arXiv subjects

Rene Vidal

Publications and source records attributed to Rene Vidal.

At least 19 recordsLinked to original sources

arXiv2026

SGD at the Edge of Stability: Stochastic Stabilization with Large Learning Rates

Modern deep learning has been shown to operate at the edge of stability, routinely using learning rates far larger than those justified by classical optimization theory. Most prior analyses of the edge of stability phenomenon focus on deterministic gradient descent, leaving the stochastic setting largely unexplored. In this work, we provide sharp convergence guarantees for Stochastic Gradient Descent (SGD) applied to the multiclass cross-entropy loss, for both linear classifiers and two-layer neural networks. We show that the stochasticity of SGD may cause the dynamics to alternate between an edge-of-stability regime that is dominated by curvature-driven oscillations, and a stable regime in which the expected loss decreases at a controlled rate. Despite that, we prove that SGD self-stabilizes the dynamics, ensuring that the iterates return to stability in a fixed number of iterations and allowing convergence in the best-iterate sense even with large learning rates. Experiments validate our theoretical findings and illustrate the benefits of SGD in the large-stepsize regime.

stat.ML↗

arXiv2026

See What I See, Know What I Think: Dense Latent Communication Across Heterogeneous Agents

Multi-agent systems communicate mostly through text, paying a lossy and expensive decode and re-encode cost. KV-cache communication is a promising alternative, yet most prior work is homogeneous, using duplicate copies of the same model, and avoids the central challenge of cross-model latent alignment; existing heterogeneous methods are also restrictive, typically assuming shared input and using transferred caches mainly for steering. We study a more fundamental question: can heterogeneous agents be aligned well enough to perform real "mind reading" and transfer both what one agent sees and how it thinks? Our information-structure analysis reveals a duality: context-aware transfer is driven by sparse reasoning signals, while context-unaware transfer, where the receiver sees no input, requires dense contextual knowledge preservation. Motivated by this, we propose dense alignment for heterogeneous KV-cache communication via a lightweight cross-model cache transformation and two-phase training: reconstruction followed by generation. Across all six directions of {Qwen3-4B, 8B, 14B} and six in-domain and out-of-domain benchmarks, our method outperforms prior heterogeneous baselines, matches or exceeds text communication in context-aware settings at roughly 2 to 3 times lower compute, and remains effective in context-unaware transfer where prior methods collapse.

cs.MA↗

arXiv2026

Transformers Learn the Optimal DDPM Denoiser for Multi-Token GMMs

Transformer-based diffusion models have demonstrated remarkable performance at generating high-quality samples. However, our theoretical understanding of the reasons for this success remains limited. For instance, existing models are typically trained by minimizing a denoising objective, which is equivalent to fitting the score function of the training data. However, we do not know why transformer-based models can match the score function for denoising, or why gradient-based methods converge to the optimal denoising model despite the non-convex loss landscape. To the best of our knowledge, this paper provides the first convergence analysis for training transformer-based diffusion models. More specifically, we consider the population Denoising Diffusion Probabilistic Model (DDPM) objective for denoising data that follow a multi-token Gaussian mixture distribution. We theoretically quantify the required number of tokens per data point and training iterations for the global convergence towards the Bayes optimal risk of the denoising objective, thereby achieving a desired score matching error. A deeper investigation reveals that the self-attention module of the trained transformer implements a mean denoising mechanism that enables the trained model to approximate the oracle Minimum Mean Squared Error (MMSE) estimator of the injected noise in the diffusion steps. Numerical experiments validate these findings.

cs.LG↗

arXiv2026

Shuffling the Data, Stretching the Step-size: Sharper Bias in constant step-size SGD

