labeled images per class) using ResNet-50, a 10X improvement in label efficiency over the previous state-of-the-art. With 10% of labels, ResNet-50 trained with our method achieves 77.5% top-1 accuracy, outperforming standard supervised training with all of the labels.

The most important unsolved problem with artificial neural networks is how to do unsupervised learning as effectively as the brain. There are currently two main approaches to unsupervised learning. In the first approach, exemplified by BERT and Variational Autoencoders, a deep neural network is used to reconstruct its input. This is problematic for images because the deepest layers of the network need to encode the fine details of the image. An alternative approach, introduced by Becker and Hinton in 1992, is to train two copies of a deep neural network to produce output vectors that have high mutual information when given two different crops of the same image as their inputs. This approach was designed to allow the representations to be untethered from irrelevant details of the input.

We explore and expand the Soft Nearest Neighbor Loss to measure the entanglement of class manifolds in representation space: i.e., how close pairs of points from the same class are relative to pairs of points from different classes. We demonstrate several use cases of the loss. As an analytical tool, it provides insights into the evolution of class similarity structures during learning. Surprisingly, we find that maximizing the entanglement of representations of different classes in the hidden layers is beneficial for discrimination in the final layer, possibly because it encourages representations to identify class-independent similarity structures. Maximizing the soft nearest neighbor loss in the hidden layers leads not only to better-calibrated estimates of uncertainty on outlier data but also marginally improved generalization. Data that is not from the training distribution can be recognized by observing that in the hidden layers, it has fewer than the normal number of neighbors from the predicted class.

Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical correlation analysis (CCA). We show that CCA belongs to a family of statistics for measuring multivariate similarity, but that neither CCA nor any other statistic that is invariant to invertible linear transformation can measure meaningful similarities between representations of higher dimension than the number of data points. We introduce a similarity index that measures the relationship between representational similarity matrices and does not suffer from this limitation. This similarity index is equivalent to centered kernel alignment (CKA) and is also closely connected to CCA. Unlike CCA, CKA can reliably identify correspondences between representations in networks trained from different initializations.

Objects are composed of a set of geometrically organized parts. We introduce an unsupervised capsule autoencoder (SCAE), which explicitly uses geometric relationships between parts to reason about objects. Since these relationships do not depend on the viewpoint, our model is robust to viewpoint changes. SCAE consists of two stages. In the first stage, the model predicts presences and poses of part templates directly from the image and tries to reconstruct the image by appropriately arranging the templates. In the second stage, the SCAE predicts parameters of a few object capsules, which are then used to reconstruct part poses. Inference in this model is amortized and performed by off-the-shelf neural encoders, unlike in previous capsule networks. We find that object capsule presences are highly informative of the object class, which leads to state-of-the-art results for unsupervised classification on SVHN (55%) and MNIST (98.7%).

The generalization and learning speed of a multi-class neural network can often be significantly improved by using soft targets that are a weighted average of the hard targets and the uniform distribution over labels. Smoothing the labels in this way prevents the network from becoming over-confident and label smoothing has been used in many state-of-the-art models, including image classification, language translation and speech recognition. Despite its widespread use, label smoothing is still poorly understood. Here we show empirically that in addition to improving generalization, label smoothing improves model calibration which can significantly improve beam search. However, we also observe that if a teacher network is trained with label smoothing, knowledge distillation into a student network is much less effective. To explain these observations, we visualize how label smoothing changes the representations learned by the penultimate layer of the network. We show that label smoothing encourages the representations of training examples from the same class to group in tight clusters. This results in loss of information in the logits about resemblances between instances of different classes, which is necessary for distillation, but does not hurt generalization or calibration of the model's predictions.

The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate schemes, such as AdaGrad and Adam and (2) accelerated schemes, such as heavy-ball and Nesterov momentum. In this paper, we propose a new optimization algorithm, Lookahead, that is orthogonal to these previous approaches and iteratively updates two sets of weights. Intuitively, the algorithm chooses a search direction by looking ahead at the sequence of ``fast weights" generated by another optimizer. We show that Lookahead improves the learning stability and lowers the variance of its inner optimizer with negligible computation and memory cost. We empirically demonstrate Lookahead can significantly improve the performance of SGD and Adam, even with their default hyperparameter settings on ImageNet, CIFAR-10/100, neural machine translation, and Penn Treebank.

Data are often labeled by many different experts with each expert only labeling a small fraction of the data and each data point being labeled by several experts. This reduces the workload on individual experts and also gives a better estimate of the unobserved ground truth. When experts disagree, the standard approaches are to treat the majority opinion as the correct label or to model the correct label as a distribution. These approaches, however, do not make any use of potentially valuable information about which expert produced which label. To make use of this extra information, we propose modeling the experts individually and then learning averaging weights for combining them, possibly in sample-specific ways. This allows us to give more weight to more reliable experts and take advantage of the unique strengths of individual experts at classifying certain types of data. Here we show that our approach leads to improvements in computer-aided diagnosis of diabetic retinopathy. We also show that our method performs better than competing algorithms by Welinder and Perona (2010); Mnih and Hinton (2012). Our work offers an innovative approach for dealing with the myriad real-world settings that use expert opinions to define labels for training.

We introduce Picturebook, a large-scale lookup operation to ground language via 'snapshots' of our physical world accessed through image search.For each word in a vocabulary, we extract the top-k images from Google image search and feed the images through a convolutional network to extract a word embedding.We introduce a multimodal gating function to fuse our Picturebook embeddings with other word representations.We also introduce Inverse Picturebook, a mechanism to map a Picturebook embedding back into words.We experiment and report results across a wide range of tasks: word similarity, natural language inference, semantic relatedness, sentiment/topic classification, image-sentence ranking and machine translation.We also show that gate activations corresponding to Picturebook embeddings are highly correlated to human judgments of concreteness ratings.

The backpropagation of error algorithm (BP) is impossible to implement in a real brain. The recent success of deep networks in machine learning and AI, however, has inspired proposals for understanding how the brain might learn across multiple layers, and hence how it might approximate BP. As of yet, none of these proposals have been rigorously evaluated on tasks where BP-guided deep learning has proved critical, or in architectures more structured than simple fully-connected networks. Here we present results on scaling up biologically motivated models of deep learning on datasets which need deep networks with appropriate architectures to achieve good performance. We present results on the MNIST, CIFAR-10, and ImageNet datasets and explore variants of target-propagation (TP) and feedback alignment (FA) algorithms, and explore performance in both fully- and locally-connected architectures. We also introduce weight-transport-free variants of difference target propagation (DTP) modified to remove backpropagation from the penultimate layer. Many of these algorithms perform well for MNIST, but for CIFAR and ImageNet we find that TP and FA variants perform significantly worse than BP, especially for networks composed of locally connected units, opening questions about whether new architectures and algorithms are required to scale these approaches. Our results and implementation details help establish baselines for biologically motivated deep learning schemes going forward.

A capsule is a group of neurons whose activity vector represents the instantiation parameters of a specific type of entity such as an object or object part. We use the length of the activity vector to represent the probability that the entity exists and its orientation to represent the instantiation parameters. Active capsules at one level make predictions, via transformation matrices, for the instantiation parameters of higher-level capsules. When multiple predictions agree, a higher level capsule becomes active. We show that a discrimininatively trained, multi-layer capsule system achieves state-of-the-art performance on MNIST and is considerably better than a convolutional net at recognizing highly overlapping digits. To achieve these results we use an iterative routing-by-agreement mechanism: A lower-level capsule prefers to send its output to higher level capsules whose activity vectors have a big scalar product with the prediction coming from the lower-level capsule.

Until recently, research on artificial neural networks was largely restricted to systems with only two types of variable: Neural activities that represent the current or recent input and weights that learn to capture regularities among inputs, outputs and payoffs. There is no good reason for this restriction. Synapses have dynamics at many different time-scales and this suggests that artificial neural networks might benefit from variables that change slower than activities but much faster than the standard weights. These ``fast weights'' can be used to store temporary memories of the recent past and they provide a neurally plausible way of implementing the type of attention to the past that has recently proven helpful in sequence-to-sequence models. By using fast weights we can avoid the need to store copies of neural activity patterns.

We present a framework for efficient inference in structured image models that explicitly reason about objects. We achieve this by performing probabilistic inference using a recurrent neural network that attends to scene elements and processes them one at a time. Crucially, the model itself learns to choose the appropriate number of inference steps. We use this scheme to learn to perform inference in partially specified 2D models (variable-sized variational auto-encoders) and fully specified 3D models (probabilistic renderers). We show that such models learn to identify multiple objects - counting, locating and classifying the elements of a scene - without any supervision, e.g., decomposing 3D images with various numbers of objects in a single forward pass of a neural network at unprecedented speed. We further show that the networks produce accurate inferences when compared to supervised counterparts, and that their structure leads to improved generalization.

Syntactic constituency parsing is a fundamental problem in naturallanguage processing which has been the subject of intensive researchand engineering for decades. As a result, the most accurate parsersare domain specific, complex, and inefficient. In this paper we showthat the domain agnostic attention-enhanced sequence-to-sequence modelachieves state-of-the-art results on the most widely used syntacticconstituency parsing dataset, when trained on a large synthetic corpusthat was annotated using existing parsers. It also matches theperformance of standard parsers when trained on a smallhuman-annotated dataset, which shows that this model is highlydata-efficient, in contrast to sequence-to-sequence models without theattention mechanism. Our parser is also fast, processing over ahundred sentences per second with an unoptimized CPU implementation.

We describe a simple but effective way of using multi-frame targets to improve the accuracy of Artificial Neural NetworkHidden Markov Model (ANN-HMM) hybrid systems. In this approach a Deep Neural Network (DNN) is trained to predict the forced-alignment state of multiple frames using a separate softmax unit for each of the frames. This is in contrast to the usual method of training a DNN to predict only the state of the central frame. By itself this is not sufficient to improve accuracy of the system significantly. However, if we average the predictions for each frame from the different contexts it is associated with we achieve state of the art results on TIMIT using a fully connected Deep Neural Network without convolutional architectures or dropout training. On a 14 hour subset of Wall Street Journal (WSJ) using a context dependent DNN-HMM system it leads to a relative improvement of 6.4% on the dev set (testdev93) and 9.3% on test set (test-eval92).

Applications of Deep Belief Nets (DBN) to various problems have been the subject of a number of recent studies ranging from image classification and speech recognition to audio classification. In this study we apply DBNs to a natural language understanding problem. The recent surge of activity in this area was largely spurred by the development of a greedy layer-wise pretraining method that uses an efficient learning algorithm called Contrastive Divergence (CD). CD allows DBNs to learn a multi-layer generative model from unlabeled data and the features discovered by this model are then used to initialize a feed-forward neural network which is fine-tuned with backpropagation. We compare a DBN-initialized neural network to three widely used text classification algorithms: Support Vector Machines (SVM), boosting and Maximum Entropy (MaxEnt). The plain DBN-based model gives a call-routing classification accuracy that is equal to the best of the other models. However, using additional unlabeled data for DBN pre-training and combining DBN-based learned features with the original features provides significant gains over SVMs, which, in turn, performed better than both MaxEnt and Boosting.

