Large language models (LLMs) can suffer from hallucinations when generating text. These hallucinations impede various applications in society and industry by making LLMs untrustworthy. Current LLMs generate text in an autoregressive fashion by predicting and appending text tokens. When an LLM is uncertain about the semantic meaning of the next tokens to generate, it is likely to start hallucinating. Thus, it has been suggested that predictive uncertainty is one of the main causes of hallucinations. We introduce Semantically Diverse Language Generation (SDLG) to quantify predictive uncertainty in LLMs. SDLG steers the LLM to generate semantically diverse yet likely alternatives for an initially generated text. This approach provides a precise measure of aleatoric semantic uncertainty, detecting whether the initial text is likely to be hallucinated. Experiments on question-answering tasks demonstrate that SDLG consistently outperforms existing methods while being the most computationally efficient, setting a new standard for uncertainty estimation in LLMs.

Transformers are widely used as generic backbones in computer vision, despite initially introduced for natural language processing. Recently, the Long Short-Term Memory (LSTM) has been extended to a scalable and performant architecture - the xLSTM - which overcomes long-standing LSTM limitations via exponential gating and parallelizable matrix memory structure. In this paper, we introduce Vision-LSTM (ViL), an adaption of the xLSTM building blocks to computer vision. ViL comprises a stack of xLSTM blocks where odd blocks process the sequence of patch tokens from top to bottom while even blocks go from bottom to top. ViL achieves strong performances on classification, transfer learning and segmentation tasks as well as a beneficial pre-training cost-to-performance trade-off. Experiments show that ViL holds promise to be further deployed as new generic backbone for computer vision architectures.

We introduce MIM (Masked Image Modeling)-Refiner, a contrastive learning boost for pre-trained MIM models. MIM-Refiner is motivated by the insight that strong representations within MIM models generally reside in intermediate layers. Accordingly, MIM-Refiner leverages multiple instance discrimination (ID) heads that are connected to different intermediate layers. In each head, a nearest neighbor ID objective constructs clusters that capture semantic information which improves performance on downstream tasks, including off-the-shelf and fine-tuning settings. The refinement process is short and simple - yet highly effective. Within a few epochs, we refine the features of MIM models from subpar to state-of-the-art, off-the-shelf features. Refining a ViT-H, pre-trained with data2vec 2.0 on ImageNet-1K, sets a new state-of-the-art in linear probing (84.7\%) and low-shot classification among models that are pre-trained on ImageNet-1K. MIM-Refiner efficiently combines the advantages of MIM and ID objectives, enabling scaling ID objectives to billion parameter models using relatively little compute. MIM-Refiner compares favorably against previous state-of-the-art SSL models on various benchmarks such as low-shot classification, long-tailed classification and semantic segmentation.

While Transformers and other sequence-parallelizable neural network architectures seem like the current state of the art in sequence modeling, they specifically lack state-tracking capabilities. These are important for time-series tasks and logical reasoning. Traditional RNNs like LSTMs and GRUs, as well as modern variants like sLSTM do have these capabilities at the cost of strictly sequential processing. While this is often seen as a strong limitation, we show how fast these networks can get with our hardware-optimization FlashRNN in Triton and CUDA, optimizing kernels to the register level on modern GPUs. We extend traditional RNNs with a parallelization variant that processes multiple RNNs of smaller hidden state in parallel, similar to the head-wise processing in Transformers. To enable flexibility on different GPU variants, we introduce a new optimization framework for hardware-internal cache sizes, memory and compute handling. It models the hardware in a setting using polyhedral-like constraints, including the notion of divisibility. This speeds up the solution process in our ConstrINT library for general integer constraint satisfaction problems (integer CSPs). We show that our kernels can achieve 50x speed-ups over a vanilla PyTorch implementation and allow 40x larger hidden sizes compared to our Triton implementation. We have open-sourced our kernels and the optimization library to boost research in the direction of state-tracking enabled RNNs and sequence modeling here: https://github.com/NX-AI/flashrnn

Learning to sample from complex unnormalized distributions over discrete domains emerged as a promising research direction with applications in statistical physics, variational inference, and combinatorial optimization. Recent work has demonstrated the potential of diffusion models in this domain. However, existing methods face limitations in memory scaling and thus the number of attainable diffusion steps since they require backpropagation through the entire generative process. To overcome these limitations we introduce two novel training methods for discrete diffusion samplers, one grounded in the policy gradient theorem and the other one leveraging Self-Normalized Neural Importance Sampling (SN-NIS). These methods yield memory-efficient training and achieve state-of-the-art results in unsupervised combinatorial optimization. Numerous scientific applications additionally require the ability of unbiased sampling. We introduce adaptations of SN-NIS and Neural Markov Chain Monte Carlo that enable for the first time the application of discrete diffusion models to this problem. We validate our methods on Ising model benchmarks and find that they outperform popular autoregressive approaches. Our work opens new avenues for applying diffusion models to a wide range of scientific applications in discrete domains that were hitherto restricted to exact likelihood models.

Language models for biological and chemical sequences enable crucial applications such as drug discovery, protein engineering, and precision medicine. Currently, these language models are predominantly based on Transformer architectures. While Transformers have yielded impressive results, their quadratic runtime dependency on sequence length complicates their use for long genomic sequences and in-context learning on proteins and chemical sequences. Recently, the recurrent xLSTM architecture has been shown to perform favorably compared to Transformers and modern state-space models (SSMs) in the natural language domain. Similar to SSMs, xLSTMs have linear runtime dependency and allow for constant-memory decoding at inference time, which makes them prime candidates for modeling long-range dependencies in biological and chemical sequences. In this work, we tailor xLSTM towards these domains and we propose a suite of language models called Bio-xLSTM. Extensive experiments in three large domains, genomics, proteins, and chemistry, were performed to assess xLSTM’s ability to model biological and chemical sequences. The results show that Bio-xLSTM is a highly proficient generative model for DNA, protein, and chemical sequences, learns rich representations, and can perform in-context learning for proteins and small molecules.

Recent breakthroughs in solving reasoning, math and coding problems with Large Language Models (LLMs) have been enabled by investing substantial computation budgets at inference time. Therefore, inference speed is one of the most critical properties of LLM architectures, and there is a growing need for LLMs that are efficient and fast at inference. Recently, LLMs built on the xLSTM architecture have emerged as a powerful alternative to Transformers, offering linear compute scaling with sequence length and constant memory usage, both highly desirable properties for efficient inference. However, such xLSTM-based LLMs have yet to be scaled to larger models and assessed and compared with respect to inference speed and efficiency. In this work, we introduce xLSTM 7B, a 7-billion-parameter LLM that combines xLSTM’s architectural benefits with targeted optimizations for fast and efficient inference. Our experiments demonstrate that xLSTM 7B achieves performance on downstream tasks comparable to other similar-sized LLMs, while providing significantly faster inference speeds and greater efficiency compared to Llama- and Mamba-based LLMs. These results establish xLSTM 7B as the fastest and most efficient 7B LLM, offering a solution for tasks that require large amounts of test-time computation. Our work highlights xLSTM’s potential as a foundational architecture for methods building on heavy use of LLM inference. Our model weights, model code and training code are open-source. Model: https://huggingface.co/NX-AI/xLSTM-7b Code: https://github.com/NX-AI/xlstm and https://github.com/NX-AI/xlstm-jax.

Geometry is a ubiquitous tool in computer graphics, design, and engineering. However, the lack of large shape datasets limits the application of state-of-the-art supervised learning methods and motivates the exploration of alternative learning strategies. To this end, we introduce geometry-informed neural networks (GINNs) -- a framework for training shape-generative neural fields without data by leveraging user-specified design requirements in the form of objectives and constraints. By adding diversity as an explicit constraint, GINNs avoid mode-collapse and can generate multiple diverse solutions, often required in geometry tasks. Experimentally, we apply GINNs to several problems spanning physics, geometry, and engineering design, showing control over geometrical and topological properties, such as surface smoothness or the number of holes. These results demonstrate the potential of training shape-generative models without data, paving the way for new generative design approaches without large datasets.