From adversarial robustness to multi-agent learning, many machine learning tasks can be cast as finite-sum min-max optimization or, more generally, as variational inequality problems (VIPs). Owing to their simplicity and scalability, stochastic gradient methods with constant step size are widely used, despite the fact that they converge only up to a constant term. Among the many heuristics adopted in practice, two classical techniques have recently attracted attention to mitigate this issue: \emph{Random Reshuffling} of data and \emph{Richardson--Romberg extrapolation} across iterates. Random Reshuffling sharpens the mean-squared error (MSE) of the estimated solution, while Richardson-Romberg extrapolation acts orthogonally, providing a second-order reduction in its bias. In this work, we show that their composition is strictly better than both, not only maintaining the enhanced MSE guarantees but also yielding an even greater cubic refinement in the bias. To the best of our knowledge, our work provides the first theoretical guarantees for such a synergy in structured non-monotone VIPs. Our analysis proceeds in two steps: (i) we smooth the discrete noise induced by reshuffling and leverage tools from continuous-state Markov chain theory to establish a novel law of large numbers and a central limit theorem for its iterates; and (ii) we employ spectral tensor techniques to prove that extrapolation debiases and sharpens the asymptotic behavior even under the biased gradient oracle induced by reshuffling. Finally, extensive experiments validate our theory, consistently demonstrating substantial speedups in practice.

math.OC↗

arXiv2026

BLISS: Global Blind Identification of Linear Systems with Sparse Inputs

Linear system identification and sparse dictionary learning can both be seen as structured matrix factorization problems. However, these two problems have historically been studied in isolation by the systems theory and machine learning communities. Although linear system identification enjoys a mature theory when inputs are known, blind linear system identification remains poorly understood beyond restrictive settings. In contrast, complete sparse dictionary learning has recently benefited from strong global identifiability results and scalable nonconvex algorithms. In this work, we bridge these two areas by showing that under a sparse input assumption, fully observed blind system identification becomes a generalization of complete dictionary learning. This connection allows us to develop global identifiability guarantees for blind system identification, by leveraging techniques from the complete dictionary learning literature. We further show empirically that a principled application of the alternating direction method of multipliers can globally recover the ground-truth system from a single trajectory, provided sufficient samples and input sparsity.

eess.SY↗

arXiv2026

Reliable and Responsible Foundation Models: A Comprehensive Survey

Foundation models, including Large Language Models (LLMs), Multimodal Large Language Models (MLLMs), Image Generative Models (i.e, Text-to-Image Models and Image-Editing Models), and Video Generative Models, have become essential tools with broad applications across various domains such as law, medicine, education, finance, science, and beyond. As these models see increasing real-world deployment, ensuring their reliability and responsibility has become critical for academia, industry, and government. This survey addresses the reliable and responsible development of foundation models. We explore critical issues, including bias and fairness, security and privacy, uncertainty, explainability, and distribution shift. Our research also covers model limitations, such as hallucinations, as well as methods like alignment and Artificial Intelligence-Generated Content (AIGC) detection. For each area, we review the current state of the field and outline concrete future research directions. Additionally, we discuss the intersections between these areas, highlighting their connections and shared challenges. We hope our survey fosters the development of foundation models that are not only powerful but also ethical, trustworthy, reliable, and socially responsible.

cs.LG↗

arXiv2025

The Future of Artificial Intelligence and the Mathematical and Physical Sciences (AI+MPS)

This community paper developed out of the NSF Workshop on the Future of Artificial Intelligence (AI) and the Mathematical and Physics Sciences (MPS), which was held in March 2025 with the goal of understanding how the MPS domains (Astronomy, Chemistry, Materials Research, Mathematical Sciences, and Physics) can best capitalize on, and contribute to, the future of AI. We present here a summary and snapshot of the MPS community's perspective, as of Spring/Summer 2025, in a rapidly developing field. The link between AI and MPS is becoming increasingly inextricable; now is a crucial moment to strengthen the link between AI and Science by pursuing a strategy that proactively and thoughtfully leverages the potential of AI for scientific discovery and optimizes opportunities to impact the development of AI by applying concepts from fundamental science. To achieve this, we propose activities and strategic priorities that: (1) enable AI+MPS research in both directions; (2) build up an interdisciplinary community of AI+MPS researchers; and (3) foster education and workforce development in AI for MPS researchers and students. We conclude with a summary of suggested priorities for funding agencies, educational institutions, and individual researchers to help position the MPS community to be a leader in, and take full advantage of, the transformative potential of AI+MPS.