Recently, pre-trained deep neural networks (DNNs) have outperformed traditional acoustic models based on Gaussian mixture models (GMMs) on a variety of large vocabulary speech recognition benchmarks. Deep neural nets have also achieved excellent results on various computer vision tasks using a random “dropout” procedure that drastically improves generalization error by randomly omitting a fraction of the hidden units in all layers. Since dropout helps avoid over-fitting, it has also been successful on a small-scale phone recognition task using larger neural nets. However, training deep neural net acoustic models for large vocabulary speech recognition takes a very long time and dropout is likely to only increase training time. Neural networks with rectified linear unit (ReLU) non-linearities have been highly successful for computer vision tasks and proved faster to train than standard sigmoid units, sometimes also improving discriminative performance. In this work, we show on a 50-hour English Broadcast News task that modified deep neural networks using ReLUs trained with dropout during frame level training provide an 4.2% relative improvement over a DNN trained with sigmoid units, and a 14.4% relative improvement over a strong GMM/HMM system. We were able to obtain our results with minimal human hyper-parameter tuning using publicly available Bayesian optimization code.

In this paper, we provide an overview of the invited and contributed papers presented at the special session at ICASSP-2013, entitled “New Types of Deep Neural Network Learning for Speech Recognition and Related Applications,” as organized by the authors. We also describe the historical context in which acoustic models based on deep neural networks have been developed. The technical overview of the papers presented in our special session is organized into five ways of improving deep learning methods: (1) better optimization; (2) better types of neural activation function and better network architectures; (3) better ways to determine the myriad hyper-parameters of deep neural networks; (4) more appropriate ways to preprocess speech for deep neural networks; and (5) ways of leveraging multiple languages or dialects that are more easily achieved with deep neural networks than with Gaussian mixture models.

Recurrent neural networks (RNNs) are a powerful model for sequential data. End-to-end training methods such as Connectionist Temporal Classification make it possible to train RNNs for sequence labelling problems where the input-output alignment is unknown. The combination of these methods with the Long Short-term Memory RNN architecture has proved particularly fruitful, delivering state-of-the-art results in cursive handwriting recognition. However RNN performance in speech recognition has so far been disappointing, with better results returned by deep feedforward networks. This paper investigates deep recurrent neural networks, which combine the multiple levels of representation that have proved so effective in deep networks with the flexible use of long range context that empowers RNNs. When trained end-to-end with suitable regularisation, we find that deep Long Short-term Memory RNNs achieve a test set error of 17.7% on the TIMIT phoneme recognition benchmark, which to our knowledge is the best recorded score.

Deep neural networks have recently become the gold standard for acoustic modeling in speech recognition systems. The key computational unit of a deep network is a linear projection followed by a point-wise non-linearity, which is typically a logistic function. In this work, we show that we can improve generalization and make training of deep networks faster and simpler by substituting the logistic units with rectified linear units. These units are linear when their input is positive and zero otherwise. In a supervised setting, we can successfully train very deep nets from random initialization on a large vocabulary speech recognition task achieving lower word error rates than using a logistic network with the same topology. Similarly in an unsupervised setting, we show how we can learn sparse features that can be useful for discriminative tasks. All our experiments are executed in a distributed environment using several hundred machines and several hundred hours of speech data.

Deep and recurrent neural networks (DNNs and RNNs respectively) are powerful models that were considered to be almost impossible to train using stochastic gradient descent with momentum. In this paper, we show that when stochastic gradient descent with momentum uses a well-designed random initialization and a particular type of slowly increasing schedule for the momentum parameter, it can train both DNNs and RNNs (on datasets with long-term dependencies) to levels of performance that were previously achievable only with Hessian-Free optimization. We find that both the initialization and the momentum are crucial since poorly initialized networks cannot be trained with momentum and well-initialized networks perform markedly worse when the momentum is absent or poorly tuned. Our success training these models suggests that previous attempts to train deep and recurrent neural networks from random initializations have likely failed due to poor initialization schemes. Furthermore, carefully tuned momentum methods suffice for dealing with the curvature issues in deep and recurrent network training objectives without the need for sophisticated second-order methods.

Factor Analysis is a statistical method that seeks to explain linear variations in data by using unobserved latent variables. Due to its additive nature, it is not suitable for modeling data that is generated by multiple groups of latent factors which interact multiplicatively. In this paper, we introduce Tensor Analyzers which are a multilinear generalization of Factor Analyzers. We describe an efficient way of sampling from the posterior distribution over factor values and we demonstrate that these samples can be used in the EM algorithm for learning interesting mixture models of natural image patches. Tensor Analyzers can also accurately recognize a face under significant pose and illumination variations when given only one previous image of that face. We also show that Tensor Analyzers can be trained in an unsupervised, semi-supervised, or fully supervised settings.

In this paper we show how we can discover non-linear features of frames of spectrograms using a novel autoencoder. The autoencoder uses a neural network encoder that predicts how a set of prototypes called templates need to be transformed to reconstruct the data, and a decoder that is a function that performs this operation of transforming prototypes and reconstructing the input. We demonstrate this method on spectrograms from the TIMIT database. The features are used in a Deep Neural Network Hidden Markov Model (DNN-HMM) hybrid system for automatic speech recognition. On the TIMIT monophone recognition task we were able to achieve gains of 0.5% over Mel log spectra, by augmenting traditional the spectra with the predicted transformation parameters. Further, using the recently discovered ‘dropout’ training, we were able to achieve a phone error rate (PER) of 17.9% on the dev set and 19.5% on the test set, which, to our knowledge is the best reported number on this task using a hybrid system.

This paper describes a Markov Random Field for real-valued image modeling that has two sets of latent variables. One set is used to gate the interactions between all pairs of pixels, while the second set determines the mean intensities of each pixel. This is a powerful model with a conditional distribution over the input that is Gaussian, with both mean and covariance determined by the configuration of latent variables, which is unlike previous models that were restricted to using Gaussians with either a fixed mean or a diagonal covariance matrix. Thanks to the increased flexibility, this gated MRF can generate more realistic samples after training on an unconstrained distribution of high-resolution natural images. Furthermore, the latent variables of the model can be inferred efficiently and can be used as very effective descriptors in recognition tasks. Both generation and discrimination drastically improve as layers of binary latent variables are added to the model, yielding a hierarchical model called a Deep Belief Network.

While Boltzmann Machines have been successful at unsupervised learning and density modeling of images and speech data, they can be very sensitive to noise in the data. In this paper, we introduce a novel model, the Robust Boltzmann Machine (RoBM), which allows Boltzmann Machines to be robust to corruptions. In the domain of visual recognition, the RoBM is able to accurately deal with occlusions and noise by using multiplicative gating to induce a scale mixture of Gaussians over pixels. Image denoising and in-painting correspond to posterior inference in the RoBM. Our model is trained in an unsupervised fashion with unlabeled noisy data and can learn the spatial structure of the occluders. Compared to standard algorithms, the RoBM is significantly better at recognition and denoising on several face databases.

Deep Belief Networks (DBNs) are a very competitive alternative to Gaussian mixture models for relating states of a hidden Markov model to frames of coefficients derived from the acoustic input. They are competitive for three reasons: DBNs can be fine-tuned as neural networks; DBNs have many non-linear hidden layers; and DBNs are generatively pre-trained. This paper illustrates how each of these three aspects contributes to the DBN's good recognition performance using both phone recognition performance on the TIMIT corpus and a dimensionally reduced visualization of the relationships between the feature vectors learned by the DBNs that preserves the similarity structure of the feature vectors at multiple scales. The same two methods are also used to investigate the most suitable type of input representation for a DBN.

We trained a large, deep convolutional neural network to classify the 1.3 million high-resolution images in the LSVRC-2010 ImageNet training set into the 1000 different classes. On the test data, we achieved top-1 and top-5 error rates of 39.7\% and 18.9\% which is considerably better than the previous state-of-the-art results. The neural network, which has 60 million parameters and 500,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and two globally connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implementation of convolutional nets. To reduce overfitting in the globally connected layers we employed a new regularization method that proved to be very effective.

We describe how the pre-training algorithm for Deep Boltzmann Machines (DBMs) is related to the pre-training algorithm for Deep Belief Networks and we show that under certain conditions, the pre-training procedure improves the variational lower bound of a two-hidden-layer DBM. Based on this analysis, we develop a different method of pre-training DBMs that distributes the modelling work more evenly over the hidden layers. Our results on the MNIST and NORB datasets demonstrate that the new pre-training algorithm allows us to learn better generative models.

Techniques for multidimensional scaling visualize objects as points in a low-dimensional metric map. As a result, the visualizations are subject to the fundamental limitations of metric spaces. These limitations prevent multidimensional scaling from faithfully representing non-metric similarity data such as word associations or event co-occurrences. In particular, multidimensional scaling cannot faithfully represent intransitive pairwise similarities in a visualization, and it cannot faithfully visualize “central” objects. In this paper, we present an extension of a recently proposed multidimensional scaling technique called t-SNE. The extension aims to address the problems of traditional multidimensional scaling techniques when these techniques are used to visualize non-metric similarities. The new technique, called multiple maps t-SNE, alleviates these problems by constructing a collection of maps that reveal complementary structure in the similarity data. We apply multiple maps t-SNE to a large data set of word association data and to a data set of NIPS co-authorships, demonstrating its ability to successfully visualize non-metric similarities.

We present a new learning algorithm for Boltzmann machines that contain many layers of hidden variables. Data-dependent statistics are estimated using a variational approximation that tends to focus on a single mode, and data-independent statistics are estimated using persistent Markov chains. The use of two quite different techniques for estimating the two types of statistic that enter into the gradient of the log likelihood makes it practical to learn Boltzmann machines with multiple hidden layers and millions of parameters. The learning can be made more efficient by using a layer-by-layer pretraining phase that initializes the weights sensibly. The pretraining also allows the variational inference to be initialized sensibly with a single bottom-up pass. We present results on the MNIST and NORB data sets showing that deep Boltzmann machines learn very good generative models of handwritten digits and 3D objects. We also show that the features discovered by deep Boltzmann machines are a very effective way to initialize the hidden layers of feedforward neural nets, which are then discriminatively fine-tuned.

Gaussian mixture models are currently the dominant technique for modeling the emission distribution of hidden Markov models for speech recognition. We show that better phone recognition on the TIMIT dataset can be achieved by replacing Gaussian mixture models by deep neural networks that contain many layers of features and a very large number of parameters. These networks are first pre-trained as a multi-layer generative model of a window of spectral feature vectors without making use of any discriminative information. Once the generative pre-training has designed the features, we perform discriminative fine-tuning using backpropagation to adjust the features slightly to make them better at predicting a probability distribution over the states of monophone hidden Markov models.

Current speech recognition systems, for example, typically use Gaussian mixture models (GMMs), to estimate the observation (or emission) probabilities of hidden Markov models (HMMs), and GMMs are generative models that have only one layer of latent variables. Instead of developing more powerful models, most of the research effort has gone into finding better ways of estimating the GMM parameters so that error rates are decreased or the margin between different classes is increased. The same observation holds for natural language processing (NLP) in which maximum entropy (MaxEnt) models and conditional random fields (CRFs) have been popular for the last decade. Both of these approaches use shallow models whose success largely depends on the use of carefully handcrafted features.

