The ability to design molecules while preserving similarity to a target molecule and/or property is crucial for various applications in drug discovery, chemical design, and biology. We introduce in this paper an efficient training-free method for navigating and sampling from the molecular space with a generative Chemical Language Model (CLM), while using the molecular similarity to the target as a guide. Our method leverages the contextual representations learned from the CLM itself to estimate the molecular similarity, which is then used to adjust the autoregressive sampling strategy of the CLM. At each step of the decoding process, the method tracks the distance of the current generations from the target and updates the logits to encourage the preservation of similarity in generations. We implement the method using a recently proposed ~47M parameter SMILES-based CLM, GP-MoLFormer, and therefore refer to the method as GP-MoLFormer-Sim, which enables a test-time update of the deep generative policy to reflect the contextual similarity to a set of guide molecules. The method is further integrated into a genetic algorithm (GA) and tested on a set of standard molecular optimization benchmarks involving property optimization, molecular rediscovery, and structure-based drug design. Results show that, GP-MoLFormer-Sim, combined with GA (GP-MoLFormer-Sim+GA) outperforms existing training-free baseline methods, when the oracle remains black-box. The findings in this work are a step forward in understanding and guiding the generative mechanisms of CLMs.

Reducing the likelihood of generating harmful and toxic output is an essential task when aligning large language models (LLMs). Existing methods mainly rely on training an external reward model (i.e., another language model) or fine-tuning the LLM using self-generated data to influence the outcome. In this paper, we show that LLMs have the capability of self-detoxification without external reward model learning or retraining of the LM. We propose \textit{Self-disciplined Autoregressive Sampling (SASA)}, a lightweight controlled decoding algorithm for toxicity reduction of LLMs. SASA leverages the contextual representations from an LLM to learn linear subspaces from labeled data characterizing toxic v.s. non-toxic output in analytical forms. When auto-completing a response token-by-token, SASA dynamically tracks the margin of the current output to steer the generation away from the toxic subspace, by adjusting the autoregressive sampling strategy. Evaluated on LLMs of different scale and nature, namely Llama-3.1-Instruct (8B), Llama-2 (7B), and GPT2-L models with the RealToxicityPrompts, BOLD, and AttaQ benchmarks, SASA markedly enhances the quality of the generated sentences relative to the original models and attains comparable performance to state-of-the-art detoxification techniques, significantly reducing the toxicity level by only using the LLM's internal representations.

Recent methods for aligning large language models (LLMs) with human feedback predominantly rely on a single reference model, which limits diversity, model overfitting, and underutilizes the wide range of available pre-trained models. Incorporating multiple reference models has the potential to address these limitations by broadening perspectives, reducing bias, and leveraging the strengths of diverse open-source LLMs. However, integrating multiple reference models into reinforcement learning with human feedback (RLHF) frameworks poses significant theoretical challenges, where achieving exact solutions has remained an open problem. This paper presents the first \emph{exact solution} to the multiple reference model problem in reverse KL-regularized RLHF. We introduce a comprehensive theoretical framework that includes rigorous statistical analysis and provides sample complexity guarantees. Additionally, we extend our analysis to forward KL-regularized RLHF, offering new insights into sample complexity requirements in multiple reference scenarios. Our contributions lay the foundation for more advanced and adaptable LLM alignment techniques, enabling the effective use of multiple reference models. This work paves the way for developing alignment frameworks that are both theoretically sound and better suited to the challenges of modern AI ecosystems.

We propose a distributional framework for benchmarking socio-technical risks of foundation models with quantified statistical significance. Our approach hinges on a new statistical relative testing based on first and second order stochastic dominance of real random variables. We show that the second order statistics in this test are linked to mean-risk models commonly used in econometrics and mathematical finance to balance risk and utility when choosing between alternatives. Using this framework, we formally develop a risk-aware approach for foundation model selection given guardrails quantified by specified metrics. Inspired by portfolio optimization and selection theory in mathematical finance, we define a metrics portfolio for each model as a means to aggregate a collection of metrics, and perform model selection based on the stochastic dominance of these portfolios. The statistical significance of our tests is backed theoretically by an asymptotic analysis via central limit theorems instantiated in practice via a bootstrap variance estimate. We use our framework to compare various large language models regarding risks related to drifting from instructions and outputting toxic content.