In recent years, there has been a trend in the field of Reinforcement Learning (RL) towards large action models trained offline on large-scale datasets via sequence modeling. Existing models are primarily based on the Transformer architecture, which results in powerful agents. However, due to slow inference times, Transformer-based approaches are impractical for real-time applications, such as robotics. Recently, modern recurrent architectures, such as xLSTM and Mamba, have been proposed that exhibit parallelization benefits during training similar to the Transformer architecture while offering fast inference. In this work, we study the aptitude of these modern recurrent architectures for large action models. Consequently, we propose a Large Recurrent Action Model (LRAM) with an xLSTM at its core that comes with linear-time inference complexity and natural sequence length extrapolation abilities. Experiments on 432 tasks from 6 domains show that LRAM compares favorably to Transformers in terms of performance and speed.

Ensembles of Deep Neural Networks, Deep Ensembles, are widely used as a simple way to boost predictive performance. However, their impact on algorithmic fairness is not well understood yet. Algorithmic fairness examines how a model’s performance varies across socially relevant groups defined by protected attributes such as age, gender, or race. In this work, we explore the interplay between the performance gains from Deep Ensembles and fairness. Our analysis reveals that they unevenly favor different groups, a phenomenon that we term the disparate benefits effect. We empirically investigate this effect using popular facial analysis and medical imaging datasets with protected group attributes and find that it affects multiple established group fairness metrics, including statistical parity and equal opportunity. Furthermore, we identify that the per-group differences in predictive diversity of ensemble members can explain this effect. Finally, we demonstrate that the classical Hardt post-processing method is particularly effective at mitigating the disparate benefits effect of Deep Ensembles by leveraging their better-calibrated predictive distributions.

In-context learning, the ability of large language models to perform tasks using only examples provided in the prompt, has recently been adapted for time series forecasting. This paradigm enables zero-shot prediction, where past values serve as context for forecasting future values, making powerful forecasting tools accessible to non-experts and increasing the performance when training data are scarce. Most existing zero-shot forecasting approaches rely on transformer architectures, which, despite their success in language, often fall short of expectations in time series forecasting, where recurrent models like LSTMs frequently have the edge. Conversely, while LSTMs are well-suited for time series modeling due to their state-tracking capabilities, they lack strong in-context learning abilities. We introduce *TiRex* that closes this gap by leveraging xLSTM, an enhanced LSTM with competitive in-context learning skills. Unlike transformers, state-space models, or parallelizable RNNs such as RWKV, TiRex retains state tracking, a critical property for long-horizon forecasting. To further facilitate its state-tracking ability, we propose a training-time masking strategy called CPM. TiRex sets a new state of the art in zero-shot time series forecasting on the Hugging Face benchmarks *GiftEval* and *Chronos-ZS*, outperforming significantly larger models including *TabPFN-TS* (Prior Labs), *Chronos Bolt* (Amazon), *TimesFM* (Google), and *Moirai* (Salesforce) across both short- and long-term forecasts.

Linear RNNs with gating recently demonstrated competitive performance compared to Transformers in language modeling. Although their linear compute scaling in sequence length offers theoretical runtime advantages over Transformers, realizing these benefits in practice requires optimized custom kernels, as Transformers rely on the highly efficient Flash Attention kernels (Dao, 2024). Leveraging the chunkwise-parallel formulation of linear RNNs, Flash Linear Attention (FLA) (Yang & Zhang, 2024) shows that linear RNN kernels are faster than Flash Attention, by parallelizing over chunks of the input sequence. However, since the chunk size of FLA is limited, many intermediate states must be materialized in GPU memory. This leads to low arithmetic intensity and causes high memory consumption and IO cost, especially for long-context pre-training. In this work, we present Tiled Flash Linear Attention (TFLA), a novel kernel algorithm for linear RNNs, that enables arbitrary large chunk sizes and high arithmetic intensity by introducing an additional level of sequence parallelization within each chunk. First, we apply TFLA to the xLSTM with matrix memory, the mLSTM (Beck et al., 2024). Second, we propose an mLSTM variant with sigmoid input gate and reduced computation for even faster kernel runtimes at equal language modeling performance. In our speed benchmarks, we show that our new mLSTM kernels based on TFLA outperform highly optimized Flash Attention, Linear Attention and Mamba kernels, setting a new state of the art for efficient long-context sequence modeling primitives. Our code is available at: https://github.com/NX-AI/mlstm_kernels

Foundation models (FMs) are pre-trained on large-scale datasets and then fine-tuned for a specific downstream task. The most common fine-tuning method is to update pretrained weights via low-rank adaptation (LoRA). Existing initialization strategies for LoRA often rely on singular value decompositions (SVD) of gradients or weight matrices. However, they do not provably maximize the expected gradient signal, which is critical for fast adaptation. To this end, we introduce **E**xplained **V**ariance **A**daptation (EVA), an initialization scheme that uses the directions capturing the most activation variance, provably maximizing the expected gradient signal and accelerating fine-tuning. EVA performs incremental SVD on minibatches of activation vectors and selects the right-singular vectors for initialization once they converged. Further, by selecting the directions that capture the most activation-variance for a given rank budget, EVA accommodates adaptive ranks that reduce the number of trainable parameters. We apply EVA to a variety of fine-tuning tasks as language generation and understanding, image classification, and reinforcement learning. EVA exhibits faster convergence than competitors and achieves the highest average score across a multitude of tasks per domain while reducing the number of trainable parameters through rank redistribution. In summary, EVA establishes a new Pareto frontier compared to existing LoRA initialization schemes in both accuracy and efficiency.

Modern recurrent architectures, such as xLSTM and Mamba, have recently challenged the Transformer in language modeling. However, their structure constrains their applicability to sequences only or requires processing multi-dimensional data structures, such as images or molecular graphs, in a pre-defined sequential order. In contrast, Multi-Dimensional RNNs (MDRNNs) are well suited for data with a higher level structure, like 2D grids, trees, and directed acyclic graphs (DAGs). In this work, we extend the notion of multi-dimensionality to linear RNNs. We introduce parallelizable Linear Source Transition Mark networks (pLSTMs) using Source, Transition, and Mark gates that act on the linegraph of a general DAG. This enables parallelization in analogy to parallel associative scans and the chunkwise-recurrent form of sequential linear RNNs, but for DAGs. For regular grids (1D and 2D), like images, this scheme can be efficiently implemented using einsum operations, concatenations, and padding in logarithmic time. pLSTMs tackle the vanishing/exploding activation/gradient problem for long distances in DAGs via two distinct modes: a directed propagation mode (P-mode) and a diffusive distribution mode (D-mode). To showcase the long-range capabilities of pLSTM, we introduce arrow-pointing extrapolation as a synthetic computer vision task that contains long-distance directional information. We demonstrate that pLSTMs generalize well to larger image sizes, whereas Transformers struggle to extrapolate. On established molecular graph and computer vision benchmarks, pLSTMs also show strong performance. The complete code is available at https://github.com/ml-jku/plstm_experiments.

Diffusion bridges are a promising class of deep-learning methods for sampling from unnormalized distributions. Recent works show that the Log Variance (LV) loss consistently outperforms the reverse Kullback-Leibler (rKL) loss when using the reparametrization trick to compute rKL-gradients. While the on-policy LV loss yields identical gradients to the rKL loss when combined with the log-derivative trick for diffusion samplers with non-learnable forward processes, this equivalence does not hold for diffusion bridges or when diffusion coefficients are learned. Based on this insight we argue that for diffusion bridges the LV loss does not represent an optimization objective that can be motivated like the rKL loss via the data processing inequality. Our analysis shows that employing the rKL loss with the log-derivative trick (rKL-LD) does not only avoid these conceptual problems but also consistently outperforms the LV loss. Experimental results with different types of diffusion bridges on challenging benchmarks show that samplers trained with the rKL-LD loss achieve better performance. From a practical perspective we find that rKL-LD requires significantly less hyperparameter optimization and yields more stable training behavior.

Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, there is no universal agreement on how to best quantify predictive uncertainty. In this work, we revisit core concepts to propose a framework for information-theoretic measures of predictive uncertainty. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We extensively evaluate these measures across a broad set of tasks, identifying conditions under which certain measures excel. Our findings show the importance of aligning the choice of uncertainty measure with the predicting model on in-distribution (ID) data, the limitations of epistemic uncertainty measures for out-of-distribution (OOD) data, and that the disentanglement between measures varies substantially between ID and OOD data. Together, these insights provide a more comprehensive understanding of predictive uncertainty measures, revealing their implicit assumptions and relationships.