The most popular way to use probabilistic models in vision is first to extract some descriptors of small image patches or object parts using well-engineered features, and then to use statistical learning tools to model the dependencies among these features and eventual labels. Learning probabilistic models directly on the raw pixel values has proved to be much more difficult and is typically only used for regularizing discriminative methods. In this work, we use one of the best, pixel-level, generative models of natural images-a gated MRF-as the lowest level of a deep belief network (DBN) that has several hidden layers. We show that the resulting DBN is very good at coping with occlusion when predicting expression categories from face images, and it can produce features that perform comparably to SIFT descriptors for discriminating different types of scene. The generative ability of the model also makes it easy to see what information is captured and what is lost at each level of representation.

We describe a generative model of the relationship between two images. The model is defined as a factored three-way Boltzmann machine, in which hidden variables collaborate to define the joint correlation matrix for image pairs. Modeling the joint distribution over pairs makes it possible to efficiently match images that are the same according to a learned measure of similarity. We apply the model to several face matching tasks, and show that it learns to represent the input images using task-specific basis functions. Matching performance is superior to previous similar generative models, including recent conditional models of transformations. We also show that the model can be used as a plug-in matching score to perform invariant classification.

State of the art speech recognition systems rely on preprocessed speech features such as Mel cepstrum or linear predictive coding coefficients that collapse high dimensional speech sound waves into low dimensional encodings. While these have been successfully applied in speech recognition systems, such low dimensional encodings may lose some relevant information and express other information in a way that makes it difficult to use for discrimination. Higher dimensional encodings could both improve performance in recognition tasks, and also be applied to speech synthesis by better modeling the statistical structure of the sound waves. In this paper we present a novel approach for modeling speech sound waves using a Restricted Boltzmann machine (RBM) with a novel type of hidden variable and we report initial results demonstrating phoneme recognition performance better than the current state-of-the-art for methods based on Mel cepstrum coefficients.

Deep Belief Networks (DBNs) are multi-layer generative models. They can be trained to model windows of coefficients extracted from speech and they discover multiple layers of features that capture the higher-order statistical structure of the data. These features can be used to initialize the hidden units of a feed-forward neural network that is then trained to predict the HMM state for the central frame of the window. Initializing with features that are good at generating speech makes the neural network perform much better than initializing with random weights. DBNs have already been used successfully for phone recognition with input coefficients that are MFCCs or filterbank outputs. In this paper, we demonstrate that they work even better when their inputs are speaker adaptive, discriminative features. On the standard TIMIT corpus, they give phone error rates of 19.6% using monophone HMMs and a bigram language model and 19.4% using monophone HMMs and a trigram language model.

This paper considers application of Deep Belief Nets (DBNs) to natural language call routing. DBNs have been successfully applied to a number of tasks, including image, audio and speech classification, thanks to the recent discovery of an efficient learning technique. DBNs learn a multi-layer generative model from unlabeled data and the features discovered by this model are then used to initialize a feed-forward neural network which is fine-tuned with backpropagation. We compare a DBN-initialized neural network to three widely used text classification algorithms; Support Vector machines (SVM), Boosting and Maximum Entropy (MaxEnt). The DBN-based model gives a call-routing classification accuracy that is equal to the best of the other models even though it currently uses an impoverished representation of the input.

Learning a generative model of natural images is a useful way of extracting features that capture interesting regularities. Previous work on learning such models has focused on methods in which the latent features are used to determine the mean and variance of each pixel independently, or on methods in which the hidden units determine the covariance matrix of a zero-mean Gaussian distribution. In this work, we propose a probabilistic model that combines these two approaches into a single framework. We represent each image using one set of binary latent features that model the image-specific covariance and a separate set that model the mean. We show that this approach provides a probabilistic framework for the widely used simple-cell complex-cell architecture, it produces very realistic samples of natural images and it extracts features that yield state-of-the-art recognition accuracy on the challenging CIFAR 10 dataset.

We introduce a new class of probabilistic latent variable model called the Implicit Mixture of Conditional Restricted Boltzmann Machines (imCRBM) for use in human pose tracking. Key properties of the imCRBM are as follows: (1) learning is linear in the number of training exemplars so it can be learned from large datasets; (2) it learns coherent models of multiple activities; (3) it automatically discovers atomic “movemes” and (4) it can infer transitions between activities, even when such transitions are not present in the training set. We describe the model and how it is learned and we demonstrate its use in the context of Bayesian filtering for multi-view and monocular pose tracking. The model handles difficult scenarios including multiple activities and transitions among activities. We report state-of-the-art results on the HumanEva dataset.

For decades, Hidden Markov Models (HMMs) have been the state-of-the-art technique for acoustic modeling despite their unrealistic independence assumptions and the very limited representational capacity of their hidden states. Conditional Restricted Boltzmann Machines (CRBMs) have recently proved to be very effective for modeling motion capture sequences and this paper investigates the application of this more powerful type of generative model to acoustic modeling. On the standard TIMIT corpus, one type of CRBM outperforms HMMs and is comparable with the best other methods, achieving a phone error rate (PER) of 26.7% on the TIMIT core test set.

This paper reports our recent exploration of the layer-by-layer learning strategy for training a multi-layer generative model of patches of speech spectrograms. The top layer of the generative model learns binary codes that can be used for efficient compression of speech and could also be used for scalable speech recognition or rapid speech content retrieval. Each layer of the generative model is fully connected to the layer below and the weights on these connections are pretrained efficiently by using the contrastive divergence approximation to the log likelihood gradient. After layer-bylayer pre-training we “unroll” the generative model to form a deep auto-encoder, whose parameters are then fine-tuned using back-propagation. To reconstruct the full-length speech spectrogram, individual spectrogram segments predicted by their respective binary codes are combined using an overlapand-add method. Experimental results on speech spectrogram coding demonstrate that the binary codes produce a logspectral distortion that is approximately 2 dB lower than a subband vector quantization technique over the entire frequency range of wide-band speech. Index Terms: deep learning, speech feature extraction, neural networks, auto-encoder, binary codes, Boltzmann machine

Straightforward application of Deep Belief Nets (DBNs) to acoustic modeling produces a rich distributed representation of speech data that is useful for recognition and yields impressive results on the speaker-independent TIMIT phone recognition task. However, the first-layer Gaussian-Bernoulli Restricted Boltzmann Machine (GRBM) has an important limitation, shared with mixtures of diagonal-covariance Gaussians: GRBMs treat different components of the acoustic input vector as conditionally independent given the hidden state. The mean-covariance restricted Boltzmann machine (mcRBM), first introduced for modeling natural images, is a much more representationally efficient and powerful way of modeling the covariance structure of speech data. Every configuration of the precision units of the mcRBM specifies a different precision matrix for the conditional distribution over the acoustic space. In this work, we use the mcRBM to learn features of speech data that serve as input into a standard DBN. The mcRBM features combined with DBNs allow us to achieve a phone error rate of 20.5\%, which is superior to all published results on speaker-independent TIMIT to date.

We describe a model based on a Boltzmann machine with third-order connections that can learn how to accumulate information about a shape over several fixations. The model uses a retina that only has enough high resolution pixels to cover a small area of the image, so it must decide on a sequence of fixations and it must combine the glimpse" at each fixation with the location of the fixation before integrating the information with information from other glimpses of the same object. We evaluate this model on a synthetic dataset and two image classification datasets, showing that it can perform at least as well as a model trained on whole images."

We describe a log-bilinear" model that computes class probabilities by combining an input vector multiplicatively with a vector of binary latent variables. Even though the latent variables can take on exponentially many possible combinations of values, we can efficiently compute the exact probability of each class by marginalizing over the latent variables. This makes it possible to get the exact gradient of the log likelihood. The bilinear score-functions are defined using a three-dimensional weight tensor, and we show that factorizing this tensor allows the model to encode invariances inherent in a task by learning a dictionary of invariant basis functions. Experiments on a set of benchmark problems show that this fully probabilistic model can achieve classification performance that is competitive with (kernel) SVMs, backpropagation, and deep belief nets."

Probabilistic models of natural images are usually evaluated by measuring performance on rather indirect tasks, such as denoising and inpainting. A more direct way to evaluate a generative model is to draw samples from it and to check whether statistical properties of the samples match the statistics of natural images. This method is seldom used with high-resolution images, because current models produce samples that are very different from natural images, as assessed by even simple visual inspection. We investigate the reasons for this failure and we show that by augmenting existing models so that there are two sets of latent variables, one set modelling pixel intensities and the other set modelling image-specific pixel covariances, we are able to generate high-resolution images that look much more realistic than before. The overall model can be interpreted as a gated MRF where both pair-wise dependencies and mean intensities of pixels are modulated by the states of latent variables. Finally, we confirm that if we disallow weight-sharing between receptive fields that overlap each other, the gated MRF learns more efficient internal representations, as demonstrated in several recognition tasks.

To allow the hidden units of a restricted Boltzmann machine to model the transformation between two successive images, Memisevic and Hinton (2007) introduced three-way multiplicative interactions that use the intensity of a pixel in the first image as a multiplicative gain on a learned, symmetric weight between a pixel in the second image and a hidden unit. This creates cubically many parameters, which form a three-dimensional interaction tensor. We describe a low-rank approximation to this interaction tensor that uses a sum of factors, each of which is a three-way outer product. This approximation allows efficient learning of transformations between larger image patches. Since each factor can be viewed as an image filter, the model as a whole learns optimal filter pairs for efficiently representing transformations. We demonstrate the learning of optimal filter pairs from various synthetic and real image sequences. We also show how learning about image transformations allows the model to perform a simple visual analogy task, and we show how a completely unsupervised network trained on transformations perceives multiple motions of transparent dot patterns in the same way as humans.

We compare 10 methods of classifying fMRI volumes by applying them to data from a longitudinal study of stroke recovery: adaptive Fisher's linear and quadratic discriminant; gaussian naive Bayes; support vector machines with linear, quadratic, and radial basis function (RBF) kernels; logistic regression; two novel methods based on pairs of restricted Boltzmann machines (RBM); and K-nearest neighbors. All methods were tested on three binary classification tasks, and their out-of-sample classification accuracies are compared. The relative performance of the methods varies considerably across subjects and classification tasks. The best overall performers were adaptive quadratic discriminant, support vector machines with RBF kernels, and generatively trained pairs of RBMs.

We evaluate the ability of the popular Field-of-Experts (FoE) to model structure in images. As a test case we focus on modeling synthetic and natural textures. We find that even for modeling single textures, the FoE provides insufficient flexibility to learn good generative models – it does not perform any better than the much simpler Gaussian FoE. We propose an extended version of the FoE (allowing for bimodal potentials) and demonstrate that this novel formulation, when trained with a better approximation of the likelihood gradient, gives rise to a more powerful generative model of specific visualstructure that produces significantly better results for the texture task.