Current LLM alignment techniques use pairwise human preferences at a sample level, and as such, they do not imply an alignment on the distributional level. We propose in this paper Alignment via Optimal Transport (AOT), a novel method for distributional preference alignment of LLMs. AOT aligns LLMs on unpaired preference data by making the reward distribution of the positive samples stochastically dominant in the first order on the distribution of negative samples. We introduce a convex relaxation of this first-order stochastic dominance and cast it as an optimal transport problem with a smooth and convex cost. Thanks to the one-dimensional nature of the resulting optimal transport problem and the convexity of the cost, it has a closed-form solution via sorting on empirical measures. We fine-tune LLMs with this AOT objective, which enables alignment by penalizing the violation of the stochastic dominance of the reward distribution of the positive samples on the reward distribution of the negative samples. We analyze the sample complexity of AOT by considering the dual of the OT problem and show that it converges at the parametric rate. Empirically, we show on a diverse set of alignment datasets and LLMs that AOT leads to state-of-the-art models in the 7B family of models when evaluated with Open LLM Benchmarks and AlpacaEval. Code for $\mathsf{AOT}$ is available in the Hugging Face TRL library \url{https://ibm.biz/AOT_TRL}.

Stochastic dominance is an important concept in probability theory, econometrics and social choice theory for robustly modeling agents' preferences between random outcomes. While many works have been dedicated to the univariate case, little has been done in the multivariate scenario, wherein an agent has to decide between different multivariate outcomes. By exploiting a characterization of multivariate first stochastic dominance in terms of couplings, we introduce a statistic that assesses multivariate almost stochastic dominance under the framework of Optimal Transport with a smooth cost. Further, we introduce an entropic regularization of this statistic, and establish a central limit theorem (CLT) and consistency of the bootstrap procedure for the empirical statistic. Armed with this CLT, we propose a hypothesis testing framework as well as an efficient implementation using the Sinkhorn algorithm. We showcase our method in comparing and benchmarking Large Language Models that are evaluated on multiple metrics. Our multivariate stochastic dominance test allows us to capture the dependencies between the metrics in order to make an informed and statistically significant decision on the relative performance of the models.

Discrepancy measures between probability distributions are at the core of statistical inference and machine learning. In many applications, distributions of interest are supported on different spaces, and yet a meaningful correspondence between data points is desired. Motivated to explicitly encode consistent bidirectional maps into the discrepancy measure, this work proposes a novel unbalanced Monge optimal transport formulation for matching, up to isometries, distributions on different spaces. Our formulation arises as a principled relaxation of the Gromov-Haussdroff distance between metric spaces, and employs two cycle-consistent maps that push forward each distribution onto the other. We study structural properties of the proposed discrepancy and, in particular, show that it captures the popular cycle-consistent generative adversarial network (GAN) framework as a special case, thereby providing the theory to explain it. Motivated by computational efficiency, we then kernelize the discrepancy and restrict the mappings to parametric function classes. The resulting kernelized version is coined the generalized maximum mean discrepancy (GMMD). Convergence rates for empirical estimation of GMMD are studied and experiments to support our theory are provided.

Image captioning has recently demonstrated impressive progress largely owing to the introduction of neural network algorithms trained on curated dataset like MS-COCO. Often work in this field is motivated by the promise of deployment of captioning systems in practical applications. However, the scarcity of data and contexts in many competition datasets renders the utility of systems trained on these datasets limited as an assistive technology in real-world settings, such as helping visually impaired people navigate and accomplish everyday tasks. This gap motivated the introduction of the novel VizWiz dataset, which consists of images taken by the visually impaired and captions that have useful, task-oriented information. In an attempt to help the machine learning computer vision field realize its promise of producing technologies that have positive social impact, the curators of the VizWiz dataset host several competitions, including one for image captioning. This work details the theory and engineering from our winning submission to the 2020 captioning competition. Our work provides a step towards improved assistive image captioning systems. This article appears in the special track on AI & Society.