Masked Image Modeling (MIM) methods, like Masked Autoencoders (MAE), efficiently learn a rich representation of the input. However, for adapting to downstream tasks, they require a sufficient amount of labeled data since their rich features code not only objects but also less relevant image background. In contrast, Instance Discrimination (ID) methods focus on objects. In this work, we study how to combine the efficiency and scalability of MIM with the ability of ID to perform downstream classification in the absence of large amounts of labeled data. To this end, we introduce Masked Autoencoder Contrastive Tuning (MAE-CT), a sequential approach that utilizes the implicit clustering of the Nearest Neighbor Contrastive Learning (NNCLR) objective to induce abstraction in the topmost layers of a pre-trained MAE. MAE-CT tunes the rich features such that they form semantic clusters of objects without using any labels. Notably, MAE-CT does not rely on hand-crafted augmentations and frequently achieves its best performances while using only minimal augmentations (crop & flip). Further, MAE-CT is compute efficient as it requires at most 10% overhead compared to MAE re-training. Applied to large and huge Vision Transformer (ViT) models, MAE-CT excels over previous self-supervised methods trained on ImageNet in linear probing, k-NN and low-shot classification accuracy as well as in unsupervised clustering accuracy. With ViT-H/16 MAE-CT achieves a new state-of-the-art in linear probing of 82.2%. Project page: github.com/ml-jku/MAE-CT.

Estimating the ratio of two probability densities from finitely many samples, is a central task in machine learning and statistics. In this work, we show that a large class of kernel methods for density ratio estimation suffers from error saturation, which prevents algorithms from achieving fast error convergence rates on highly regular learning problems. To resolve saturation, we introduce iterated regularization in density ratio estimation to achieve fast error rates. Our methods outperform its non-iteratively regularized versions on benchmarks for density ratio estimation as well as on large-scale evaluations for importance-weighted ensembling of deep unsupervised domain adaptation models.

Learning to sample from intractable distributions over discrete sets without relying on corresponding training data is a central problem in a wide range of fields, including Combinatorial Optimization. Currently, popular deep learning-based approaches rely primarily on generative models that yield exact sample likelihoods. This work introduces a method that lifts this restriction and opens the possibility to employ highly expressive latent variable models like diffusion models. Our approach is conceptually based on a loss that upper bounds the reverse Kullback-Leibler divergence and evades the requirement of exact sample likelihoods. We experimentally validate our approach in data-free Combinatorial Optimization and demonstrate that our method achieves a new state-of-the-art on a wide range of benchmark problems.

In the 1990s, the constant error carousel and gating were introduced as the central ideas of the Long Short-Term Memory (LSTM). Since then, LSTMs have stood the test of time and contributed to numerous deep learning success stories, in particular they constituted the first Large Language Models (LLMs). However, the advent of the Transformer technology with parallelizable self-attention at its core marked the dawn of a new era, outpacing LSTMs at scale. We now raise a simple question: How far do we get in language modeling when scaling LSTMs to billions of parameters, leveraging the latest techniques from modern LLMs, but mitigating known limitations of LSTMs? Firstly, we introduce exponential gating with appropriate normalization and stabilization techniques. Secondly, we modify the LSTM memory structure, obtaining: (i) sLSTM with a scalar memory, a scalar update, and new memory mixing, (ii) mLSTM that is fully parallelizable with a matrix memory and a covariance update rule. Integrating these LSTM extensions into residual block backbones yields xLSTM blocks that are then residually stacked into xLSTM architectures. Exponential gating and modified memory structures boost xLSTM capabilities to perform favorably when compared to state-of-the-art Transformers and State Space Models, both in performance and scaling.

Out-of-distribution (OOD) detection is critical when deploying machine learning models in the real world. Outlier exposure methods, which incorporate auxiliary outlier data in the training process, can drastically improve OOD detection performance compared to approaches without advanced training strategies. We introduce Hopfield Boosting, a boosting approach, which leverages modern Hopfield energy to sharpen the decision boundary between the in-distribution and OOD data. Hopfield Boosting encourages the model to focus on hard-to-distinguish auxiliary outlier examples that lie close to the decision boundary between in-distribution and auxiliary outlier data. Our method achieves a new state-of-the-art in OOD detection with outlier exposure, improving the FPR95 from 2.28 to 0.92 on CIFAR-10, from 11.76 to 7.94 on CIFAR-100, and from 50.74 to 36.60 on ImageNet-1K.

The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric boundaries. Triangularized geometric boundaries are well understood and ubiquitous in engineering applications. However, it is notoriously difficult to integrate them into machine learning approaches due to their heterogeneity with respect to size and orientation. In this work, we introduce an effective theory to model particle-boundary interactions, which leads to our new Boundary Graph Neural Networks (BGNNs) that dynamically modify graph structures to obey boundary conditions. The new BGNNs are tested on complex 3D granular flow processes of hoppers, rotating drums and mixers, which are all standard components of modern industrial machinery but still have complicated geometry. BGNNs are evaluated in terms of computational efficiency as well as prediction accuracy of particle flows and mixing entropies. BGNNs are able to accurately reproduce 3D granular flows within simulation uncertainties over hundreds of thousands of simulation timesteps. Most notably, in our experiments, particles stay within the geometric objects without using handcrafted conditions or restrictions.

Activity and property prediction models are the central workhorses in drug discovery and materials sciences, but currently, they have to be trained or fine-tuned for new tasks. Without training or fine-tuning, scientific language models could be used for such low-data tasks through their announced zero- and few-shot capabilities. However, their predictive quality at activity prediction is lacking. In this work, we envision a novel type of activity prediction model that is able to adapt to new prediction tasks at inference time, via understanding textual information describing the task. To this end, we propose a new architecture with separate modules for chemical and natural language inputs, and a contrastive pretraining objective on data from large biochemical databases. In extensive experiments, we show that our method CLAMP yields improved predictive performance on few-shot learning benchmarks and zero-shot problems in drug discovery. We attribute the advances of our method to the modularized architecture and to our pre-training objective.

To quantify uncertainty, conformal prediction methods are gaining continuously more interest and have already been successfully applied to various domains. However, they are difficult to apply to time series as the autocorrelative structure of time series violates basic assumptions required by conformal prediction. We propose HopCPT, a novel conformal prediction approach for time series that not only copes with temporal structures but leverages them. We show that our approach is theoretically well justified for time series where temporal dependencies are present. In experiments, we demonstrate that our new approach outperforms state-of-the-art conformal prediction methods on multiple real-world time series datasets from four different domains.

Reinforcement learning agents deployed in the real world often have to cope with partially observable environments. Therefore, most agents employ memory mechanisms to approximate the state of the environment. Recently, there have been impressive success stories in mastering partially observable environments, mostly in the realm of computer games like Dota 2, StarCraft II, or MineCraft. However, existing methods lack interpretability in the sense that it is not comprehensible for humans what the agent stores in its memory. In this regard, we propose a novel memory mechanism that represents past events in human language. Our method uses CLIP to associate visual inputs with language tokens. Then we feed these tokens to a pretrained language model that serves the agent as memory and provides it with a coherent and human-readable representation of the past. We train our memory mechanism on a set of partially observable environments and find that it excels on tasks that require a memory component, while mostly attaining performance on-par with strong baselines on tasks that do not. On a challenging continuous recognition task, where memorizing the past is crucial, our memory mechanism converges two orders of magnitude faster than prior methods. Since our memory mechanism is human-readable, we can peek at an agent's memory and check whether crucial pieces of information have been stored. This significantly enhances troubleshooting and paves the way toward more interpretable agents.

Several recent unsupervised learning methods use probabilistic approaches to solve combinatorial optimization (CO) problems based on the assumption of statistically independent solution variables. We demonstrate that this assumption imposes performance limitations in particular on difficult problem instances. Our results corroborate that an autoregressive approach which captures statistical dependencies among solution variables yields superior performance on many popular CO problems. We introduce Subgraph Tokenization in which the configuration of a set of solution variables is represented by a single token. This tokenization technique alleviates the drawback of the long sequential sampling procedure which is inherent to autoregressive methods without sacrificing expressivity. Importantly, we theoretically motivate an annealed entropy regularization and show empirically that it is essential for efficient and stable learning.

