arXiv subjects

Sarthak Mittal

Publications and source records attributed to Sarthak Mittal.

29 records · Page 2Linked to original sources

arXiv2024

Recurrent Interpolants for Probabilistic Time Series Prediction

Sequential models like recurrent neural networks and transformers have become standard for probabilistic multivariate time series forecasting across various domains. Despite their strengths, they struggle with capturing high-dimensional distributions and cross-feature dependencies. Recent work explores generative approaches using diffusion or flow-based models, extending to time series imputation and forecasting. However, scalability remains a challenge. This work proposes a novel method combining recurrent neural networks' efficiency with diffusion models' probabilistic modeling, based on stochastic interpolants and conditional generation with control features, offering insights for future developments in this dynamic field.

cs.LG↗

arXiv2024

Iterated Denoising Energy Matching for Sampling from Boltzmann Densities

Efficiently generating statistically independent samples from an unnormalized probability distribution, such as equilibrium samples of many-body systems, is a foundational problem in science. In this paper, we propose Iterated Denoising Energy Matching (iDEM), an iterative algorithm that uses a novel stochastic score matching objective leveraging solely the energy function and its gradient -- and no data samples -- to train a diffusion-based sampler. Specifically, iDEM alternates between (I) sampling regions of high model density from a diffusion-based sampler and (II) using these samples in our stochastic matching objective to further improve the sampler. iDEM is scalable to high dimensions as the inner matching objective, is simulation-free, and requires no MCMC samples. Moreover, by leveraging the fast mode mixing behavior of diffusion, iDEM smooths out the energy landscape enabling efficient exploration and learning of an amortized sampler. We evaluate iDEM on a suite of tasks ranging from standard synthetic energy functions to invariant $n$-body particle systems. We show that the proposed approach achieves state-of-the-art performance on all metrics and trains $2-5\times$ faster, which allows it to be the first method to train using energy on the challenging $55$-particle Lennard-Jones system.

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arXiv2023

MixupE: Understanding and Improving Mixup from Directional Derivative Perspective

Mixup is a popular data augmentation technique for training deep neural networks where additional samples are generated by linearly interpolating pairs of inputs and their labels. This technique is known to improve the generalization performance in many learning paradigms and applications. In this work, we first analyze Mixup and show that it implicitly regularizes infinitely many directional derivatives of all orders. Based on this new insight, we propose an improved version of Mixup, theoretically justified to deliver better generalization performance than the vanilla Mixup. To demonstrate the effectiveness of the proposed method, we conduct experiments across various domains such as images, tabular data, speech, and graphs. Our results show that the proposed method improves Mixup across multiple datasets using a variety of architectures, for instance, exhibiting an improvement over Mixup by 0.8% in ImageNet top-1 accuracy.

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arXiv2023

Leveraging Synthetic Targets for Machine Translation

In this work, we provide a recipe for training machine translation models in a limited resource setting by leveraging synthetic target data generated using a large pre-trained model. We show that consistently across different benchmarks in bilingual, multilingual, and speech translation setups, training models on synthetic targets outperforms training on the actual ground-truth data. This performance gap grows bigger with increasing limits on the amount of available resources in the form of the size of the dataset and the number of parameters in the model. We also provide preliminary analysis into whether this boost in performance is linked to ease of optimization or more deterministic nature of the predictions, and whether this paradigm leads to better out-of-distribution performance across different testing domains.

cs.CL↗

arXiv2022

From Points to Functions: Infinite-dimensional Representations in Diffusion Models

Diffusion-based generative models learn to iteratively transfer unstructured noise to a complex target distribution as opposed to Generative Adversarial Networks (GANs) or the decoder of Variational Autoencoders (VAEs) which produce samples from the target distribution in a single step. Thus, in diffusion models every sample is naturally connected to a random trajectory which is a solution to a learned stochastic differential equation (SDE). Generative models are only concerned with the final state of this trajectory that delivers samples from the desired distribution. Abstreiter et. al showed that these stochastic trajectories can be seen as continuous filters that wash out information along the way. Consequently, it is reasonable to ask if there is an intermediate time step at which the preserved information is optimal for a given downstream task. In this work, we show that a combination of information content from different time steps gives a strictly better representation for the downstream task. We introduce an attention and recurrence based modules that ``learn to mix'' information content of various time-steps such that the resultant representation leads to superior performance in downstream tasks.

cs.LG↗

arXiv2022

On Neural Architecture Inductive Biases for Relational Tasks

Current deep learning approaches have shown good in-distribution generalization performance, but struggle with out-of-distribution generalization. This is especially true in the case of tasks involving abstract relations like recognizing rules in sequences, as we find in many intelligence tests. Recent work has explored how forcing relational representations to remain distinct from sensory representations, as it seems to be the case in the brain, can help artificial systems. Building on this work, we further explore and formalize the advantages afforded by 'partitioned' representations of relations and sensory details, and how this inductive bias can help recompose learned relational structure in newly encountered settings. We introduce a simple architecture based on similarity scores which we name Compositional Relational Network (CoRelNet). Using this model, we investigate a series of inductive biases that ensure abstract relations are learned and represented distinctly from sensory data, and explore their effects on out-of-distribution generalization for a series of relational psychophysics tasks. We find that simple architectural choices can outperform existing models in out-of-distribution generalization. Together, these results show that partitioning relational representations from other information streams may be a simple way to augment existing network architectures' robustness when performing out-of-distribution relational computations.

cs.NE↗

arXiv2022

Is a Modular Architecture Enough?