We propose to estimate the KL divergence using a relaxed likelihood ratio estimation in a Reproducing Kernel Hilbert space. We show that the dual of our ratio estimator for KL in the particular case of Mutual Information estimation corresponds to a lower bound on the MI that is related to the so called Donsker Varadhan lower bound. In this dual form, MI is estimated via learning a witness function discriminating between the joint density and the product of marginal, as well as an auxiliary scalar variable that enforces a normalization constraint on the likelihood ratio. By extending the function space to neural networks, we propose an efficient neural MI estimator, and validate its performance on synthetic examples, showing advantage over the existing baselines. We demonstrate its strength in large-scale self-supervised representation learning through MI maximization.

We consider the maximum mean discrepancy MMD GAN problem and propose a parametric kernelized gradient flow that mimics the min-max game in gradient regularized MMD GAN. We show that this flow provides a descent direction minimizing the MMD on a statistical manifold of probability distributions. We then derive an explicit condition which ensures that gradient descent on the parameter space of the generator in gradient regularized MMD GAN is globally convergent to the target distribution. Under this condition , we give non asymptotic convergence results for MMD GAN. Another contribution of this paper is the introduction of a dynamic formulation of a regularization of MMD and demonstrating that the parametric kernelized descent for MMD is the gradient flow of this functional with respect to the new Riemannian structure. Our obtained theoretical result allows ones to treat gradient flows for quite general functionals and thus has potential applications to other types of variational inferences on a statistical manifold beyond GANs. Finally, numerical experiments suggest that our parametric kernelized gradient flow stabilizes GAN training and guarantees convergence.

Tabular datasets are ubiquitous in data science applications. Given their importance, it seems natural to apply state-of-the-art deep learning algorithms in order to fully unlock their potential. Here we propose neural network models that represent tabular time series that can optionally leverage their hierarchical structure. This results in two architectures for tabular time series: one for learning representations that is analogous to BERT and can be pre-trained end-to-end and used in downstream tasks, and one that is akin to GPT and can be used for generation of realistic synthetic tabular sequences. We demonstrate our models on two datasets: a synthetic credit card transaction dataset, where the learned representations are used for fraud detection and synthetic data generation, and on a real pollution dataset, where the learned encodings are used to predict atmospheric pollutant concentrations. Code and data are available at https://github.com/IBM/TabFormer.

Understanding the generalization of deep neural networks is one of the most important tasks in deep learning. Although much progress has been made, theoretical error bounds still often behave disparately from empirical observations. In this work, we develop margin-based generalization bounds, where the margins are normalized with optimal transport costs between independent random subsets sampled from the training distribution. In particular, the optimal transport cost can be interpreted as a generalization of variance which captures the structural properties of the learned feature space. Our bounds robustly predict the generalization error, given training data and network parameters, on large scale datasets. Theoretically, we demonstrate that the concentration and separation of features play crucial roles in generalization, supporting empirical results in the literature.

Several works in implicit and explicit generative modeling empirically observed that feature-learning discriminators outperform fixed-kernel discriminators in terms of the sample quality of the models. We provide separation results between probability metrics with fixed-kernel and feature-learning discriminators using the function classes $\mathcal{F}_2$ and $\mathcal{F}_1$ respectively, which were developed to study overparametrized two-layer neural networks. In particular, we construct pairs of distributions over hyper-spheres that can not be discriminated by fixed kernel $(\mathcal{F}_2)$ integral probability metric (IPM) and Stein discrepancy (SD) in high dimensions, but that can be discriminated by their feature learning ($\mathcal{F}_1$) counterparts. To further study the separation we provide links between the $\mathcal{F}_1$ and $\mathcal{F}_2$ IPMs with sliced Wasserstein distances. Our work suggests that fixed-kernel discriminators perform worse than their feature learning counterparts because their corresponding metrics are weaker.