Reinforcement Learning (RL) has been successful in various domains like robotics, game playing, and simulation. While RL agents have shown impressive capabilities in their specific tasks, they insufficiently adapt to new tasks. In supervised learning, this adaptation problem is addressed by large-scale pre-training followed by fine-tuning to new down-stream tasks. Recently, pre-training on multiple tasks has been gaining traction in RL. However, fine-tuning a pre-trained model often suffers from catastrophic forgetting. That is, the performance on the pre-training tasks deteriorates when fine-tuning on new tasks. To investigate the catastrophic forgetting phenomenon, we first jointly pre-train a model on datasets from two benchmark suites, namely Meta-World and DMControl. Then, we evaluate and compare a variety of fine-tuning methods prevalent in natural language processing, both in terms of performance on new tasks, and how well performance on pre-training tasks is retained. Our study shows that with most fine-tuning approaches, the performance on pre-training tasks deteriorates significantly. Therefore, we propose a novel method, Learning-to-Modulate (L2M), that avoids the degradation of learned skills by modulating the information flow of the frozen pre-trained model via a learnable modulation pool. Our method achieves state-of-the-art performance on the Continual-World benchmark, while retaining performance on the pre-training tasks. Finally, to aid future research in this area, we release a dataset encompassing 50 Meta-World and 16 DMControl tasks.

Quantifying uncertainty is important for actionable predictions in real-world applications. A crucial part of predictive uncertainty quantification is the estimation of epistemic uncertainty, which is defined as an integral of the product between a divergence function and the posterior. Current methods such as Deep Ensembles or MC dropout underperform at estimating the epistemic uncertainty, since they primarily consider the posterior when sampling models. We suggest Quantification of Uncertainty with Adversarial Models (QUAM) to better estimate the epistemic uncertainty. QUAM identifies regions where the whole product under the integral is large, not just the posterior. Consequently, QUAM has lower approximation error of the epistemic uncertainty compared to previous methods. Models for which the product is large correspond to adversarial models (not adversarial examples!). Adversarial models have both a high posterior as well as a high divergence between their predictions and that of a reference model. Our experiments show that QUAM excels in capturing epistemic uncertainty for deep learning models and outperforms previous methods on challenging tasks in the vision domain.

The synthesis of high-resolution remote sensing images based on text descriptions has great potential in many practical application scenarios. Although deep neural networks have achieved great success in many important remote sensing tasks, generating realistic remote sensing images from text descriptions is still very difficult. To address this challenge, we propose a novel text-to-image modern Hopfield network (Txt2Img-MHN). The main idea of Txt2Img-MHN is to conduct hierarchical prototype learning on both text and image embeddings with modern Hopfield layers. Instead of directly learning concrete but highly diverse text-image joint feature representations for different semantics, Txt2Img-MHN aims to learn the most representative prototypes from text-image embeddings, achieving a coarse-to-fine learning strategy. These learned prototypes can then be utilized to represent more complex semantics in the text-to-image generation task. To better evaluate the realism and semantic consistency of the generated images, we further conduct zero-shot classification on real remote sensing data using the classification model trained on synthesized images. Despite its simplicity, we find that the overall accuracy in the zero-shot classification may serve as a good metric to evaluate the ability to generate an image from text. Extensive experiments on the benchmark remote sensing text-image dataset demonstrate that the proposed Txt2Img-MHN can generate more realistic remote sensing images than existing methods. Code and pre-trained models are available online (https://github.com/YonghaoXu/Txt2Img-MHN).

In a partially observable Markov decision process (POMDP), an agent typically uses a representation of the past to approximate the underlying MDP. We propose to utilize a frozen Pretrained Language Transformer (PLT) for history representation and compression to improve sample efficiency. To avoid training of the Transformer, we introduce FrozenHopfield, which automatically associates observations with pretrained token embeddings. To form these associations, a modern Hopfield network stores these token embeddings, which are retrieved by queries that are obtained by a random but fixed projection of observations. Our new method, HELM, enables actor-critic network architectures that contain a pretrained language Transformer for history representation as a memory module. Since a representation of the past need not be learned, HELM is much more sample efficient than competitors. On Minigrid and Procgen environments HELM achieves new state-of-the-art results. Our code is available at https://github.com/ml-jku/helm.

Reinforcement learning algorithms require many samples when solving complex hierarchical tasks with sparse and delayed rewards. For such complex tasks, the recently proposed RUDDER uses reward redistribution to leverage steps in the Q-function that are associated with accomplishing sub-tasks. However, often only few episodes with high rewards are available as demonstrations since current exploration strategies cannot discover them in reasonable time. In this work, we introduce Align-RUDDER, which utilizes a profile model for reward redistribution that is obtained from multiple sequence alignment of demonstrations. Consequently, Align-RUDDER employs reward redistribution effectively and, thereby, drastically improves learning on few demonstrations. Align-RUDDER outperforms competitors on complex artificial tasks with delayed rewards and few demonstrations. On the Minecraft ObtainDiamond task, Align-RUDDER is able to mine a diamond, though not frequently. Code is available at github.com/ml-jku/align-rudder.

CLIP yielded impressive results on zero-shot transfer learning tasks and is considered as a foundation model like BERT or GPT3. CLIP vision models that have a rich representation are pre-trained using the InfoNCE objective and natural language supervision before they are fine-tuned on particular tasks. Though CLIP excels at zero-shot transfer learning, it suffers from an explaining away problem, that is, it focuses on one or few features, while neglecting other relevant features. This problem is caused by insufficiently extracting the covariance structure in the original multi-modal data. We suggest to use modern Hopfield networks to tackle the problem of explaining away. Their retrieved embeddings have an enriched covariance structure derived from co-occurrences of features in the stored embeddings. However, modern Hopfield networks increase the saturation effect of the InfoNCE objective which hampers learning. We propose to use the InfoLOOB objective to mitigate this saturation effect. We introduce the novel "Contrastive Leave One Out Boost" (CLOOB), which uses modern Hopfield networks for covariance enrichment together with the InfoLOOB objective. In experiments we compare CLOOB to CLIP after pre-training on the Conceptual Captions and the YFCC dataset with respect to their zero-shot transfer learning performance on other datasets. CLOOB consistently outperforms CLIP at zero-shot transfer learning across all considered architectures and datasets.

Weather forecasting is both a high impact application as well as a complex Big Data modelling challenge. Recent advances in machine learning have already demonstrated the power of non-physical modelling approaches for the prediction of rainfall. The Weather4cast competitions now provide a unique multi-channel benchmark for the prediction of up to 8 hours of weather with high temporal and spatial resolutions (15 min, 4 km) for a diverse set of large regions across Earth. This diversity, for the first time, also permits a meaningful spatial transfer learning challenge in weather forecasting.Weather4cast introduces multi-channel weather ‘movies’ that encode temperature, rainfall, cloud properties, and turbulence as derived from the meteorological satellites by the EUMETSAT NWC SAF. Inspired by the Traffic4cast competitions at the NeurIPS conferences in 2019 and 2020, weather forecasting is thus presented as a video frame prediction task. As then, the U-Net based models developed for photographic image analysis intriguingly did well on these artificial videos. In contrast, however, the winning submission did not employ a U-Net but a recurrent convolutional network with residual units.Weather4cast introduces the first spatial transfer learning challenge in weather forecasting: only one-hour short snippets from spatial regions never seen before were provided as input to models. We can thus now present first insights from submissions to this spatial transfer learning challenge. Notably, models with better core prediction performance also generalized better. Moreover, the two top-ranked models – one RCN based, one U-Net based – were further ahead of the remaining top-ranked submissions for spatial transfer learning (+6%) than in the core prediction challenge (+1%).While submissions tested varying strategies for input data selection and training, there remains a wide range of additional complementary approaches to be explored in future analyses. The competition and its leaderboards remain available and open for new submissions on the weather4cast.ai website.