The Conditional Restricted Boltzmann Machine (CRBM) is a recently proposed model for time series that has a rich, distributed hidden state and permits simple, exact inference. We present a new model, based on the CRBM that preserves its most important computational properties and includes multiplicative three-way interactions that allow the effective interaction weight between two units to be modulated by the dynamic state of a third unit. We factor the three-way weight tensor implied by the multiplicative model, reducing the number of parameters from O(N3) to O(N2). The result is an efficient, compact model whose effectiveness we demonstrate by modeling human motion. Like the CRBM, our model can capture diverse styles of motion with a single set of parameters, and the three-way interactions greatly improve the model's ability to blend motion styles or to transition smoothly among them.

The most commonly used learning algorithm for restricted Boltzmann machines is contrastive divergence which starts a Markov chain at a data point and runs the chain for only a few iterations to get a cheap, low variance estimate of the sufficient statistics under the model. Tieleman (2008) showed that better learning can be achieved by estimating the model's statistics using a small set of persistent "fantasy particles" that are not reinitialized to data points after each weight update. With sufficiently small weight updates, the fantasy particles represent the equilibrium distribution accurately but to explain why the method works with much larger weight updates it is necessary to consider the interaction between the weight updates and the Markov chain. We show that the weight updates force the Markov chain to mix fast, and using this insight we develop an even faster mixing chain that uses an auxiliary set of "fast weights" to implement a temporary overlay on the energy landscape. The fast weights learn rapidly but also decay rapidly and do not contribute to the normal energy landscape that defines the model.

No abstract available.

We introduce a new type of Deep Belief Net and evaluate it on a 3D object recognition task. The top-level model is a third-order Boltzmann machine, trained using a hybrid algorithm that combines both generative and discriminative gradients. Performance is evaluated on the NORB database(normalized-uniform version), which contains stereo-pair images of objects under different lighting conditions and viewpoints. Our model achieves 6.5% error on the test set, which is close to the best published result for NORB (5.9%) using a convolutional neural net that has built-in knowledge of translation invariance. It substantially outperforms shallow models such as SVMs (11.6%). DBNs are especially suited for semi-supervised learning, and to demonstrate this we consider a modified version of the NORB recognition task in which additional unlabeled images are created by applying small translations to the images in the database. With the extra unlabeled data (and the same amount of labeled data as before), our model achieves 5.2% error, making it the current best result for NORB.

We consider the problem of zero-shot learning, where the goal is to learn a classifier $f: X \rightarrow Y$ that must predict novel values of $Y$ that were omitted from the training set. To achieve this, we define the notion of a semantic output code classifier (SOC) which utilizes a knowledge base of semantic properties of $Y$ to extrapolate to novel classes. We provide a formalism for this type of classifier and study its theoretical properties in a PAC framework, showing conditions under which the classifier can accurately predict novel classes. As a case study, we build a SOC classifier for a neural decoding task and show that it can often predict words that people are thinking about from functional magnetic resonance images (fMRI) of their neural activity, even without training examples for those words.

We show how to model documents as bags of words using family of two-layer, undirected graphical models. Each member of the family has the same number of binary hidden units but a different number of ``softmax visible units. All of the softmax units in all of the models in the family share the same weights to the binary hidden units. We describe efficient inference and learning procedures for such a family. Each member of the family models the probability distribution of documents of a specific length as a product of topic-specific distributions rather than as a mixture and this gives much better generalization than Latent Dirichlet Allocation for modeling the log probabilities of held-out documents. The low-dimensional topic vectors learned by the undirected family are also much better than LDA topic vectors for retrieving documents that are similar to a query document. The learned topics are more general than those found by LDA because precision is achieved by intersecting many general topics rather than by selecting a single precise topic to generate each word.

Neural probabilistic language models (NPLMs) have been shown to be competitive with and occasionally superior to the widely-used n-gram language models. The main drawback of NPLMs is their extremely long training and testing times. Morin and Bengio have proposed a hierarchical language model built around a binary tree of words that was two orders of magnitude faster than the non-hierarchical language model it was based on. However, it performed considerably worse than its non-hierarchical counterpart in spite of using a word tree created using expert knowledge. We introduce a fast hierarchical language model along with a simple feature-based algorithm for automatic construction of word trees from the data. We then show that the resulting models can outperform non-hierarchical models and achieve state-of-the-art performance.

We present a mixture model whose components are Restricted Boltzmann Machines (RBMs). This possibility has not been considered before because computing the partition function of an RBM is intractable, which appears to make learning a mixture of RBMs intractable as well. Surprisingly, when formulated as a third-order Boltzmann machine, such a mixture model can be learned tractably using contrastive divergence. The energy function of the model captures three-way interactions among visible units, hidden units, and a single hidden multinomial unit that represents the cluster labels. The distinguishing feature of this model is that, unlike other mixture models, the mixing proportions are not explicitly parameterized. Instead, they are defined implicitly via the energy function and depend on all the parameters in the model. We present results for the MNIST and NORB datasets showing that the implicit mixture of RBMs learns clusters that reflect the class structure in the data.

Neuroimaging datasets often have a very large number of voxels and a very small number of training cases, which means that overfitting of models for this data can become a very serious problem. Working with a set of fMRI images from a study on stroke recovery, we consider a classification task for which logistic regression performs poorly, even when L1- or L2- regularized. We show that much better discrimination can be achieved by fitting a generative model to each separate condition and then seeing which model is most likely to have generated the data. We compare discriminative training of exactly the same set of models, and we also consider convex blends of generative and discriminative training.

We describe a way of learning matrix representations of objects and relationships. The goal of learning is to allow multiplication of matrices to represent symbolic relationships between objects and symbolic relationships between relationships, which is the main novelty of the method. We demonstrate that this leads to excellent generalization in two different domains: modular arithmetic and family relationships. We show that the same system can learn first-order propositions such as $(2, 5) \member +\!3$ or $(Christopher, Penelope)\member has\_wife$, and higher-order propositions such as $(3, +\!3) \member plus$ and $(+\!3, -\!3) \member inverse$ or $(has\_husband, has\_wife)\in higher\_oppsex$. We further demonstrate that the system understands how higher-order propositions are related to first-order ones by showing that it can correctly answer questions about first-order propositions involving the relations $+\!3$ or $has\_wife$ even though it has not been trained on any first-order examples involving these relations.

The Temporal Restricted Boltzmann Machine (TRBM) is a probabilistic model for sequences that is able to successfully model (i.e., generate nice-looking samples of) several very high dimensional sequences, such as motion capture data and the pixels of low resolution videos of balls bouncing in a box. The major disadvantage of the TRBM is that exact inference is extremely hard, since even computing a Gibbs update for a single variable of the posterior is exponentially expensive. This difficulty has necessitated the use of a heuristic inference procedure, that nonetheless was accurate enough for successful learning. In this paper we introduce the Recurrent TRBM, which is a very slight modification of the TRBM for which exact inference is very easy and exact gradient learning is almost tractable. We demonstrate that the RTRBM is better than an analogous TRBM at generating motion capture and videos of bouncing balls.

In this note, we show that exponentially deep belief networks can approximate any distribution over binary vectors to arbitrary accuracy, even when the width of each layer is limited to the dimensionality of the data. We further show that such networks can be greedily learned in an easy yet impractical way.

We describe a probabilistic model for learning rich, distributed representations of image transformations. The basic model is defined as a gated conditional random field that is trained to predict transformations of its inputs using a factorial set of latent variables. Inference in the model consists in extracting the transformation, given a pair of images, and can be performed exactly and efficiently. We show that, when trained on natural videos, the model develops domain specific motion features, in the form of fields of locally transformed edge filters. When trained on affine, or more general, transformations of still images, the model develops codes for these transformations, and can subsequently perform recognition tasks that are invariant under these transformations. It can also fantasize new transformations on previously unseen images. We describe several variations of the basic model and provide experimental results that demonstrate its applicability to a variety of tasks.

The supremacy of n-gram models in statistical language modelling has recently been challenged by parametric models that use distributed representations to counteract the difficulties caused by data sparsity. We propose three new probabilistic language models that define the distribution of the next word in a sequence given several preceding words by using distributed representations of those words. We show how real-valued distributed representations for words can be learned at the same time as learning a large set of stochastic binary hidden features that are used to predict the distributed representation of the next word from previous distributed representations. Adding connections from the previous states of the binary hidden features improves performance as does adding direct connections between the real-valued distributed representations. One of our models significantly outperforms the very best n-gram models.

Most of the existing approaches to collaborative filtering cannot handle very large data sets. In this paper we show how a class of two-layer undirected graphical models, called Restricted Boltzmann Machines (RBM's), can be used to model tabular data, such as user's ratings of movies. We present efficient learning and inference procedures for this class of models and demonstrate that RBM's can be successfully applied to the Netflix data set, containing over 100 million user/movie ratings. We also show that RBM's slightly outperform carefully-tuned SVD models. When the predictions of multiple RBM models and multiple SVD models are linearly combined, we achieve an error rate that is well over 6% better than the score of Netflix's own system.

We describe an efficient learning procedure for multilayer generative models that combine the best aspects of Markov random fields and deep, directed belief nets. The generative models can be learned one layer at a time and when learning is complete they have a very fast inference procedure for computing a good approximation to the posterior distribution in all of the hidden layers. Each hidden layer has its own MRF whose energy function is modulated by the top-down directed connections from the layer above. To generate from the model, each layer in turn must settle to equilibrium given its top-down input. We show that this type of model is good at capturing the statistics of patches of natural images.

We show how to use unlabeled data and a deep belief net (DBN) to learn a good covariance kernel for a Gaussian process. We first learn a deep generative model of the unlabeled data using the fast, greedy algorithm introduced by Hinton et.al. If the data is high-dimensional and highly-structured, a Gaussian kernel applied to the top layer of features in the DBN works much better than a similar kernel applied to the raw input. Performance at both regression and classification can then be further improved by using backpropagation through the DBN to discriminatively fine-tune the covariance kernel.

We propose a non-linear generative model for human motion data that uses an undirected model with binary latent variables and real-valued "visible" variables that represent joint angles. The latent and visible variables at each time step receive directed connections from the visible variables at the last few time-steps. Such an architecture makes on-line inference efficient and allows us to use a simple approximate learning procedure. After training, the model finds a single set of parameters that simultaneously capture several different kinds of motion. We demonstrate the power of our approach by synthesizing various motion sequences and by performing on-line filling in of data lost during motion capture. Website: http://www.cs.toronto.edu/gwtaylor/publications/nips2006mhmublv/

We show how to use "complementary priors" to eliminate the explaining-away effects that make inference difficult in densely connected belief nets that have many hidden layers. Using complementary priors, we derive a fast, greedy algorithm that can learn deep, directed belief networks one layer at a time, provided the top two layers form an undirected associative memory. The fast, greedy algorithm is used to initialize a slower learning procedure that fine-tunes the weights using a contrastive version of the wake-sleep algorithm. After fine-tuning, a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels. This generative model gives better digit classification than the best discriminative learning algorithms. The low-dimensional manifolds on which the digits lie are modeled by long ravines in the free-energy landscape of the top-level associative memory, and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind.