Inkit Padhi, Pierre Dognin, Ke Bai, Cícero Nogueira dos Santos, Vijil Chenthamarakshan, Youssef Mroueh, Payel Das. Proceedings of the 58th Annual Meeting of the Association for Computational Linguistics. 2020.

This paper focuses on the problem of unsupervised alignment of hierarchical data such as ontologies or lexical databases. This problem arises across areas, from natural language processing to bioinformatics, and is typically solved by appeal to outside knowledge bases and label-textual similarity. In contrast, we approach the problem from a purely geometric perspective: given only a vector-space representation of the items in the two hierarchies, we seek to infer correspondences across them. Our work derives from and interweaves hyperbolic-space representations for hierarchical data, on one hand, and unsupervised word-alignment methods, on the other. We first provide a set of negative results showing how and why Euclidean methods fail in this hyperbolic setting. We then propose a novel approach based on optimal transport over hyperbolic spaces, and show that it outperforms standard embedding alignment techniques in various experiments on cross-lingual WordNet alignment and ontology matching tasks.

We propose Gaussian optimal transport for image style transfer in an Encoder/Decoder framework. Optimal transport for Gaussian measures has closed forms Monge mappings from source to target distributions. Moreover, interpolating between a content and a style image can be seen as geodesics in the Wasserstein Geometry. Using this insight, we show how to mix different target styles , using Wasserstein barycenter of Gaussian measures. Since Gaussians are closed under Wasserstein barycenter, this allows us a simple style transfer and style mixing and interpolation. Moreover we show how mixing different styles can be achieved using other geodesic metrics between gaussians such as the Fisher Rao metric, while the transport of the content to the new interpolate style is still performed with Gaussian OT maps. Our simple methodology allows to generate new stylized content interpolating between many artistic styles. The metric used in the interpolation results in different stylizations. A demo is available on https: //wasserstein-transfer.github.io.

Decentralized Parallel SGD (D-PSGD) and its asynchronous variant Asynchronous Parallel SGD (AD-PSGD) is a family of distributed learning algorithms that have been demonstrated to perform well for large-scale deep learning tasks. One drawback of (A)D-PSGD is that the spectral gap of the mixing matrix decreases when the number of learners in the system increases, which hampers convergence. In this paper, we investigate techniques to accelerate (A)D-PSGD based training by improving the spectral gap while minimizing the communication cost. We demonstrate the effectiveness of our proposed techniques by running experiments on the 2000-hour Switchboard speech recognition task and the ImageNet computer vision task. On an IBM P9 supercomputer, our system is able to train an LSTM acoustic model in 2.28 hours with 7.5% WER on the Hub5-2000 Switchboard (SWB) test set and 13.3% WER on the CallHome (CH) test set using 64 V100 GPUs and in 1.98 hours with 7.7% WER on SWB and 13.3% WER on CH using 128 V100 GPUs, the fastest training time reported to date.

Generative Adversarial Networks (GANs) are a powerful class of generative models in the deep learning community. Current practice on large-scale GAN training utilizes large models and distributed large-batch training strategies, and is implemented on deep learning frameworks (e.g., TensorFlow, PyTorch, etc.) designed in a centralized manner. In the centralized network topology, every worker needs to either directly communicate with the central node or indirectly communicate with all other workers in every iteration. However, when the network bandwidth is low or network latency is high, the performance would be significantly degraded. Despite recent progress on decentralized algorithms for training deep neural networks, it remains unclear whether it is possible to train GANs in a decentralized manner. The main difficulty lies at handling the nonconvex-nonconcave min-max optimization and the decentralized communication simultaneously. In this paper, we address this difficulty by designing the \textbf{first gradient-based decentralized parallel algorithm} which allows workers to have multiple rounds of communications in one iteration and to update the discriminator and generator simultaneously, and this design makes it amenable for the convergence analysis of the proposed decentralized algorithm. Theoretically, our proposed decentralized algorithm is able to solve a class of non-convex non-concave min-max problems with provable non-asymptotic convergence to first-order stationary point. Experimental results on GANs demonstrate the effectiveness of the proposed algorithm.