High-resolution remote sensing technology for Earth Observation (EO) has radically changed how we monitor the state of our planet around the clock. An effective interpretation of the resulting complex large-scale time series adopts the best machine learning techniques from signal processing, computer vision, pattern recognition, and artificial intelligence. The First Workshop on Complex Data Challenges in Earth Observation was open to both method development and advanced applications in a wide range of related topics, including image and signal processing, gap-filling, data fusion, feature extraction, prediction of spatio-temporal features, and the detection of rules underlying the observed state transitions and causal relationships. The full agenda, featuring keynotes and a selection of high quality contributed talks is available online at www.iarai.ac.at/cdceo21

The success of Convolutional Neural Networks (CNNs) in computer vision is mainly driven by their strong inductive bias, which is strong enough to allow CNNs to solve vision-related tasks with random weights, meaning without learning. Similarly, Long Short-Term Memory (LSTM) has a strong inductive bias towards storing information over time. However, many real-world systems are governed by conservation laws, which lead to the redistribution of particular quantities {—} e.g.in physical and economical systems. Our novel Mass-Conserving LSTM (MC-LSTM) adheres to these conservation laws by extending the inductive bias of LSTM to model the redistribution of those stored quantities. MC-LSTMs set a new state-of-the-art for neural arithmetic units at learning arithmetic operations, such as addition tasks,which have a strong conservation law, as the sum is constant over time. Further, MC-LSTM is applied to traffic forecasting, modeling a pendulum, and a large benchmark dataset in hydrology, where it sets a new state-of-the-art for predicting peak flows. In the hydrology example, we show that MC-LSTM states correlate with real world processes and are therefore interpretable.

A central mechanism in machine learning is to identify, store, and recognize patterns. How to learn, access, and retrieve such patterns is crucial in Hopfield networks and the more recent transformer architectures. We show that the attention mechanism of transformer architectures is actually the update rule of modern Hopfield networks that can store exponentially many patterns. We exploit this high storage capacity of modern Hopfield networks to solve a challenging multiple instance learning (MIL) problem in computational biology: immune repertoire classification. In immune repertoire classification, a vast number of immune receptors are used to predict the immune status of an individual. This constitutes a MIL problem with an unprecedentedly massive number of instances, two orders of magnitude larger than currently considered problems, and with an extremely low witness rate. Accurate and interpretable machine learning methods solving this problem could pave the way towards new vaccines and therapies, which is currently a very relevant research topic intensified by the COVID-19 crisis. In this work, we present our novel method DeepRC that integrates transformer-like attention, or equivalently modern Hopfield networks, into deep learning architectures for massive MIL such as immune repertoire classification. We demonstrate that DeepRC outperforms all other methods with respect to predictive performance on large-scale experiments including simulated and real-world virus infection data and enables the extraction of sequence motifs that are connected to a given disease class. Source code and datasets: https://github.com/ml-jku/DeepRC

We propose RUDDER, a novel reinforcement learning approach for delayed rewards in finite Markov decision processes (MDPs). In MDPs the Q-values are equal to the expected immediate reward plus the expected future rewards. The latter are related to bias problems in temporal difference (TD) learning and to high variance problems in Monte Carlo (MC) learning. Both problems are even more severe when rewards are delayed. RUDDER aims at making the expected future rewards zero, which simplifies Q-value estimation to computing the mean of the immediate reward. We propose the following two new concepts to push the expected future rewards toward zero. (i) Reward redistribution that leads to return-equivalent decision processes with the same optimal policies and, when optimal, zero expected future rewards. (ii) Return decomposition via contribution analysis which transforms the reinforcement learning task into a regression task at which deep learning excels. On artificial tasks with delayed rewards, RUDDER is significantly faster than MC and exponentially faster than Monte Carlo Tree Search (MCTS), TD(λ), and reward shaping approaches. At Atari games, RUDDER on top of a Proximal Policy Optimization (PPO) baseline improves the scores, which is most prominent at games with delayed rewards.

GANs excel at learning high dimensional distributions, but they can update generator parameters in directions that do not correspond to the steepest descent direction of the objective. Prominent examples of problematic update directions include those used in both Goodfellow’s original GAN and the WGAN-GP. To formally describe an optimal update direction, we introduce a theoretical framework which allows the derivation of requirements on both the divergence and corresponding method for determining an update direction, with these requirements guaranteeing unbiased mini-batch updates in the direction of steepest descent. We propose a novel divergence which approximates the Wasserstein distance while regularizing the critic’s first order information. Together with an accompanying update direction, this divergence fulfills the requirements for unbiased steepest descent updates. We verify our method, the First Order GAN, with image generation on CelebA, LSUN and CIFAR-10 and set a new state of the art on the One Billion Word language generation task.

Motivation: While drug combination therapies are a well-established concept in cancer treatment, identifying novel synergistic combinations is challenging due to the size of combinatorial space. However, computational approaches have emerged as a time- and cost-efficient way to prioritize combinations to test, based on recently available large-scale combination screening data. Recently, Deep Learning has had an impact in many research areas by achieving new state-of-the-art model performance. However, Deep Learning has not yet been applied to drug synergy prediction, which is the approach we present here, termed DeepSynergy. DeepSynergy uses chemical and genomic information as input information, a normalization strategy to account for input data heterogeneity, and conical layers to model drug synergies. Results: DeepSynergy was compared to other machine learning methods such as Gradient Boosting Machines, Random Forests, Support Vector Machines and Elastic Nets on the largest publicly available synergy dataset with respect to mean squared error. DeepSynergy significantly outperformed the other methods with an improvement of 7.2% over the second best method at the prediction of novel drug combinations within the space of explored drugs and cell lines. At this task, the mean Pearson correlation coefficient between the measured and the predicted values of DeepSynergy was 0.73. Applying DeepSynergy for classification of these novel drug combinations resulted in a high predictive performance of an AUC of 0.90. Furthermore, we found that all compared methods exhibit low predictive performance when extrapolating to unexplored drugs or cell lines, which we suggest is due to limitations in the size and diversity of the dataset. We envision that DeepSynergy could be a valuable tool for selecting novel synergistic drug combinations. Availability and implementation: DeepSynergy is available via www.bioinf.jku.at/software/DeepSynergy. Contact: [email protected]. Supplementary information: Supplementary data are available at Bioinformatics online.

Generative Adversarial Networks (GANs) excel at creating realistic images with complex models for which maximum likelihood is infeasible. However, the convergence of GAN training has still not been proved. We propose a two time-scale update rule (TTUR) for training GANs with stochastic gradient descent on arbitrary GAN loss functions. TTUR has an individual learning rate for both the discriminator and the generator. Using the theory of stochastic approximation, we prove that the TTUR converges under mild assumptions to a stationary local Nash equilibrium. The convergence carries over to the popular Adam optimization, for which we prove that it follows the dynamics of a heavy ball with friction and thus prefers flat minima in the objective landscape. For the evaluation of the performance of GANs at image generation, we introduce the `Fréchet Inception Distance'' (FID) which captures the similarity of generated images to real ones better than the Inception Score. In experiments, TTUR improves learning for DCGANs and Improved Wasserstein GANs (WGAN-GP) outperforming conventional GAN training on CelebA, CIFAR-10, SVHN, LSUN Bedrooms, and the One Billion Word Benchmark.

Deep Learning has revolutionized vision via convolutional neural networks (CNNs) and natural language processing via recurrent neural networks (RNNs). However, success stories of Deep Learning with standard feed-forward neural networks (FNNs) are rare. FNNs that perform well are typically shallow and, therefore cannot exploit many levels of abstract representations. We introduce self-normalizing neural networks (SNNs) to enable high-level abstract representations. While batch normalization requires explicit normalization, neuron activations of SNNs automatically converge towards zero mean and unit variance. The activation function of SNNs are "scaled exponential linear units" (SELUs), which induce self-normalizing properties. Using the Banach fixed-point theorem, we prove that activations close to zero mean and unit variance that are propagated through many network layers will converge towards zero mean and unit variance -- even under the presence of noise and perturbations. This convergence property of SNNs allows to (1) train deep networks with many layers, (2) employ strong regularization, and (3) to make learning highly robust. Furthermore, for activations not close to unit variance, we prove an upper and lower bound on the variance, thus, vanishing and exploding gradients are impossible. We compared SNNs on (a) 121 tasks from the UCI machine learning repository, on (b) drug discovery benchmarks, and on (c) astronomy tasks with standard FNNs and other machine learning methods such as random forests and support vector machines. For FNNs we considered (i) ReLU networks without normalization, (ii) batch normalization, (iii) layer normalization, (iv) weight normalization, (v) highway networks, (vi) residual networks. SNNs significantly outperformed all competing FNN methods at 121 UCI tasks, outperformed all competing methods at the Tox21 dataset, and set a new record at an astronomy data set. The winning SNN architectures are often very deep.