cs.AI↗

arXiv2025

A Local Polyak-Lojasiewicz and Descent Lemma of Gradient Descent For Overparametrized Linear Models

Most prior work on the convergence of gradient descent (GD) for overparameterized neural networks relies on strong assumptions on the step size (infinitesimal), the hidden-layer width (infinite), or the initialization (large, spectral, balanced). Recent efforts to relax these assumptions focus on two-layer linear networks trained with the squared loss. In this work, we derive a linear convergence rate for training two-layer linear neural networks with GD for general losses and under relaxed assumptions on the step size, width, and initialization. A key challenge in deriving this result is that classical ingredients for deriving convergence rates for nonconvex problems, such as the Polyak-{\L}ojasiewicz (PL) condition and Descent Lemma, do not hold globally for overparameterized neural networks. Here, we prove that these two conditions hold locally with local constants that depend on the weights. Then, we provide bounds on these local constants, which depend on the initialization of the weights, the current loss, and the global PL and smoothness constants of the non-overparameterized model. Based on these bounds, we derive a linear convergence rate for GD. Our convergence analysis not only improves upon prior results but also suggests a better choice for the step size, as verified through our numerical experiments.

cs.LG↗

arXiv2025

Understanding the Learning Dynamics of LoRA: A Gradient Flow Perspective on Low-Rank Adaptation in Matrix Factorization

Despite the empirical success of Low-Rank Adaptation (LoRA) in fine-tuning pre-trained models, there is little theoretical understanding of how first-order methods with carefully crafted initialization adapt models to new tasks. In this work, we take the first step towards bridging this gap by theoretically analyzing the learning dynamics of LoRA for matrix factorization (MF) under gradient flow (GF), emphasizing the crucial role of initialization. For small initialization, we theoretically show that GF converges to a neighborhood of the optimal solution, with smaller initialization leading to lower final error. Our analysis shows that the final error is affected by the misalignment between the singular spaces of the pre-trained model and the target matrix, and reducing the initialization scale improves alignment. To address this misalignment, we propose a spectral initialization for LoRA in MF and theoretically prove that GF with small spectral initialization converges to the fine-tuning task with arbitrary precision. Numerical experiments from MF and image classification validate our findings.

cs.LG↗

arXiv2025

Disentangling Safe and Unsafe Corruptions via Anisotropy and Locality

State-of-the-art machine learning systems are vulnerable to small perturbations to their input, where ``small'' is defined according to a threat model that assigns a positive threat to each perturbation. Most prior works define a task-agnostic, isotropic, and global threat, like the $\ell_p$ norm, where the magnitude of the perturbation fully determines the degree of the threat and neither the direction of the attack nor its position in space matter. However, common corruptions in computer vision, such as blur, compression, or occlusions, are not well captured by such threat models. This paper proposes a novel threat model called \texttt{Projected Displacement} (PD) to study robustness beyond existing isotropic and global threat models. The proposed threat model measures the threat of a perturbation via its alignment with \textit{unsafe directions}, defined as directions in the input space along which a perturbation of sufficient magnitude changes the ground truth class label. Unsafe directions are identified locally for each input based on observed training data. In this way, the PD threat model exhibits anisotropy and locality. Experiments on Imagenet-1k data indicate that, for any input, the set of perturbations with small PD threat includes \textit{safe} perturbations of large $\ell_p$ norm that preserve the true label, such as noise, blur and compression, while simultaneously excluding \textit{unsafe} perturbations that alter the true label. Unlike perceptual threat models based on embeddings of large-vision models, the PD threat model can be readily computed for arbitrary classification tasks without pre-training or finetuning. Further additional task annotation such as sensitivity to image regions or concept hierarchies can be easily integrated into the assessment of threat and thus the PD threat model presents practitioners with a flexible, task-driven threat specification.