We introduce Unbalanced Sobolev Descent (USD), a particle descent algorithm for transporting a high dimensional source distribution to a target distribution that does not necessarily have the same mass. We define the Sobolev-Fisher discrepancy between distributions and show that it relates to advection-reaction transport equations and the Wasserstein-Fisher-Rao metric between distributions. USD transports particles along gradient flows of the witness function of the Sobolev-Fisher discrepancy (advection step) and reweighs the mass of particles with respect to this witness function (reaction step). The reaction step can be thought of as a birth-death process of the particles with rate of growth proportional to the witness function. When the Sobolev-Fisher witness function is estimated in a Reproducing Kernel Hilbert Space (RKHS), under mild assumptions we show that USD converges asymptotically (in the limit of infinite particles) to the target distribution in the Maximum Mean Discrepancy (MMD) sense. We then give two methods to estimate the Sobolev-Fisher witness with neural networks, resulting in two Neural USD algorithms. The first one implements the reaction step with mirror descent on the weights, while the second implements it through a birth-death process of particles. We show on synthetic examples that USD transports distributions with or without conservation of mass faster than previous particle descent algorithms, and finally demonstrate its use for molecular biology analyses where our method is naturally suited to match developmental stages of populations of differentiating cells based on their single-cell RNA sequencing profile. Code is available at http://github.com/ibm/usd.

Kernels are powerful and versatile tools in machine learning and statistics. Although the notion of universal kernels and characteristic kernels has been studied, kernel selection still greatly influences the empirical performance. While learning the kernel in a data driven way has been investigated, in this paper we explore learning the spectral distribution of kernel via implicit generative models parametrized by deep neural networks. We called our method Implicit Kernel Learning (IKL). The proposed framework is simple to train and inference is performed via sampling random Fourier features. We investigate two applications of the proposed IKL as examples, including generative adversarial networks with MMD (MMD GAN) and standard supervised learning. Empirically, MMD GAN with IKL outperforms vanilla predefined kernels on both image and text generation benchmarks; using IKL with Random Kitchen Sinks also leads to substantial improvement over existing state-of-the-art kernel learning algorithms on popular supervised learning benchmarks. Theory and conditions for using IKL in both applications are also studied as well as connections to previous state-of-the-art methods.

We study a simplification of GAN training: the problem of transporting particles from a source to a target distribution. Starting from the Sobolev GAN critic, part of the gradient regularized GAN family, we show a strong relation with Optimal Transport (OT). Specifically with the less popular *dynamic* formulation of OT that finds a path of distributions from source to target minimizing a "kinetic energy". We introduce Sobolev descent that constructs similar paths by following gradient flows of a critic function in a kernel space or parametrized by a neural network. In the kernel version, we show convergence to the target distribution in the MMD sense. We show in theory and experiments that regularization has an important role in favoring smooth transitions between distributions, avoiding large gradients from the critic. This analysis in a simplified particle setting provides insight in paths to equilibrium in GANs.

In this paper, we study image captioning as a conditional GAN training, proposing both a context-aware LSTM captioner and co-attentive discriminator, which enforces semantic alignment between images and captions. We empirically focus on the viability of two training methods: Self-critical Sequence Training (SCST) and Gumbel Straight-Through (ST) and demonstrate that SCST shows more stable gradient behavior and improved results over Gumbel ST, even without accessing discriminator gradients directly. We also address the problem of automatic evaluation for captioning models and introduce a new semantic score, and show its correlation to human judgement. As an evaluation paradigm, we argue that an important criterion for a captioner is the ability to generalize to compositions of objects that do not usually co-occur together. To this end, we introduce a small captioned Out of Context (OOC) test set. The OOC set, combined with our semantic score, are the proposed new diagnosis tools for the captioning community. When evaluated on OOC and MS-COCO benchmarks, we show that SCST-based training has a strong performance in both semantic score and human evaluation, promising to be a valuable new approach for efficient discrete GAN training.