MOTIVATION: Biclustering has become a major tool for analyzing large datasets given as matrix of samples times features and has been successfully applied in life sciences and e-commerce for drug design and recommender systems, respectively. actor nalysis for cluster cquisition (FABIA), one of the most successful biclustering methods, is a generative model that represents each bicluster by two sparse membership vectors: one for the samples and one for the features. However, FABIA is restricted to about 20 code units because of the high computational complexity of computing the posterior. Furthermore, code units are sometimes insufficiently decorrelated and sample membership is difficult to determine. We propose to use the recently introduced unsupervised Deep Learning approach Rectified Factor Networks (RFNs) to overcome the drawbacks of existing biclustering methods. RFNs efficiently construct very sparse, non-linear, high-dimensional representations of the input via their posterior means. RFN learning is a generalized alternating minimization algorithm based on the posterior regularization method which enforces non-negative and normalized posterior means. Each code unit represents a bicluster, where samples for which the code unit is active belong to the bicluster and features that have activating weights to the code unit belong to the bicluster. RESULTS: On 400 benchmark datasets and on three gene expression datasets with known clusters, RFN outperformed 13 other biclustering methods including FABIA. On data of the 1000 Genomes Project, RFN could identify DNA segments which indicate, that interbreeding with other hominins starting already before ancestors of modern humans left Africa. AVAILABILITY AND IMPLEMENTATION: https://github.com/bioinf-jku/librfn. CONTACT: [email protected] or [email protected].

We propose rectified factor networks (RFNs) to efficiently construct very sparse, non-linear, high-dimensional representations of the input. RFN models identify rare and small events, have a low interference between code units, have a small reconstruction error, and explain the data covariance structure. RFN learning is a generalized alternating minimization algorithm derived from the posterior regularization method which enforces non-negative and normalized posterior means. We proof convergence and correctness of the RFN learning algorithm.On benchmarks, RFNs are compared to other unsupervised methods like autoencoders, RBMs, factor analysis, ICA, and PCA. In contrast to previous sparse coding methods, RFNs yield sparser codes, capture the data's covariance structure more precisely, and have a significantly smaller reconstruction error. We test RFNs as pretraining technique of deep networks on different vision datasets, where RFNs were superior to RBMs and autoencoders. On gene expression data from two pharmaceutical drug discovery studies, RFNs detected small and rare gene modules that revealed highly relevant new biological insights which were so far missed by other unsupervised methods.RFN package for GPU/CPU is available at http://www.bioinf.jku.at/software/rfn.

UNLABELLED: Although the R platform and the add-on packages of the Bioconductor project are widely used in bioinformatics, the standard task of multiple sequence alignment has been neglected so far. The msa package, for the first time, provides a unified R interface to the popular multiple sequence alignment algorithms ClustalW, ClustalOmega and MUSCLE. The package requires no additional software and runs on all major platforms. Moreover, the msa package provides an R interface to the powerful package shade which allows for flexible and customizable plotting of multiple sequence alignments. AVAILABILITY AND IMPLEMENTATION: msa is available via the Bioconductor project: http://bioconductor.org/packages/release/bioc/html/msa.html. Further information and the R code of the example presented in this paper are available at http://www.bioinf.jku.at/software/msa/.

UNLABELLED: We have developed Rchempp, a web service that identifies structurally similar compounds (structural analogs) in large-scale molecule databases. The service allows compounds to be queried in the widely used ChEMBL, DrugBank and the Connectivity Map databases. Rchemcpp utilizes the best performing similarity functions, i.e. molecule kernels, as measures for structural similarity. Molecule kernels have proven superior performance over other similarity measures and are currently excelling at machine learning challenges. To considerably reduce computational time, and thereby make it feasible as a web service, a novel efficient prefiltering strategy has been developed, which maintains the sensitivity of the method. By exploiting information contained in public databases, the web service facilitates many applications crucial for the drug development process, such as prioritizing compounds after screening or reducing adverse side effects during late phases. Rchemcpp was used in the DeepTox pipeline that has won the Tox21 Data Challenge and is frequently used by researchers in pharmaceutical companies. AVAILABILITY AND IMPLEMENTATION: The web service and the R package are freely available via http://shiny.bioinf.jku.at/Analoging/ and via Bioconductor. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Abstract Summary: KeBABS provides a powerful, flexible and easy to use framework for kernel-based analysis of biological sequences in R. It includes efficient implementations of the most important sequence kernels, also including variants that allow for taking sequence annotations and positional information into account. KeBABS seamlessly integrates three common support vector machine (SVM) implementations with a unified interface. It allows for hyperparameter selection by cross validation, nested cross validation and also features grouped cross validation. The biological interpretation of SVM models is supported by (1) the computation of weights of sequence patterns and (2) prediction profiles that highlight the contributions of individual sequence positions or sections. Availability and implementation: The R package kebabs is available via the Bioconductor project: http://bioconductor.org/packages/release/bioc/html/kebabs.html. Further information and the R code of the example in this paper are available at http://www.bioinf.jku.at/software/kebabs/. Contact: [email protected] or [email protected]

BACKGROUND: Cluster analysis is widely used to discover patterns in multi-dimensional data. Clustered heatmaps are the standard technique for visualizing one-way and two-way clustering results. In clustered heatmaps, rows and/or columns are reordered, resulting in a representation that shows the clusters as contiguous blocks. However, for biclustering results, where clusters can overlap, it is not possible to reorder the matrix in this way without duplicating rows and/or columns. RESULTS: We present Furby, an interactive visualization technique for analyzing biclustering results. Our contribution is twofold. First, the technique provides an overview of a biclustering result, showing the actual data that forms the individual clusters together with the information which rows and columns they share. Second, for fuzzy clustering results, the proposed technique additionally enables analysts to interactively set the thresholds that transform the fuzzy (soft) clustering into hard clusters that can then be investigated using heatmaps or bar charts. Changes in the membership value thresholds are immediately reflected in the visualization. We demonstrate the value of Furby by loading biclustering results applied to a multi-tissue dataset into the visualization. CONCLUSIONS: The proposed tool allows analysts to assess the overall quality of a biclustering result. Based on this high-level overview, analysts can then interactively explore the individual biclusters in detail. This novel way of handling fuzzy clustering results also supports analysts in finding the optimal thresholds that lead to the best clusters.

SUMMARY: Affinity propagation (AP) clustering has recently gained increasing popularity in bioinformatics. AP clustering has the advantage that it allows for determining typical cluster members, the so-called exemplars. We provide an R implementation of this promising new clustering technique to account for the ubiquity of R in bioinformatics. This article introduces the package and presents an application from structural biology. AVAILABILITY: The R package apcluster is available via CRAN-The Comprehensive R Archive Network: http://cran.r-project.org/web/packages/apcluster CONTACT: [email protected]; [email protected].

MOTIVATION: Biclustering of transcriptomic data groups genes and samples simultaneously. It is emerging as a standard tool for extracting knowledge from gene expression measurements. We propose a novel generative approach for biclustering called 'FABIA: Factor Analysis for Bicluster Acquisition'. FABIA is based on a multiplicative model, which accounts for linear dependencies between gene expression and conditions, and also captures heavy-tailed distributions as observed in real-world transcriptomic data. The generative framework allows to utilize well-founded model selection methods and to apply Bayesian techniques. RESULTS: On 100 simulated datasets with known true, artificially implanted biclusters, FABIA clearly outperformed all 11 competitors. On these datasets, FABIA was able to separate spurious biclusters from true biclusters by ranking biclusters according to their information content. FABIA was tested on three microarray datasets with known subclusters, where it was two times the best and once the second best method among the compared biclustering approaches. AVAILABILITY: FABIA is available as an R package on Bioconductor (http://www.bioconductor.org). All datasets, results and software are available at http://www.bioinf.jku.at/software/fabia/fabia.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We describe a fast sequential minimal optimization (SMO) procedure for solving the dual optimization problem of the recently proposed potential support vector machine (P-SVM). The new SMO consists of a sequence of iteration steps in which the Lagrangian is optimized with respect to either one (single SMO) or two (dual SMO) of the Lagrange multipliers while keeping the other variables fixed. An efficient selection procedure for Lagrange multipliers is given, and two heuristics for improving the SMO procedure are described: block optimization and annealing of the regularization parameter epsilon. A comparison of the variants shows that the dual SMO, including block optimization and annealing, performs efficiently in terms of computation time. In contrast to standard support vector machines (SVMs), the P-SVM is applicable to arbitrary dyadic data sets, but benchmarks are provided against libSVM's epsilon-SVR and C-SVC implementations for problems that are also solvable by standard SVM methods. For those problems, computation time of the P-SVM is comparable to or somewhat higher than the standard SVM. The number of support vectors found by the P-SVM is usually much smaller for the same generalization performance.