cs.CV↗

arXiv2024

Guarantees of a Preconditioned Subgradient Algorithm for Overparameterized Asymmetric Low-rank Matrix Recovery

In this paper, we focus on a matrix factorization-based approach to recover low-rank {\it asymmetric} matrices from corrupted measurements. We propose an {\it Overparameterized Preconditioned Subgradient Algorithm (OPSA)} and provide, for the first time in the literature, linear convergence rates independent of the rank of the sought asymmetric matrix in the presence of gross corruptions. Our work goes beyond existing results in preconditioned-type approaches addressing their current limitation, i.e., the lack of convergence guarantees in the case of {\it asymmetric matrices of unknown rank}. By applying our approach to (robust) matrix sensing, we highlight its merits when the measurement operator satisfies a mixed-norm restricted isometry property. Lastly, we present extensive numerical experiments that validate our theoretical results and demonstrate the effectiveness of our approach for different levels of overparameterization and outlier corruptions.

math.OC↗

arXiv2024

Recommendation with Generative Models

Generative models are a class of AI models capable of creating new instances of data by learning and sampling from their statistical distributions. In recent years, these models have gained prominence in machine learning due to the development of approaches such as generative adversarial networks (GANs), variational autoencoders (VAEs), and transformer-based architectures such as GPT. These models have applications across various domains, such as image generation, text synthesis, and music composition. In recommender systems, generative models, referred to as Gen-RecSys, improve the accuracy and diversity of recommendations by generating structured outputs, text-based interactions, and multimedia content. By leveraging these capabilities, Gen-RecSys can produce more personalized, engaging, and dynamic user experiences, expanding the role of AI in eCommerce, media, and beyond. Our book goes beyond existing literature by offering a comprehensive understanding of generative models and their applications, with a special focus on deep generative models (DGMs) and their classification. We introduce a taxonomy that categorizes DGMs into three types: ID-driven models, large language models (LLMs), and multimodal models. Each category addresses unique technical and architectural advancements within its respective research area. This taxonomy allows researchers to easily navigate developments in Gen-RecSys across domains such as conversational AI and multimodal content generation. Additionally, we examine the impact and potential risks of generative models, emphasizing the importance of robust evaluation frameworks.

cs.IR↗

arXiv2024

Multi-modal Generative Models in Recommendation System

Many recommendation systems limit user inputs to text strings or behavior signals such as clicks and purchases, and system outputs to a list of products sorted by relevance. With the advent of generative AI, users have come to expect richer levels of interactions. In visual search, for example, a user may provide a picture of their desired product along with a natural language modification of the content of the picture (e.g., a dress like the one shown in the picture but in red color). Moreover, users may want to better understand the recommendations they receive by visualizing how the product fits their use case, e.g., with a representation of how a garment might look on them, or how a furniture item might look in their room. Such advanced levels of interaction require recommendation systems that are able to discover both shared and complementary information about the product across modalities, and visualize the product in a realistic and informative way. However, existing systems often treat multiple modalities independently: text search is usually done by comparing the user query to product titles and descriptions, while visual search is typically done by comparing an image provided by the customer to product images. We argue that future recommendation systems will benefit from a multi-modal understanding of the products that leverages the rich information retailers have about both customers and products to come up with the best recommendations. In this chapter we review recommendation systems that use multiple data modalities simultaneously.