Perceptual features (PFs) have been used with great success in tasks such as transfer learning, style transfer, and super-resolution. However, the efficacy of PFs as key source of information for learning generative models is not well studied. We investigate here the use of PFs in the context of learning implicit generative models through moment matching (MM). More specifically, we propose a new effective MM approach that learns implicit generative models by performing mean and covariance matching of features extracted from pretrained ConvNets. Our proposed approach improves upon existing MM methods by: (1) breaking away from the problematic min/max game of adversarial learning; (2) avoiding online learning of kernel functions; and (3) being efficient with respect to both number of used moments and required minibatch size. Our experimental results demonstrate that, due to the expressiveness of PFs from pretrained deep ConvNets, our method achieves state-of-the-art results for challenging benchmarks.

We propose the Sobolev Independence Criterion (SIC), an interpretable dependency measure between a high dimensional random variable X and a response variable Y. SIC decomposes to the sum of feature importance scores and hence can be used for nonlinear feature selection. SIC can be seen as a gradient regularized Integral Probability Metric (IPM) between the joint distribution of the two random variables and the product of their marginals. We use sparsity inducing gradient penalties to promote input sparsity of the critic of the IPM. In the kernel version we show that SIC can be cast as a convex optimization problem by introducing auxiliary variables that play an important role in feature selection as they are normalized feature importance scores. We then present a neural version of SIC where the critic is parameterized as a homogeneous neural network, improving its representation power as well as its interpretability. We conduct experiments validating SIC for feature selection in synthetic and real-world experiments. We show that SIC enables reliable and interpretable discoveries, when used in conjunction with the holdout randomization test and knockoffs to control the False Discovery Rate. Code is available at http://github.com/ibm/sic.

We introduce co-occurring directions sketching, a deterministic algorithm for approximate matrix product (AMM), in the streaming model. We show that co-occurring directions achieves a better error bound for AMM than other randomized and deterministic approaches for AMM. Co-occurring directions gives a (1 + epsilon) - approximation of the optimal low rank approximation of a matrix product. Empirically our algorithm outperforms competing methods for AMM, for a small sketch size. We validate empirically our theoretical findings and algorithms.

Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a group and propose an approach based on kernel methods to derive local group invariant representations. Locality is achieved by defining a suitable probability distribution over the group which in turn induces distributions in the input feature space. We learn a decision function over these distributions by appealing to the powerful framework of kernel methods and generate local invariant random feature maps via kernel approximations. We show uniform convergence bounds for kernel approximation and provide generalization bounds for learning with these features. We evaluate our method on three real datasets, including Rotated MNIST and CIFAR-10, and observe that it outperforms competing kernel based approaches. The proposed method also outperforms deep CNN on Rotated MNIST and performs comparably to the recently proposed group-equivariant CNN.

Recently it has been shown that policy-gradient methods for reinforcement learning can be utilized to train deep end-to-end systems directly on non-differentiable metrics for the task at hand. In this paper we consider the problem of optimizing image captioning systems using reinforcement learning, and show that by carefully optimizing our systems using the test metrics of the MSCOCO task, significant gains in performance can be realized. Our systems are built using a new optimization approach that we call self-critical sequence training (SCST). SCST is a form of the popular REINFORCE algorithm that, rather than estimating a baseline to normalize the rewards and reduce variance, utilizes the output of its own test-time inference algorithm to normalize the rewards it experiences. Using this approach, estimating the reward signal (as actor-critic methods must do) and estimating normalization (as REINFORCE algorithms typically do) is avoided, while at the same time harmonizing the model with respect to its test-time inference procedure. Empirically we find that directly optimizing the CIDEr metric with SCST and greedy decoding at test-time is highly effective. Our results on the MSCOCO evaluation sever establish a new state-of-the-art on the task, improving the best result in terms of CIDEr from 104.9 to 114.7.