We present an energy-based model that uses a product of generalized Student-t distributions to capture the statistical structure in data sets. This model is inspired by and particularly applicable to "natural" data sets such as images. We begin by providing the mathematical framework, where we discuss complete and overcomplete models and provide algorithms for training these models from data. Using patches of natural scenes, we demonstrate that our approach represents a viable alternative to independent component analysis as an interpretive model of biological visual systems. Although the two approaches are similar in flavor, there are also important differences, particularly when the representations are overcomplete. By constraining the interactions within our model, we are also able to study the topographic organization of Gabor-like receptive fields that our model learns. Finally, we discuss the relation of our new approach to previous work--in particular, gaussian scale mixture models and variants of independent components analysis.

We describe an approach to improve iterative dimensionality reduction methods by using information contained in the leading eigenvectors of a data affinity matrix. Using an insight from the area of spectral clustering, we suggest modifying the gradient of an iterative method, so that latent space elements belonging to the same cluster are encouraged to move in similar directions during optimization. We also describe way to achieve this without actually having to explicitly perform an eigendecomposition. Preliminary experiments show that our approach makes it possible to speed up iterative methods and helps them to find better local minima of their objective function.

Certain datasets can be efficiently modelled in terms of constraints that are usually satisfied but sometimes are strongly violated. We propose using energy-based density models (EBMs) implementing products of frequently approximately satisfied nonlinear constraints for modelling such datasets. We demonstrate the feasibility of this approach by training an EBM using contrastive backpropagation on a dataset of idealized trajectories of two balls bouncing in a box and showing that the model learns an accurate and efficient representation of the dataset, taking advantage of the approximate independence between subsets of variables.

We describe a generative model for handwritten digits that uses two pairs of opposing springs whose stiffnesses are controlled by a motor program. We show how neural networks can be trained to infer the motor programs required to accurately reconstruct the MNIST digits. The inferred motor programs can be used directly for digit classification, but they can also be used in other ways. By adding noise to the motor program inferred from an MNIST image we can generate a large set of very different images of the same class, thus enlarging the training set available to other methods. We can also use the motor programs as additional, highly informative outputs which reduce overfitting when training a feed-forward classifier. 1 Overview The idea that patterns can be recognized by figuring out how they were generated has been around for at least half a century [1, 2] and one of the first proposed applications was the recognition of handwriting using a generative model that involved pairs of opposing springs [3, 4]. The “analysis-by-synthesis” approach is attractive because the true generative model should provide the most natural way to characterize a class of patterns. The handwritten 2’s in figure 1, for example, are very variable when viewed as pixels but they have very similar motor programs. Despite its obvious merits, analysis-by-synthesis has had few successes, partly because it is computationally expensive to invert non-linear generative models and partly because the underlying parameters of the generative model are unknown for most large data sets. For example, the only source of information about how the MNIST digits were drawn is the images themselves. We describe a simple generative model in which a pen is controlled by two pairs of op- posing springs whose stiffnesses are specified by a motor program. If the sequence of stiffnesses is specified correctly, the model can produce images which look very like the MNIST digits. Using a separate network for each digit class, we show that backpropaga- tion can be used to learn a “recognition” network that maps images to the motor programs required to produce them. An interesting aspect of this learning is that the network creates its own training data, so it does not require the training images to be labelled with motor programs. Each recognition network starts with a single example of a motor program and grows an “island of competence” around this example, progressively extending the region over which it can map small changes in the image to the corresponding small changes in the motor program (see figure 2). Figure 1: An MNIST image of a 2 and the additional images that can be generated by infer- ring the motor program and then adding random noise to it. The pixels are very different, but they are all clearly twos. Fairly good digit recognition can be achieved by using the 10 recognition networks to find 10 motor programs for a test image and then scoring each motor program by its squared error in reconstructing the image. The 10 scores are then fed into a softmax classifier. Recognition can be improved by using PCA to model the distribution of motor trajectories for each class and using the distance of a motor trajectory from the relevant PCA hyperplane as an additional score. Each recognition network is solving a difficult global search problem in which the correct motor program must be found by a single, “open-loop” pass through the network. More accurate recognition can be achieved by using this open-loop global search to initialize an iterative, closed-loop local search which uses the error in the reconstructed image to re- vise the motor program. This requires reconstruction errors in pixel space to be mapped to corrections in the space of spring stiffnesses. We cannot backpropagate errors through the generative model because it is just a hand-coded computer program. So we learn “genera- tive” networks, one per digit class, that emulate the generator. After learning, backpropa- gation through these generative networks is used to convert pixel reconstruction errors into stiffness corrections. Our final system gives 1.82% error on the MNIST test set which is similar to the 1.7% achieved by a very different generative approach [5] but worse than the 1.53% produced by the best backpropagation networks or the 1.4% produced by support vector machines [6]. It is much worse than the 0.4% produced by convolutional neural networks that use cleverly enhanced training sets [7]. Recognition of test images is quite slow because it uses ten different recognition networks followed by iterative local search. There is, however, a much more efficient way to make use of our ability to extract motor programs. They can be treated as additional output labels when using backpropagation to train a single, multi- layer, discriminative neural network. These additional labels act as a very informative regularizer that reduces the error rate from 1.53% to 1.27% in a network with two hidden layers of 500 units each. This is a new method of improving performance that can be used in conjunction with other tricks such as preprocessing the images, enhancing the training set or using convolutional neural nets [8, 7]. 2 A simple generative model for drawing digits The generative model uses two pairs of opposing springs at right angles. One end of each spring is attached to a frictionless horizontal or vertical rail that is 39 pixels from the center of the image. The other end is attached to a “pen” that has significant mass. The springs themselves are weightless and have zero rest length. The pen starts at the equilibrium position defined by the initial stiffnesses of the four springs. It then follows a trajectory that is determined by the stiffness of each spring at each of the 16 subsequent time steps in the motor program. The mass is large compared with the rate at which the stiffnesses change, so the system is typically far from equilibrium as it follows the smooth trajectory. On each time step, the momentum is multiplied by 0.9 to simulate viscosity. A coarse-grain trajectory is computed by using one step of forward integration for each time step in the motor program, so it contains 17 points. The code is at www.cs.toronto.edu/∼ hinton/code. Figure 2: The training data for each class-specific recognition network is produced by adding noise to motor programs that are inferred from MNIST images using the current parameters of the recognition network. To initiate this process, the biases of the output units are set by hand so that they represent a prototypical motor program for the class. Given a coarse-grain trajectory, we need a way of assigning an intensity to each pixel. We tried various methods until we hand-evolved one that was able to reproduce the MNIST im- ages fairly accurately, but we suspect that many other methods would be just as good. For each point on the coarse trajectory, we share two units of ink between the the four closest pixels using bilinear interpolation. We also use linear interpolation to add three fine-grain trajectory points between every pair of coarse-grain points. These fine-grain points also contribute ink to the pixels using bilinear interpolation, but the amount of ink they con- tribute is zero if they are less than one pixel apart and rises linearly to the same amount as the coarse-grain points if they are more than two pixels apart. This generates a thin skeleton with a fairly uniform ink density. To flesh-out the skeleton, we use two “ink parameters”, a, b, to specify a 3 × 3 kernel of the form b(1 + a)[ a 12 ] which is convolved with the image four times. Finally, the pixel intensities are clipped to lie in the interval [0,1]. The matlab code is at www.cs.toronto.edu/∼ hinton/code. The values of 2a and b/1.5 are additional, logistic outputs of the recognition networks1.

In this paper we propose a novel method for learning a Mahalanobis distance measure to be used in the KNN classification algorithm. The algorithm directly maximizes a stochastic variant of the leave-one-out KNN score on the training set. It can also learn a low-dimensional lin- ear embedding of labeled data that can be used for data visualization and fast classification. Unlike other methods, our classification model is non-parametric, making no assumptions about the shape of the class distributions or the boundaries between them. The performance of the method is demonstrated on several data sets, both for metric learning and linear dimensionality reduction.

We describe a way of using multiple different types of similarity rela- tionship to learn a low-dimensional embedding of a dataset. Our method chooses different, possibly overlapping representations of similarity by individually reweighting the dimensions of a common underlying latent space. When applied to a single similarity relation that is based on Eu- clidean distances between the input data points, the method reduces to simple dimensionality reduction. If additional information is available about the dataset or about subsets of it, we can use this information to clean up or otherwise improve the embedding. We demonstrate the po- tential usefulness of this form of semi-supervised dimensionality reduc- tion on some simple examples.

Directed graphical models with one layer of observed random variables and one or more layers of hidden random variables have been the dom- inant modelling paradigm in many research fields. Although this ap- proach has met with considerable success, the causal semantics of these models can make it difficult to infer the posterior distribution over the hidden variables. In this paper we propose an alternative two-layer model based on exponential family distributions and the semantics of undi- rected models. Inference in these “exponential family harmoniums” is fast while learning is performed by minimizing contrastive divergence. A member of this family is then studied as an alternative probabilistic model for latent semantic indexing. In experiments it is shown that they perform well on document retrieval tasks and provide an elegant solution to searching with keywords.

Under-complete models, which derive lower dimensional representations of input data, are valuable in domains in which the number of input dimensions is very large, such as data consisting of a temporal sequence of images. This paper presents the under-complete product of experts (UPoE), where each expert models a one-dimensional projection of the data. Maximum-likelihood learning rules for this model constitute a tractable and exact algorithm for learning under-complete independent components. The learning rules for this model coincide with approximate learning rules proposed earlier for under-complete independent component analysis (UICA) models. This paper also derives an efficient sequential learning algorithm from this model and discusses its relationship to sequential independent component analysis (ICA), projection pursuit density estimation, and feature induction algorithms for additive random field models. This paper demonstrates the efficacy of these novel algorithms on high-dimensional continuous datasets.

In models that define probabilities via energies, maximum likelihood learning typically involves using Markov Chain Monte Carlo to sample from the model’s distribution. If the Markov chain is started at the data distribution, learning often works well even if the chain is only run for a few time steps [3]. But if the data distribution contains modes separated by regions of very low density, brief MCMC will not ensure that different modes have the correct relative energies because it cannot move particles from one mode to another. We show how to improve brief MCMC by allowing long-range moves that are suggested by the data distribution. If the model is approximately correct, these long-range moves have a reasonable acceptance rate.

We describe a probabilistic approach to the task of placing objects, de- scribed by high-dimensional vectors or by pairwise dissimilarities, in a low-dimensional space in a way that preserves neighbor identities. A Gaussian is centered on each object in the high-dimensional space and the densities under this Gaussian (or the given dissimilarities) are used to define a probability distribution over all the potential neighbors of the object. The aim of the embedding is to approximate this distribu- tion as well as possible when the same operation is performed on the low-dimensional “images” of the objects. A natural cost function is a sum of Kullback-Leibler divergences, one per object, which leads to a simple gradient for adjusting the positions of the low-dimensional im- ages. Unlike other dimensionality reduction methods, this probabilistic framework makes it easy to represent each object by a mixture of widely separated low-dimensional images. This allows ambiguous objects, like the document count vector for the word “bank”, to have versions close to the images of both “river” and “finance” without forcing the images of outdoor concepts to be located close to those of corporate concepts.

We propose a model for natural images in which the probability of an im- age is proportional to the product of the probabilities of some filter out- puts. We encourage the system to find sparse features by using a Student- t distribution to model each filter output. If the t-distribution is used to model the combined outputs of sets of neurally adjacent filters, the sys- tem learns a topographic map in which the orientation, spatial frequency and location of the filters change smoothly across the map. Even though maximum likelihood learning is intractable in our model, the product form allows a relatively efficient learning procedure that works well even for highly overcomplete sets of filters. Once the model has been learned it can be used as a prior to derive the “iterated Wiener filter” for the pur- pose of denoising images.