In this analytical study we compare the risk of the Monte Carlo (MC) and the least-squares TD (LSTD) estimator. We prove that for the case of acyclic Markov Reward Processes (MRPs) LSTD has minimal risk for any convex loss function in the class of unbiased estimators. When comparing the Monte Carlo estimator, which does not assume a Markov structure, and LSTD, we find that the Monte Carlo estimator is equivalent to LSTD if both estimators have the same amount of information. Theoretical results are supported by an empirical evaluation of the estimators.

MOTIVATION: As more genomes are sequenced, the demand for fast gene classification techniques is increasing. To analyze a newly sequenced genome, first the genes are identified and translated into amino acid sequences which are then classified into structural or functional classes. The best-performing protein classification methods are based on protein homology detection using sequence alignment methods. Alignment methods have recently been enhanced by discriminative methods like support vector machines (SVMs) as well as by position-specific scoring matrices (PSSM) as obtained from PSI-BLAST. However, alignment methods are time consuming if a new sequence must be compared to many known sequences-the same holds for SVMs. Even more time consuming is to construct a PSSM for the new sequence. The best-performing methods would take about 25 days on present-day computers to classify the sequences of a new genome (20,000 genes) as belonging to just one specific class--however, there are hundreds of classes. Another shortcoming of alignment algorithms is that they do not build a model of the positive class but measure the mutual distance between sequences or profiles. Only multiple alignments and hidden Markov models are popular classification methods which build a model of the positive class but they show low classification performance. The advantage of a model is that it can be analyzed for chemical properties common to the class members to obtain new insights into protein function and structure. We propose a fast model-based recurrent neural network for protein homology detection, the 'Long Short-Term Memory' (LSTM). LSTM automatically extracts indicative patterns for the positive class, but in contrast to profile methods it also extracts negative patterns and uses correlations between all detected patterns for classification. LSTM is capable to automatically extract useful local and global sequence statistics like hydrophobicity, polarity, volume, polarizability and combine them with a pattern. These properties make LSTM complementary to alignment-based approaches as it does not use predefined similarity measures like BLOSUM or PAM matrices. RESULTS: We have applied LSTM to a well known benchmark for remote protein homology detection, where a protein must be classified as belonging to a SCOP superfamily. LSTM reaches state-of-the-art classification performance but is considerably faster for classification than other approaches with comparable classification performance. LSTM is five orders of magnitude faster than methods which perform slightly better in classification and two orders of magnitude faster than the fastest SVM-based approaches (which, however, have lower classification performance than LSTM). Only PSI-BLAST and HMM-based methods show comparable time complexity as LSTM, but they cannot compete with LSTM in classification performance. To test the modeling capabilities of LSTM, we applied LSTM to PROSITE classes and interpreted the extracted patterns. In 8 out of 15 classes, LSTM automatically extracted the PROSITE motif. In the remaining 7 cases alternative motifs are generated which give better classification results on average than the PROSITE motifs. AVAILABILITY: The LSTM algorithm is available from http://www.bioinf.jku.at/software/LSTM_protein/.

MOTIVATION: DNA microarray technology typically generates many measurements of which only a relatively small subset is informative for the interpretation of the experiment. To avoid false positive results, it is therefore critical to select the informative genes from the large noisy data before the actual analysis. Most currently available filtering techniques are supervised and therefore suffer from a potential risk of overfitting. The unsupervised filtering techniques, on the other hand, are either not very efficient or too stringent as they may mix up signal with noise. We propose to use the multiple probes measuring the same target mRNA as repeated measures to quantify the signal-to-noise ratio of that specific probe set. A Bayesian factor analysis with specifically chosen prior settings, which models this probe level information, is providing an objective feature filtering technique, named informative/non-informative calls (I/NI calls). RESULTS: Based on 30 real-life data sets (including various human, rat, mice and Arabidopsis studies) and a spiked-in data set, it is shown that I/NI calls is highly effective, with exclusion rates ranging from 70% to 99%. Consequently, it offers a critical solution to the curse of high-dimensionality in the analysis of microarray data. AVAILABILITY: This filtering approach is publicly available as a function implemented in the R package FARMS (www.bioinf.jku.at/software/farms/farms.html).

The joint analysis of genetic and brain imaging data is the key to understand the genetic underpinnings of brain dysfunctions in several psychiatric diseases known to have a strong genetic component. The goal is to identify associations between genetic and functional or morphometric brain measurements. We here suggest a machine learning method to solve this task, which is based on the recently proposed Potential Support Vector Machine (P-SVM) for variable selection, a subsequent k-NN classification and an estimation of the effect of `correlations by chance'. We apply it to the detection of associations between candidate single nucleotide polymorphisms (SNPs) and volumetric MRI measurements in alcohol dependent patients and healthy controls.

MOTIVATION: We propose a new model-based technique for summarizing high-density oligonucleotide array data at probe level for Affymetrix GeneChips. The new summarization method is based on a factor analysis model for which a Bayesian maximum a posteriori method optimizes the model parameters under the assumption of Gaussian measurement noise. Thereafter, the RNA concentration is estimated from the model. In contrast to previous methods our new method called 'Factor Analysis for Robust Microarray Summarization (FARMS)' supplies both P-values indicating interesting information and signal intensity values. RESULTS: We compare FARMS on Affymetrix's spike-in and Gene Logic's dilution data to established algorithms like Affymetrix Microarray Suite (MAS) 5.0, Model Based Expression Index (MBEI), Robust Multi-array Average (RMA). Further, we compared FARMS with 43 other methods via the 'Affycomp II' competition. The experimental results show that FARMS with default parameters outperforms previous methods if both sensitivity and specificity are simultaneously considered by the area under the receiver operating curve (AUC). We measured two quantities through the AUC: correctly detected expression changes versus wrongly detected (fold change) and correctly detected significantly different expressed genes in two sets of arrays versus wrongly detected (P-value). Furthermore FARMS is computationally less expensive then RMA, MAS and MBEI. AVAILABILITY: The FARMS R package is available from http://www.bioinf.jku.at/software/farms/farms.html. SUPPLEMENTARY INFORMATION: http://www.bioinf.jku.at/publications/papers/farms/supplementary.ps

We describe a new technique for the analysis of dyadic data, where two sets of objects (row and column objects) are characterized by a matrix of numerical values that describe their mutual relationships. The new technique, called potential support vector machine (P-SVM), is a large-margin method for the construction of classifiers and regression functions for the column objects. Contrary to standard support vector machine approaches, the P-SVM minimizes a scale-invariant capacity measure and requires a new set of constraints. As a result, the P-SVM method leads to a usually sparse expansion of the classification and regression functions in terms of the row rather than the column objects and can handle data and kernel matrices that are neither positive definite nor square. We then describe two complementary regularization schemes. The first scheme improves generalization performance for classification and regression tasks; the second scheme leads to the selection of a small, informative set of row support objects and can be applied to feature selection. Benchmarks for classification, regression, and feature selection tasks are performed with toy data as well as with several real-world data sets. The results show that the new method is at least competitive with but often performs better than the benchmarked standard methods for standard vectorial as well as true dyadic data sets. In addition, a theoretical justification is provided for the new approach.