We introduce new families of Integral Probability Metrics (IPM) for training Generative Adversarial Networks (GAN). Our IPMs are based on matching statistics of distributions embedded in a finite dimensional feature space. Mean and covariance feature matching IPMs allow for stable training of GANs, which we will call McGan. McGan minimizes a meaningful loss between distributions.

Generative Adversarial Networks (GANs) are powerful models for learning complex distributions. Stable training of GANs has been addressed in many recent works which explore different metrics between distributions. In this paper we introduce Fisher GAN that fits within the Integral Probability Metrics (IPM) framework for training GANs. Fisher GAN defines a data dependent constraint on the second order moments of the critic. We show in this paper that Fisher GAN allows for stable and time efficient training that does not compromise the capacity of the critic, and does not need data independent constraints such as weight clipping. We analyze our Fisher IPM theoretically and provide an algorithm based on Augmented Lagrangian for Fisher GAN. We validate our claims on both image sample generation and semi-supervised classification using Fisher GAN.

In this paper, we present methods in deep multimodal learning for fusing speech and visual modalities for Audio-Visual Automatic Speech Recognition (AV-ASR). First, we study an approach where uni-modal deep networks are trained separately and their final hidden layers fused to obtain a joint feature space in which another deep network is built. While the audio network alone achieves a phone error rate (PER) of 41% under clean condition on the IBM large vocabulary audio-visual studio dataset, this fusion model achieves a PER of 35.83% demonstrating the tremendous value of the visual channel in phone classification even in audio with high signal to noise ratio. Second, we present a new deep network architecture that uses a bilinear softmax layer to account for class specific correlations between modalities. We show that combining the posteriors from the bilinear networks with those from the fused model mentioned above results in a further significant phone error rate reduction, yielding a final PER of 34.03%.

Reducing the amount of human supervision is a key problem in machine learning and a natural approach is that of exploiting the relations (structure) among different tasks. This is the idea at the core of multi-task learning. In this context a fundamental question is how to incorporate the tasks structure in the learning problem. We tackle this question by studying a general computational framework that allows to encode a-priori knowledge of the tasks structure in the form of a convex penalty; in this setting a variety of previously proposed methods can be recovered as special cases, including linear and non-linear approaches. Within this framework, we show that tasks and their structure can be efficiently learned considering a convex optimization problem that can be approached by means of block coordinate methods such as alternating minimization and for which we prove convergence to the global minimum.

We analyze in this paper a random feature map based on a theory of invariance (\emph{I-theory}) introduced in \cite{AnselmiLRMTP13}. More specifically, a group invariant signal signature is obtained through cumulative distributions of group-transformed random projections. Our analysis bridges invariant feature learning with kernel methods, as we show that this feature map defines an expected Haar-integration kernel that is invariant to the specified group action. We show how this non-linear random feature map approximates this group invariant kernel uniformly on a set of $N$ points. Moreover, we show that it defines a function space that is dense in the equivalent Invariant Reproducing Kernel Hilbert Space. Finally, we quantify error rates of the convergence of the empirical risk minimization, as well as the reduction in the sample complexity of a learning algorithm using such an invariant representation for signal classification, in a classical supervised learning setting

In this paper we show that the problem of phase retrieval can be efficiently and provably solved via an alternating minimization algorithm suitably initialized. Our initialization is based on One Bit Phase Retrieval that we introduced in [1], where we showed that O(n log(n)) Gaussian phase-less measurements ensure robust recovery of the phase. In this paper we improve the sample complexity bound to O(n) measurements for sufficiently large n, using a variant of Matrix Bernstein concentration inequality that exploits the intrinsic dimension, together with properties of one bit phase retrieval.

In this paper we dicuss a novel framework for multiclass learning, defined by a suitable coding/decoding strategy, namely the simplex coding, that allows to generalize to multiple classes a relaxation approach commonly used in binary classification. In this framework a relaxation error analysis can be developed avoiding constraints on the considered hypotheses class. Moreover, we show that in this setting it is possible to derive the first provably consistent regularized methods with training/tuning complexity which is {\em independent} to the number of classes. Tools from convex analysis are introduced that can be used beyond the scope of this paper.