Boosting algorithms and successful applications thereof abound for clas- sification and regression learning problems, but not for unsupervised learning. We propose a sequential approach to adding features to a ran- dom field model by training them to improve classification performance between the data and an equal-sized sample of “negative examples” gen- erated from the model’s current estimate of the data density. Training in each boosting round proceeds in three stages: first we sample negative examples from the model’s current Boltzmann distribution. Next, a fea- ture is trained to improve classification performance between data and negative examples. Finally, a coefficient is learned which determines the importance of this feature relative to ones already in the pool. Negative examples only need to be generated once to learn each new feature. The validity of the approach is demonstrated on binary digits and continuous synthetic data.

Our goal is to design and build a tool for the creation of expressive character animation. Virtual puppetry, also known as performance animation, is a technique in which the user interactively controls a character's motion. In this paper we introduce local physical models for performance animation and describe how they can augment an existing kinematic method to achieve very effective animation control. These models approximate specific physically-generated aspects of a character's motion. They automate certain behaviours, while still letting the user override such motion via a PD-controller if he so desires. Furthermore, they can be tuned to ignore certain undesirable effects, such as the risk of having a character fall over, by ignoring corresponding components of the force. Although local physical models are a quite simple approximation to real physical behaviour, we show that they are extremely useful for interactive character control, and contribute positively to the expressiveness of the character's motion. In this paper, we develop such models at the knees and ankles of an interactively-animated 3D anthropomorphic character, and demonstrate a resulting animation. This approach can be applied in a straight-forward way to other joints. Categories and Subject Descriptors (according to ACM CCS): I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism, Interaction Techniques

It is possible to combine multiple latent-variable models of the same data by multiplying their probability distributions together and then renormalizing. This way of combining individual "expert" models makes it hard to generate samples from the combined model but easy to infer the values of the latent variables of each expert, because the combination rule ensures that the latent variables of different experts are conditionally independent when given the data. A product of experts (PoE) is therefore an interesting candidate for a perceptual system in which rapid inference is vital and generation is unnecessary. Training a PoE by maximizing the likelihood of the data is difficult because it is hard even to approximate the derivatives of the renormalization term in the combination rule. Fortunately, a PoE can be trained using a different objective function called "contrastive divergence" whose derivatives with regard to the parameters can be approximated accurately and efficiently. Examples are presented of contrastive divergence learning using several types of expert on several types of data.

The product of experts learning procedure can discover a set of stochastic binary features that constitute a nonlinear generative model of handwritten images of digits. The quality of generative models learned in this way can be assessed by learning a separate model for each class of digit and then comparing the unnormalized probabilities of test images under the 10 different class-specific models. To improve discriminative performance, a hierarchy of separate models can be learned, for each digit class. Each model in the hierarchy learns a layer of binary feature detectors that model the probability distribution of vectors of activity of feature detectors in the layer below. The models in the hierarchy are trained sequentially and each model uses a layer of binary feature detectors to learn a generative model of the patterns of feature activities in the preceding layer. After training, each layer of feature detectors produces a separate, unnormalized log probability score. With three layers of feature detectors for each of the 10 digit classes, a test image produces 30 scores which can be used as inputs to a supervised, logistic classification network that is trained on separate data.

Logistic units in the first hidden layer of a feedforward neural net(cid:173) work compute the relative probability of a data point under two Gaussians. This leads us to consider substituting other density models. We present an architecture for performing discriminative learning of Hidden Markov Models using a network of many small HMM's. Experiments on speech data show it to be superior to the standard method of discriminatively training HMM's.

We present Linear Relational Embedding (LRE), a new method of learn- ing a distributed representation of concepts from data consisting of in- stances of relations between given concepts. Its final goal is to be able to generalize, i.e. infer new instances of these relations among the con- cepts. On a task involving family relationships we show that LRE can generalize better than any previously published method. We then show how LRE can be used effectively to find compact distributed representa- tions for variable-sized recursive data structures, such as trees and lists. 1 Linear Relational Embedding Our aim is to take a large set of facts about a domain expressed as tuples of arbitrary sym- bols in a simple and rigid syntactic format and to be able to infer other “common-sense” facts without having any prior knowledge about the domain. Let us imagine a situation in which we have a set of concepts and a set of relations among these concepts, and that our data consists of few instances of these relations that hold among the concepts. We want to be able to infer other instances of these relations. For example, if the concepts are the people in a certain family, the relations are kinship relations, and we are given the facts ”Alberto has-father Pietro” and ”Pietro has-brother Giovanni”, we would like to be able to infer ”Alberto has-uncle Giovanni”. Our approach is to learn appropriate distributed rep- resentations of the entities in the data, and then exploit the generalization properties of the distributed representations [2] to make the inferences. In this paper we present a method, which we have called Linear Relational Embedding (LRE), which learns a distributed rep- resentation for the concepts by embedding them in a space where the relations between concepts are linear transformations of their distributed representations. involve two concepts. Let us consider the case in which all the relations are binary, i.e. , and the problem In this case our data consists of triplets we are trying to solve is to infer missing triplets when we are given only few of them. Inferring a triplet is equivalent to being able to complete it, that is to come up with one of its elements, given the other two. Here we shall always try to complete the third element of the triplets 1. LRE will then represent each concept in the data as a learned vector in a

High dimensional data that lies on or near a low dimensional manifold can be de- scribed by a collection of local linear models. Such a description, however, does not provide a global parameterization of the manifold—arguably an important goal of unsupervised learning. In this paper, we show how to learn a collection of local linear models that solves this more difficult problem. Our local linear models are represented by a mixture of factor analyzers, and the “global coordi- nation” of these models is achieved by adding a regularizing term to the standard maximum likelihood objective function. The regularizer breaks a degeneracy in the mixture model’s parameter space, favoring models whose internal coor- dinate systems are aligned in a consistent way. As a result, the internal coor- dinates change smoothly and continuously as one traverses a connected path on the manifold—even when the path crosses the domains of many different local models. The regularizer takes the form of a Kullback-Leibler divergence and illustrates an unexpected application of variational methods: not to perform ap- proximate inference in intractable probabilistic models, but to learn more useful internal representations in tractable ones. 1 Manifold Learning Consider an ensemble of images, each of which contains a face against a neutral back- ground. Each image can be represented by a point in the high dimensional vector space of pixel intensities. This representation, however, does not exploit the strong correlations between pixels of the same image, nor does it support many useful operations for reasoning about faces. If, for example, we select two images with faces in widely different locations and then average their pixel intensities, we do not obtain an image of a face at their average location. Images of faces lie on or near a low-dimensional, curved manifold, and we can represent them more usefully by the coordinates on this manifold than by pixel intensi- ties. Using these “intrinsic coordinates”, the average of two faces is another face with the average of their locations, poses and expressions. To analyze and manipulate faces, it is helpful to imagine a “magic black box” with levers or dials corresponding to the intrinsic coordinates on this manifold. Given a setting of the levers and dials, the box generates an image of a face. Given an image of a face, the box deduces the appropriate setting of the levers and dials. In this paper, we describe a fairly general way to construct such a box automatically from an ensemble of high-dimensional vectors. We assume only that there exists an underlying manifold of low dimensionality and that the relationship between the raw data and the manifold coordinates is locally linear and smoothly varying. Thus our method applies not only to images of faces, but also to many other forms of highly distributed perceptual and scientific data (e.g., spectrograms of speech, robotic sensors, gene expression arrays, document collections). 2 Local Linear Models The global structure of perceptual manifolds (such as images of faces) tends to be highly nonlinear. Fortunately, despite their complicated global structure, we can usually char- acterize these manifolds as locally linear. Thus, to a good approximation, they can be represented by collections of simpler models, each of which describes a locally linear neighborhood[3, 6, 8]. For unsupervised learning tasks, a probabilistic model that nicely captures this intuition is a mixture of factor analyzers (MFA)[5]. The model is used to describe high dimensional data that lies on or near a lower dimensional manifold. MFAs parameterize a joint distribution over observed and hidden variables:

We introduce linear relational embedding as a means of learning a distributed representation of concepts from data consisting of binary relations between these concepts. The key idea is to represent concepts as vectors, binary relations as matrices, and the operation of applying a relation to a concept as a matrix-vector multiplication that produces an approximation to the related concept. A representation for concepts and relations is learned by maximizing an appropriate discriminative goodness function using gradient ascent. On a task involving family relationships, learning is fast and leads to good generalization.

Linear relational embedding (LRE) was introduced previously by the authors (1999) as a means of extracting a distributed representation of concepts from relational data. The original formulation cannot use negative information and cannot properly handle data in which there are multiple correct answers. In this paper we propose an extended formulation of LRE that solves both these problems. We present results in two simple domains, which show that learning leads to good generalization.

The product of experts learning procedure [1] can discover a set of stochastic binary features that constitute a non-linear generative model of handwritten images of digits. The quality of generative models learned in this way can be assessed by learning a separate model for each class of digit and then comparing the unnormalized probabilities of test images under the 10 different class-specific models. To improve discriminative performance, it is helpful to learn a hierarchy of separate models for each digit class. Each model in the hierarchy has one layer of hidden units and the nth level model is trained on data that consists of the activities of the hidden units in the already trained (n - l)th level model. After train(cid:173) ing, each level produces a separate, unnormalized log probabilty score. With a three-level hierarchy for each of the 10 digit classes, a test image produces 30 scores which can be used as inputs to a supervised, logis(cid:173) tic classification network that is trained on separate data. On the MNIST database, our system is comparable with current state-of-the-art discrimi(cid:173) native methods, demonstrating that the product of experts learning proce(cid:173) dure can produce effective generative models of high-dimensional data. 1 Learning products of stochastic binary experts Hinton [1] describes a learning algorithm for probabilistic generative models that are com(cid:173) posed of a number of experts. Each expert specifies a probability distribution over the visible variables and the experts are combined by multiplying these distributions together and renormalizing. (1) where d is a data vector in a discrete space, Om is all the parameters of individual model m, Pm(dIOm) is the probability of d under model m, and c is an index over all possible vectors in the data space. A Restricted Boltzmann machine [2, 3] is a special case of a product of experts in which each expert is a single, binary stochastic hidden unit that has symmetrical connections to a set of visible units, and connections between the hidden units are forbidden. Inference in an RBM is much easier than in a general Boltzmann machine and it is also much easier than in a causal belief net because there is no explaining away. There is therefore no need to perform any iteration to determine the activities of the hidden units. The hidden states, Sj , are conditionally independent given the visible states, Si, and the distribution of Sj is given by the standard logistic function :

The problem of reinforcement learning in large factored Markov decision processes is explored. The Q-value of a state-action pair is approximated by the free energy of a product of experts network. Network parameters are learned on-line using a modified SARSA algorithm which minimizes the inconsistency of the Q-values of consecutive state-action pairs. Ac(cid:173) tions are chosen based on the current value estimates by fixing the current state and sampling actions from the network using Gibbs sampling. The algorithm is tested on a co-operative multi-agent task. The product of experts model is found to perform comparably to table-based Q-Iearning for small instances of the task, and continues to perform well when the problem becomes too large for a table-based representation.