Inspired from human cognition, machine learning systems are gradually revealing advantages of sparser and more modular architectures. Recent work demonstrates that not only do some modular architectures generalize well, but they also lead to better out-of-distribution generalization, scaling properties, learning speed, and interpretability. A key intuition behind the success of such systems is that the data generating system for most real-world settings is considered to consist of sparsely interacting parts, and endowing models with similar inductive biases will be helpful. However, the field has been lacking in a rigorous quantitative assessment of such systems because these real-world data distributions are complex and unknown. In this work, we provide a thorough assessment of common modular architectures, through the lens of simple and known modular data distributions. We highlight the benefits of modularity and sparsity and reveal insights on the challenges faced while optimizing modular systems. In doing so, we propose evaluation metrics that highlight the benefits of modularity, the regimes in which these benefits are substantial, as well as the sub-optimality of current end-to-end learned modular systems as opposed to their claimed potential.

cs.LG↗

arXiv2022

Compositional Attention: Disentangling Search and Retrieval

Multi-head, key-value attention is the backbone of the widely successful Transformer model and its variants. This attention mechanism uses multiple parallel key-value attention blocks (called heads), each performing two fundamental computations: (1) search - selection of a relevant entity from a set via query-key interactions, and (2) retrieval - extraction of relevant features from the selected entity via a value matrix. Importantly, standard attention heads learn a rigid mapping between search and retrieval. In this work, we first highlight how this static nature of the pairing can potentially: (a) lead to learning of redundant parameters in certain tasks, and (b) hinder generalization. To alleviate this problem, we propose a novel attention mechanism, called Compositional Attention, that replaces the standard head structure. The proposed mechanism disentangles search and retrieval and composes them in a dynamic, flexible and context-dependent manner through an additional soft competition stage between the query-key combination and value pairing. Through a series of numerical experiments, we show that it outperforms standard multi-head attention on a variety of tasks, including some out-of-distribution settings. Through our qualitative analysis, we demonstrate that Compositional Attention leads to dynamic specialization based on the type of retrieval needed. Our proposed mechanism generalizes multi-head attention, allows independent scaling of search and retrieval, and can easily be implemented in lieu of standard attention heads in any network architecture.

cs.LG↗

arXiv2021

Systematic Evaluation of Causal Discovery in Visual Model Based Reinforcement Learning

Inducing causal relationships from observations is a classic problem in machine learning. Most work in causality starts from the premise that the causal variables themselves are observed. However, for AI agents such as robots trying to make sense of their environment, the only observables are low-level variables like pixels in images. To generalize well, an agent must induce high-level variables, particularly those which are causal or are affected by causal variables. A central goal for AI and causality is thus the joint discovery of abstract representations and causal structure. However, we note that existing environments for studying causal induction are poorly suited for this objective because they have complicated task-specific causal graphs which are impossible to manipulate parametrically (e.g., number of nodes, sparsity, causal chain length, etc.). In this work, our goal is to facilitate research in learning representations of high-level variables as well as causal structures among them. In order to systematically probe the ability of methods to identify these variables and structures, we design a suite of benchmarking RL environments. We evaluate various representation learning algorithms from the literature and find that explicitly incorporating structure and modularity in models can help causal induction in model-based reinforcement learning.

stat.ML↗

arXiv2020

Learning to Combine Top-Down and Bottom-Up Signals in Recurrent Neural Networks with Attention over Modules

Robust perception relies on both bottom-up and top-down signals. Bottom-up signals consist of what's directly observed through sensation. Top-down signals consist of beliefs and expectations based on past experience and short-term memory, such as how the phrase `peanut butter and~...' will be completed. The optimal combination of bottom-up and top-down information remains an open question, but the manner of combination must be dynamic and both context and task dependent. To effectively utilize the wealth of potential top-down information available, and to prevent the cacophony of intermixed signals in a bidirectional architecture, mechanisms are needed to restrict information flow. We explore deep recurrent neural net architectures in which bottom-up and top-down signals are dynamically combined using attention. Modularity of the architecture further restricts the sharing and communication of information. Together, attention and modularity direct information flow, which leads to reliable performance improvements in perceptual and language tasks, and in particular improves robustness to distractions and noisy data. We demonstrate on a variety of benchmarks in language modeling, sequential image classification, video prediction and reinforcement learning that the \emph{bidirectional} information flow can improve results over strong baselines.

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arXiv2019

A Modern Take on the Bias-Variance Tradeoff in Neural Networks

The bias-variance tradeoff tells us that as model complexity increases, bias falls and variances increases, leading to a U-shaped test error curve. However, recent empirical results with over-parameterized neural networks are marked by a striking absence of the classic U-shaped test error curve: test error keeps decreasing in wider networks. This suggests that there might not be a bias-variance tradeoff in neural networks with respect to network width, unlike was originally claimed by, e.g., Geman et al. (1992). Motivated by the shaky evidence used to support this claim in neural networks, we measure bias and variance in the modern setting. We find that both bias and variance can decrease as the number of parameters grows. To better understand this, we introduce a new decomposition of the variance to disentangle the effects of optimization and data sampling. We also provide theoretical analysis in a simplified setting that is consistent with our empirical findings.

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