We introduce a novel "importance weight" method (IW) to speed up learning of "difficult" data sets including unbalanced data, highly non-linear data, or long-term dependencies in sequences. An importance weight is assigned to every training data point and controls its contribution to the total weight update. The importance weights are obtained by solving a quadratic optimization problem and determines the learning informativeness of a data point. For linear classifiers we show, that IW is equivalent to standard support vector learning. We apply IW to feedforward multi-layer perceptrons and to recurrent neural networks (LSTM). Benchmarks with QuickProp and standard gradient descent methods show that IW is usually much faster in terms of epochs as well as in terms of absolute CPU time, and that it provides equal or better prediction results. IW improved gradient descent results on "real world" protein datasets. In the "latching benchmark" for sequence prediction, IW was able to extract dependencies between sites which are 1,000,000 sequence elements apart - a new record.

We investigate the optimal kernel for sample-based model selection in unsupervised learning if maximum likelihood approaches are intractable. Given a set of training data and a set of data generated by the model, two kernel density estimators are constructed. A model is selected through gradient descent w.r.t. the model parameters on the integrated squared difference between the density estimators. Firstly we prove that convergence is optimal, i.e. that the cost function has only one global minimum w.r.t. the locations of the model samples, if and only if the kernel in the reparametrized cost function is a Coulomb kernel. As a consequence, Gaussian kernels commonly used for density estimators are suboptimal. Secondly we show that the absolute value of the difference between model and reference density converges at least with 1/t. Finally, we apply the new methods to distribution free ICA and to nonlinear ICA.

We introduce a family of classiflers based on a physical analogy to an electrostatic system of charged conductors. The family, called Coulomb classiflers, includes the two best-known support-vector machines (SVMs), the ”{SVM and the C{SVM. In the electrostat- ics analogy, a training example corresponds to a charged conductor at a given location in space, the classiflcation function corresponds to the electrostatic potential function, and the training objective function corresponds to the Coulomb energy. The electrostatic framework provides not only a novel interpretation of existing algo- rithms and their interrelationships, but it suggests a variety of new methods for SVMs including kernels that bridge the gap between polynomial and radial-basis functions, objective functions that do not require positive-deflnite kernels, regularization techniques that allow for the construction of an optimal classifler in Minkowski space. Based on the framework, we propose novel SVMs and per- form simulation studies to show that they are comparable or su- perior to standard SVMs. The experiments include classiflcation tasks on data which are represented in terms of their pairwise prox- imities, where a Coulomb Classifler outperformed standard SVMs.

We investigate the problem of learning a classiflcation task for datasets which are described by matrices. Rows and columns of these matrices correspond to objects, where row and column ob- jects may belong to difierent sets, and the entries in the matrix express the relationships between them. We interpret the matrix el- ements as being produced by an unknown kernel which operates on object pairs and we show that - under mild assumptions - these ker- nels correspond to dot products in some (unknown) feature space. Minimizing a bound for the generalization error of a linear classi- fler which has been obtained using covering numbers we derive an objective function for model selection according to the principle of structural risk minimization. The new objective function has the advantage that it allows the analysis of matrices which are not pos- itive deflnite, and not even symmetric or square. We then consider the case that row objects are interpreted as features. We suggest an additional constraint, which imposes sparseness on the row objects and show, that the method can then be used for feature selection. Finally, we apply this method to data obtained from DNA microar- rays, where \column" objects correspond to samples, \row" objects correspond to genes and matrix elements correspond to expression levels. Benchmarks are conducted using standard one-gene classifl- cation and support vector machines and K-nearest neighbors after standard feature selection. Our new method extracts a sparse set of genes and provides superior classiflcation results.

The goal of many unsupervised learning procedures is to bring two probability distributions into alignment. Generative models such as Gaussian mixtures and Boltzmann machines can be cast in this light, as can recoding models such as ICA and projection pursuit. We propose a novel sample-based error measure for these classes of models, which applies even in situations where maximum likelihood (ML) and probability density estimation-based formulations can(cid:173) not be applied, e.g., models that are nonlinear or have intractable posteriors. Furthermore, our sample-based error measure avoids the difficulties of approximating a density function. We prove that with an unconstrained model, (1) our approach converges on the correct solution as the number of samples goes to infinity, and (2) the expected solution of our approach in the generative framework is the ML solution. Finally, we evaluate our approach via simula(cid:173) tions of linear and nonlinear models on mixture of Gaussians and ICA problems. The experiments show the broad applicability and generality of our approach.

Low-complexity coding and decoding (LOCOCODE) is a novel approach to sensory coding and unsupervised learning. Unlike previous methods, it explicitly takes into account the information-theoretic complexity of the code generator. It computes lococodes that convey information about the input data and can be computed and decoded by low-complexity mappings. We implement LOCOCODE by training autoassociators with flat minimum search, a recent, general method for discovering low-complexity neural nets. It turns out that this approach can unmix an unknown number of independent data sources by extracting a minimal number of low-complexity features necessary for representing the data. Experiments show that unlike codes obtained with standard autoencoders, lococodes are based on feature detectors, never unstructured, usually sparse, and sometimes factorial or local (depending on statistical properties of the data). Although LOCOCODE is not explicitly designed to enforce sparse or factorial codes, it extracts optimal codes for difficult versions of the "bars" benchmark problem, whereas independent component analysis (ICA) and principal component analysis (PCA) do not. It produces familiar, biologically plausible feature detectors when applied to real-world images and codes with fewer bits per pixel than ICA and PCA. Unlike ICA, it does not need to know the number of independent sources. As a preprocessor for a vowel recognition benchmark problem, it sets the stage for excellent classification performance. Our results reveal an interesting, previously ignored connection between two important fields: regularizer research and ICA-related research. They may represent a first step toward unification of regularization and unsupervised learning.

Recurrent nets are in principle capable to store past inputs to produce the currently desired output. Because of this property recurrent nets are used in time series prediction and process control. Practical applications involve temporal dependencies spanning many time steps, e.g. between relevant inputs and desired outputs. In this case, however, gradient based learning methods take too much time. The extremely increased learning time arises because the error vanishes as it gets propagated back. In this article the de-caying error flow is theoretically analyzed. Then methods trying to overcome vanishing gradients are briefly discussed. Finally, experiments comparing conventional algorithms and alternative methods are presented. With advanced methods long time lag problems can be solved in reasonable time.

Learning to store information over extended time intervals by recurrent backpropagation takes a very long time, mostly because of insufficient, decaying error backflow. We briefly review Hochreiter's (1991) analysis of this problem, then address it by introducing a novel, efficient, gradient-based method called long short-term memory (LSTM). Truncating the gradient where this does not do harm, LSTM can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units. Multiplicative gate units learn to open and close access to the constant error flow. LSTM is local in space and time; its computational complexity per time step and weight is O(1). Our experiments with artificial data involve local, distributed, real-valued, and noisy pattern representations. In comparisons with real-time recurrent learning, back propagation through time, recurrent cascade correlation, Elman nets, and neural sequence chunking, LSTM leads to many more successful runs, and learns much faster. LSTM also solves complex, artificial long-time-lag tasks that have never been solved by previous recurrent network algorithms.

We present a new algorithm for finding low-complexity neural networks with high generalization capability. The algorithm searches for a "flat" minimum of the error function. A flat minimum is a large connected region in weight space where the error remains approximately constant. An MDL-based, Bayesian argument suggests that flat minima correspond to "simple" networks and low expected overfitting. The argument is based on a Gibbs algorithm variant and a novel way of splitting generalization error into underfitting and overfitting error. Unlike many previous approaches, ours does not require gaussian assumptions and does not depend on a "good" weight prior. Instead we have a prior over input-output functions, thus taking into account net architecture and training set. Although our algorithm requires the computation of second-order derivatives, it has backpropagation's order of complexity. Automatically, it effectively prunes units, weights, and input lines. Various experiments with feedforward and recurrent nets are described. In an application to stock market prediction, flat minimum search outperforms conventional backprop, weight decay, and "optimal brain surgeon/optimal brain damage".

We present a new algorithm for finding low complexity networks with high generalization capability. The algorithm searches for large connected regions of so-called ''fiat'' minima of the error func(cid:173) tion. In the weight-space environment of a "flat" minimum, the error remains approximately constant. Using an MDL-based ar(cid:173) gument, flat minima can be shown to correspond to low expected overfitting. Although our algorithm requires the computation of second order derivatives, it has backprop's order of complexity. Experiments with feedforward and recurrent nets are described. In an application to stock market prediction, the method outperforms conventional backprop, weight decay, and "optimal brain surgeon" .