We describe a neurally-inspired, unsupervised learning algorithm that builds a non-linear generative model for pairs of face images from the same individual. Individuals are then recognized by finding the highest relative probability pair among all pairs that consist of a test image and an image whose identity is known. Our method compares favorably with other methods in the literature. The generative model consists of a single layer of rate-coded, non-linear feature detectors and it has the property that, given a data vector, the true posterior probability distribution over the feature detector activities can be inferred rapidly without iteration or approximation. The weights of the feature detectors are learned by com(cid:173) paring the correlations of pixel intensities and feature activations in two phases: When the network is observing real data and when it is observing reconstructions of real data generated from the feature activations.

We introduce a new statistical model for time series that iteratively segments data into regimes with approximately linear dynamics and learnsthe parameters of each of these linear regimes. This model combines and generalizes two of the most widely used stochastic time-series models -- hidden Markov models and linear dynamical systems -- and is closely related to models that are widely used in the control and econometrics literatures. It can also be derived by extending the mixture of experts neural network (Jacobs, Jordan, Nowlan, & Hinton, 1991) to its fully dynamical version, in which both expert and gating networks are recurrent. Inferring the posterior probabilities of the hidden states of this model is computationally intractable, and therefore the exact expectation maximization (EM) algorithm cannot be applied. However, we present a variational approximation that maximizes a lower bound on the log-likelihood and makes use of both the forward and backward recursions for hidden Markov models and the Kalman filter recursions for linear dynamical systems. We tested the algorithm on artificial data sets and a natural data set of respiration force from a patient with sleep apnea. The results suggest that variational approximations are a viable method for inference and learning in switching state-space models.

We present a split-and-merge expectation-maximization (SMEM) algorithm to overcome the local maxima problem in parameter estimation of finite mixture models. In the case of mixture models, local maxima often involve having too many components of a mixture model in one part of the space and too few in another, widely separated part of the space. To escape from such configurations, we repeatedly perform simultaneous split-and-merge operations using a new criterion for efficiently selecting the split-and-merge candidates. We apply the proposed algorithm to the training of gaussian mixtures and mixtures of factor analyzers using synthetic and real data and show the effectiveness of using the split-and-merge operations to improve the likelihood of both the training data and of held-out test data. We also show the practical usefulness of the proposed algorithm by applying it to image compression and pattern recognition problems.

We view perceptual tasks such as vision and speech recognition as inference problems where the goal is to estimate the posterior distribution over latent variables (e.g., depth in stereo vision) given the sensory input. The recent flurry of research in independent component analysis exemplifies the importance of inferring the continuous-valued latent variables of input data. The latent variables found by this method are linearly related to the input, but perception requires nonlinear inferences such as classification and depth estimation. In this article, we present a unifying framework for stochastic neural networks with nonlinear latent variables. Nonlinear units are obtained by passing the outputs of linear gaussian units through various nonlinearities. We present a general variational method that maximizes a lower bound on the likelihood of a training set and give results on two visual feature extraction problems. We also show how the variational method can be used for pattern classification and compare the performance of these nonlinear networks with other methods on the problem of handwritten digit recognition.

Animation through the numerical simulation of physics- based graphics models offers unsurpassed realism, but it can be computationally demanding. Likewise, the search for controllers that enable physics-based models to produce desired animations usually entails formidable computational cost. This paper demon- strates the possibility of replacing the numerical simulation and control of dynamic models with a dramatically more efficient al- ternative. In particular, we propose the NeuroAnimator, a novel ap- proach to creating physically realistic animation that exploits neu- ral networks. NeuroAnimators are automatically trained off-line to emulate physical dynamics through the observation of physics- based models in action. Depending on the model, its neural net- work emulator can yield physically realistic animation one or two orders of magnitude faster than conventional numerical simulation. Furthermore, by exploiting the network structure of the NeuroAni- mator, we introduce a fast algorithm for learning controllers that en- ables either physics-based models or their neural network emulators to synthesize motions satisfying prescribed animation goals. We demonstrate NeuroAnimators for a variety of physics-based mod- els.

Glove-Talk II is a system which translates hand gestures to speech through an adaptive interface. Hand gestures are mapped continuously to ten control parameters of a parallel formant speech synthesizer. The mapping allows the hand to act as an artificial vocal tract that produces speech in real time. This gives an unlimited vocabulary in addition to direct control of fundamental frequency and volume. Currently, the best version of Glove-Talk II uses several input devices, a parallel formant speech synthesizer, and three neural networks. The gesture-to-speech task is divided into vowel and consonant production by using a gating network to weight the outputs of a vowel and a consonant neural network. The gating network and the consonant network are trained with examples from the user. The vowel network implements a fixed user-defined relationship between hand position and vowel sound and does not require any training examples from the user. Volume, fundamental frequency, and stop consonants are produced with a fixed mapping from the input devices. With Glove-Talk II, the subject can speak slowly but with far more natural sounding pitch variations than a text-to-speech synthesizer.

We discuss Hinton's (1989) relative payoff procedure (RPP), a static reinforcement learning algorithm whose foundation is not stochastic gradient ascent. We show circumstances under which applying the RPP is guaranteed to increase the mean return, even though it can make large changes in the values of the parameters. The proof is based on a mapping between the RPP and a form of the expectation-maximization procedure of Dempster, Laird, and Rubin (1977).

We show how a neural network can be used to allow a mobile robot to derive an accurate estimate of its location from noisy sonar sensors and noisy motion information. The robot's model of its location is in the form of a probability distribution across a grid of possible locations. This distribution is updated using both the motion information and the predictions of a neural network that maps locations into likelihood distributions across possible sonar readings. By predicting sonar readings from locations, rather than vice versa, the robot can handle the very nongaussian noise in the sonar sensors. By using the constraint provided by the noisy motion information, the robot can use previous readings to improve its estimate of its current location. By treating the resulting estimates as if they were correct, the robot can learn the relationship between location and sonar readings without requiring an external supervision signal that specifies the actual location of the robot. It can learn to locate itself in a new environment with almost no supervision, and it can maintain its location ability even when the environment is nonstationary.

Glove-Talk II is a system which translates hand gestures to speech through an adaptive interface. Hand gestures are mapped continuously to ten control parameters of a parallel formant speech synthesizer. The mapping allows the hand to act as an artificial vocal tract that produces speech in real time. This gives an unlimited vocabulary in addition to direct control of fundamental frequency and volume. Currently, the best version of Glove-Talk II uses several input devices, a parallel formant speech synthesizer, and three neural networks. The gesture-to-speech task is divided into vowel and consonant production by using a gating network to weight the outputs of a vowel and a consonant neural network. The gating network and the consonant network are trained with examples from the user. The vowel network implements a fixed user-defined relationship between hand position and vowel sound and does not require any training examples from the user. Volume, fundamental frequency, and stop consonants are produced with a fixed mapping from the input devices. With Glove-Talk II, the subject can speak slowly but with far more natural sounding pitch variations than a text-to-speech synthesizer.

This paper describes two new methods for modeling the manifolds of digitized images of handwritten digits. The models allow a priori information about the structure of the manifolds to be combined with empirical data. Accurate modeling of the manifolds allows digits to be discriminated using the relative probability densities under the alternative models. One of the methods is grounded in principal components analysis, the other in factor analysis. Both methods are based on locally linear low-dimensional approximations to the underlying data manifold. Links with other methods that model the manifold are discussed.

We introduce a new approach to the problem of optimal compression when a source code produces multiple codewords for a given symbol. It may seem that the most sensible codeword to use in this case is the shortest one. However, in the proposed free energy approach, random codeword selection yields an effective codeword length that can be less than the shortest codeword length. If the random choices are Boltzmann distributed, the effective length is optimal for the given source code. The expectation-maximization parameter estimation algorithms minimize this effective codeword length. We illustrate the performance of free energy coding on a simple problem where a compression factor of two is gained by using the new method.

We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable B-splines with Gaussian "ink generators" spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the expectation maximization algorithm that maximizes the likelihood of the model generating the data. This approach has many advantages: 1) the system not only produces a classification of the digit but also a rich description of the instantiation parameters which can yield information such as the writing style; 2) the generative models can perform recognition driven segmentation; 3) the method involves a relatively small number of parameters and hence training is relatively easy and fast; and 4) unlike many other recognition schemes, it does not rely on some form of pre-normalization of input images, but can handle arbitrary scalings, translations and a limited degree of image rotation. We have demonstrated that our method of fitting models to images does not get trapped in poor local minima. The main disadvantage of the method is that it requires much more computation than more standard OCR techniques.

Article Glove-TalkII: an adaptive gesture-to-formant interface Share on Authors: Sidney Fels Department of Computer Science & Department of Computer Science, University of Toronto & University of Toronto, Toronto, ON, Canada, M5S 1A4 & Toronto, ON, Canada, M5S 1A4 Department of Computer Science & Department of Computer Science, University of Toronto & University of Toronto, Toronto, ON, Canada, M5S 1A4 & Toronto, ON, Canada, M5S 1A4View Profile , Geoffrey Hinton Department of Computer Science & Department of Computer Science, University of Toronto & University of Toronto, Toronto, ON, Canada, M5S 1A4 & Toronto, ON, Canada, M5S 1A4 Department of Computer Science & Department of Computer Science, University of Toronto & University of Toronto, Toronto, ON, Canada, M5S 1A4 & Toronto, ON, Canada, M5S 1A4View Profile Authors Info & Claims CHI '95: Proceedings of the SIGCHI Conference on Human Factors in Computing SystemsMay 1995 Pages 456–463https://doi.org/10.1145/223904.223966Online:01 May 1995Publication History 24citation473DownloadsMetricsTotal Citations24Total Downloads473Last 12 Months18Last 6 weeks4 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterized stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative models, each pattern can be generated in exponentially many ways. It is thus intractable to adjust the parameters to maximize the probability of the observed patterns. We describe a way of finessing this combinatorial explosion by maximizing an easily computed lower bound on the probability of the observations. Our method can be viewed as a form of hierarchical self-supervised learning that may relate to the function of bottom-up and top-down cortical processing pathways.

The minimum description length (MDL) principle can be used to train the hidden units of a neural network to extract a representation that is cheap to describe but nonetheless allows the input to be reconstructed accurately. We show how MDL can be used to develop highly redundant population codes. Each hidden unit has a location in a low-dimensional implicit space. If the hidden unit activities form a bump of a standard shape in this space, they can be cheaply encoded by the center of this bump. So the weights from the input units to the hidden units in an autoencoder are trained to make the activities form a standard bump. The coordinates of the hidden units in the implicit space are also learned, thus allowing flexibility, as the network develops a discontinuous topography when presented with different input classes.

Glove-TaikII is a system which translates hand gestures to speech through an adaptive interface. Hand gestures are mapped contin(cid:173) uously to 10 control parameters of a parallel formant speech syn(cid:173) thesizer. The mapping allows the hand to act as an artificial vocal tract that produces speech in real time. This gives an unlimited vocabulary in addition to direct control of fundamental frequency and volume. Currently, the best version of Glove-TalkII uses sev(cid:173) eral input devices (including a CyberGlove, a ContactGlove, a 3- space tracker, and a foot-pedal), a parallel formant speech synthe(cid:173) sizer and 3 neural networks. The gesture-to-speech task is divided into vowel and consonant production by using a gating network to weight the outputs of a vowel and a consonant neural network. The gating network and the consonant network are trained with examples from the user. The vowel network implements a fixed, user-defined relationship between hand-position and vowel sound and does not require any training examples from the user. Volume, fundamental frequency and stop consonants are produced with a fixed mapping from the input devices. One subject has trained to speak intelligibly with Glove-TalkII. He speaks slowly with speech quality similar to a text-to-speech synthesizer but with far more natural-sounding pitch variations. 844 S. Sidney Fe Is, Geoffrey Hinton

We construct a mixture of locally linear generative models of a col(cid:173) lection of pixel-based images of digits, and use them for recogni(cid:173) tion. Different models of a given digit are used to capture different styles of writing, and new images are classified by evaluating their log-likelihoods under each model. We use an EM-based algorithm in which the M-step is computationally straightforward principal components analysis (PCA). Incorporating tangent-plane informa(cid:173) tion [12] about expected local deformations only requires adding tangent vectors into the sample covariance matrices for the PCA, and it demonstrably improves performance.

Deformable models are an attractive approach to recognizing non(cid:173) rigid objects which have considerable within class variability. How(cid:173) ever, there are severe search problems associated with fitting the models to data. We show that by using neural networks to provide better starting points, the search time can be significantly reduced. The method is demonstrated on a character recognition task. In previous work we have developed an approach to handwritten character recogni(cid:173) tion based on the use of deformable models (Hinton, Williams and Revow, 1992a; Revow, Williams and Hinton, 1993). We have obtained good performance with this method, but a major problem is that the search procedure for fitting each model to an image is very computationally intensive, because there is no efficient algorithm (like dynamic programming) for this task. In this paper we demonstrate that it is possible to "compile down" some of the knowledge gained while fitting models to data to obtain better starting points that significantly reduce the search time. 1 DEFORMABLE MODELS FOR DIGIT RECOGNITION The basic idea in using deformable models for digit recognition is that each digit has a model, and a test image is classified by finding the model which is most likely to have generated it. The quality of the match between model and test image depends on the deformation of the model, the amount of ink that is attributed to noise and the distance of the remaining ink from the deformed model. ·Current address: Department of Computer Science and Applied Mathematics, Aston University, Birmingham B4 7ET, UK. 966 Christopher K. T. Williams, Michael D. Revow, Geoffrey E. Hinton More formally, the two important terms in assessing the fit are the prior probabil(cid:173) ity distribution for the instantiation parameters of a model (which penalizes very distorted models), and the imaging model that characterizes the probability distri(cid:173) bution over possible images given the instantiated model l . Let I be an image, M be a model and z be its instantiation parameters. Then the evidence for model M is given by P(IIM) = J P(zIM)P(IIM, z)dz (1) The first term in the integrand is the prior on the instantiation parameters and the second is the imaging model i.e., the likelihood of the data given the instantiated model. P(MII) is directly proportional to P(IIM), as we assume a uniform prior on each digit. Equation 1 is formally correct, but if z has more than a few dimensions the evalua(cid:173) tion of this integral is very computationally intensive. However, it is often possible to make an approximation based on the assumption that the integrand is strongly peaked around a (global) maximum value z*. In this case, the evidence can be ap(cid:173) proximated by the highest peak of the integrand times a volume factor ~(zII, M), which measures the sharpness of the peak2 . P(IIM) ~ P(zIM)P(Ilz, M)~(zII, M) (2) By Taylor expanding around z* to second order it can be shown that the volume factor depends on the determinant of the Hessian of 10gP(z, 11M) . Taking logs of equation 2, defining EdeJ as the negative log of P(z*IM), and EJit as the cor(cid:173) responding term for the imaging model, then the aim of the search is to find the minimum of E tot = EdeJ + EJit . Of course the total energy will have many local minima; for the character recognition task we aim to find the global minimum by using a continuation method (see section 1.2). 1.1 SPLINES, AFFINE TRANSFORMS AND IMAGING MODELS This section presents a brief overview of our work on using deformable models for digit recognition. For a fuller treatment, see Revow, Williams and Hinton (1993) . Each digit is modelled by a cubic B-spline whose shape is determined by the posi(cid:173) tions of the control points in the object-based frame. The models have eight control points, except for the one model which has three, and the seven model which has five. To generate an ideal example of a digit the control points are positioned at their "home" locations. Deformed characters are produced by perturbing the con(cid:173) trol points away from their home locations. The home locations and covariance matrix for each model were adapted in order to improve the performance. The deformation energy only penalizes shape deformations. Affine transformations, i.e., translation, rotation, dilation, elongation, and shear, do not change the under(cid:173) lying shape of an object so we want the deformation energy to be invariant under them . We achieve this by giving each model its own "object-based frame" and computing the deformation energy relative to this frame. lThis framework has been used by many authors, e.g. Grenander et al (1991) . 2The Gaussian approximation has been popularized in the neural net community by

We propose an alternative model for mixtures of experts which uses a different parametric form for the gating network. The modified model is trained by the EM algorithm. In comparison with earlier models-trained by either EM or gradient ascent-there is no need to select a learning stepsize. We report simulation experiments which show that the new architecture yields faster convergence. We also apply the new model to two problem domains: piecewise nonlinear function approximation and the combination of multiple previously trained classifiers.

Supervised neural networks generalize well if there is much less information in the weights than there is in the output vectors of the training cases. So during learning, it is important to keep the weights simple by penalizing the amount of information they contain. The amount of information in a weight can be controlled by adding Gaussian noise and the noise level can be adapted during learning to optimize the trade-off between the expected squared error of the network and the amount of information in the weights. We describe a method of computing the derivatives of the expected squared error and of the amount of information in the noisy weights in a network that contains a layer of non-linear hidden units. Provided the output units are linear, the exact derivatives can be computed efficiently without time-consuming Monte Carlo simulations. The idea of minimizing the amount of information that is required to communicate the weights of a neural network leads to a number of interesting...

We have previously described an unsupervised learning procedure that discovers spatially coherent properties of the world by maximizing the information that parameters extracted from different parts of the sensory input convey about some common underlying cause. When given random dot stereograms of curved surfaces, this procedure learns to extract surface depth because that is the property that is coherent across space. It also learns how to interpolate the depth at one location from the depths at nearby locations (Becker and Hinton 1992b). In this paper, we propose two new models that handle surfaces with discontinuities. The first model attempts to detect cases of discontinuities and reject them. The second model develops a mixture of expert interpolators. It learns to detect the locations of discontinuities and to invoke specialized, asymmetric interpolators that do not cross the discontinuities.

An adaptation algorithm for equalizers operating on very distorted channels is presented. The algorithm is based on the idea of adjusting the equalizer tap gains to maximize the likelihood that the equalizer outputs would be generated by a mixture of two Gaussians with known means. The decision-directed least-mean-square algorithm is shown to be an approximation to maximizing the likelihood that the equalizer outputs come from such an independently and identically distributed source. The algorithm is developed in the context of a binary pulse-amplitude-modulation channel, and simulations demonstrate that the algorithm converges in channels for which the decision-directed LMS algorithms does not converge.>

To illustrate the potential of multilayer neural networks for adaptive interfaces, a VPL Data-Glove connected to a DECtalk speech synthesizer via five neural networks was used to implement a hand-gesture to speech system. Using minor variations of the standard backpropagation learning procedure, the complex mapping of hand movements to speech is learned using data obtained from a single ;speaker' in a simple training phase. With a 203 gesture-to-word vocabulary, the wrong word is produced less than 1% of the time, and no word is produced about 5% of the time. Adaptive control of the speaking rate and word stress is also available. The training times and final performance speed are improved by using small, separate networks for each naturally defined subtask. The system demonstrates that neural networks can be used to develop the complex mappings required in a high bandwidth interface that adapts to the individual user.

One way of simplifying neural networks so they generalize better is to add an extra term to the error function that will penalize complexity. Simple versions of this approach include penalizing the sum of the squares of the weights or penalizing the number of nonzero weights. We propose a more complicated penalty term in which the distribution of weight values is modeled as a mixture of multiple gaussians. A set of weights is simple if the weights have high probability density under the mixture model. This can be achieved by clustering the weights into subsets with the weights in each cluster having very similar values. Since we do not know the appropriate means or variances of the clusters in advance, we allow the parameters of the mixture model to adapt at the same time as the network learns. Simulations on two different problems demonstrate that this complexity term is more effective than previous complexity terms.

We present a new supervised learning procedure for systems composed of many separate networks, each of which learns to handle a subset of the complete set of training cases. The new procedure can be viewed either as a modular version of a multilayer supervised network, or as an associative version of competitive learning. It therefore provides a new link between these two apparently different approaches. We demonstrate that the learning procedure divides up a vowel discrimination task into appropriate subtasks, each of which can be solved by a very simple expert network.

An algorithm that is widely used for adaptive equalization in current modems is the “bootstrap” or “decision-directed” version of the Widrow-Hoff rule. We show that this algorithm can be viewed as an unsupervised clustering algorithm in which the data points are transformed so that they form two clusters that are as tight as possible. The standard algorithm performs gradient ascent in a crude model of the log likelihood of generating the transformed data points from two gaussian distributions with fixed centers. Better convergence is achieved by using the exact gradient of the log likelihood.

The Boltzmann machine learning procedure has been successfully applied in deterministic networks of analog units that use a mean field approximation to efficiently simulate a truly stochastic system (Peterson and Anderson 1987). This type of “deterministic Boltzmann machine” (DBM) learns much faster than the equivalent “stochastic Boltzmann machine” (SBM), but since the learning procedure for DBM's is only based on an analogy with SBM's, there is no existing proof that it performs gradient descent in any function, and it has only been justified by simulations. By using the appropriate interpretation for the way in which a DBM represents the probability of an output vector given an input vector, it is shown that the DBM performs steepest descent in the same function as the original SBM, except at rare discontinuities. A very simple way of forcing the weights to become symmetrical is also described, and this makes the DBM more biologically plausible than back-propagation (Werbos 1974; Parker 1985; Rumelhart et al. 1986).

A time-delay neural network (TDNN) for phoneme recognition is discussed. By the use of two hidden layers in addition to an input and output layer it is capable of representing complex nonlinear decision surfaces. Three important properties of the TDNNs have been observed. First, it was able to invent without human interference meaningful linguistic abstractions in time and frequency such as formant tracking and segmentation. Second, it has learned to form alternate representations linking different acoustic events with the same higher level concept. In this fashion it can implement trading relations between lower level acoustic events leading to robust recognition performance despite considerable variability in the input speech. Third, the network is translation-invariant and does not rely on precise alignment or segmentation of the input. The TDNNs performance is compared with the best of hidden Markov models (HMMs) on a speaker-dependent phoneme-recognition task. The TDNN achieved a recognition of 98.5% compared to 93.7% for the HMM, i.e., a fourfold reduction in error.>