cs.IR↗

arXiv2024

Large Language Model Driven Recommendation

While previous chapters focused on recommendation systems (RSs) based on standardized, non-verbal user feedback such as purchases, views, and clicks -- the advent of LLMs has unlocked the use of natural language (NL) interactions for recommendation. This chapter discusses how LLMs' abilities for general NL reasoning present novel opportunities to build highly personalized RSs -- which can effectively connect nuanced and diverse user preferences to items, potentially via interactive dialogues. To begin this discussion, we first present a taxonomy of the key data sources for language-driven recommendation, covering item descriptions, user-system interactions, and user profiles. We then proceed to fundamental techniques for LLM recommendation, reviewing the use of encoder-only and autoregressive LLM recommendation in both tuned and untuned settings. Afterwards, we move to multi-module recommendation architectures in which LLMs interact with components such as retrievers and RSs in multi-stage pipelines. This brings us to architectures for conversational recommender systems (CRSs), in which LLMs facilitate multi-turn dialogues where each turn presents an opportunity not only to make recommendations, but also to engage with the user in interactive preference elicitation, critiquing, and question-answering.

cs.AI↗

arXiv2024

Invertibility of Discrete-Time Linear Systems with Sparse Inputs

One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics, and spectral structure of a system have been used to characterize the well-posedness of this problem, without assumptions on the inputs. However, certain structural assumptions, such as input sparsity, have been shown to translate to practical gains in the performance of inversion algorithms, surpassing classical guarantees. Establishing necessary and sufficient conditions for left invertibility of systems with sparse inputs is therefore a crucial step toward understanding the performance limits of system inversion under structured input assumptions. In this work, we provide the first necessary and sufficient characterizations of left invertibility for linear systems with sparse inputs, echoing classic characterizations for standard linear systems. The key insight in deriving these results is in establishing the existence of two novel geometric invariants unique to the sparse-input setting, the weakly unobservable and strongly reachable subspace arrangements. By means of a concrete example, we demonstrate the utility of these characterizations. We conclude by discussing extensions and applications of this framework to several related problems in sparse control.

math.OC↗

arXiv2023

Semantic-aware Video Representation for Few-shot Action Recognition

Recent work on action recognition leverages 3D features and textual information to achieve state-of-the-art performance. However, most of the current few-shot action recognition methods still rely on 2D frame-level representations, often require additional components to model temporal relations, and employ complex distance functions to achieve accurate alignment of these representations. In addition, existing methods struggle to effectively integrate textual semantics, some resorting to concatenation or addition of textual and visual features, and some using text merely as an additional supervision without truly achieving feature fusion and information transfer from different modalities. In this work, we propose a simple yet effective Semantic-Aware Few-Shot Action Recognition (SAFSAR) model to address these issues. We show that directly leveraging a 3D feature extractor combined with an effective feature-fusion scheme, and a simple cosine similarity for classification can yield better performance without the need of extra components for temporal modeling or complex distance functions. We introduce an innovative scheme to encode the textual semantics into the video representation which adaptively fuses features from text and video, and encourages the visual encoder to extract more semantically consistent features. In this scheme, SAFSAR achieves alignment and fusion in a compact way. Experiments on five challenging few-shot action recognition benchmarks under various settings demonstrate that the proposed SAFSAR model significantly improves the state-of-the-art performance.

cs.CV↗

arXiv2023

Clustering-based Domain-Incremental Learning

We consider the problem of learning multiple tasks in a continual learning setting in which data from different tasks is presented to the learner in a streaming fashion. A key challenge in this setting is the so-called "catastrophic forgetting problem", in which the performance of the learner in an "old task" decreases when subsequently trained on a "new task". Existing continual learning methods, such as Averaged Gradient Episodic Memory (A-GEM) and Orthogonal Gradient Descent (OGD), address catastrophic forgetting by minimizing the loss for the current task without increasing the loss for previous tasks. However, these methods assume the learner knows when the task changes, which is unrealistic in practice. In this paper, we alleviate the need to provide the algorithm with information about task changes by using an online clustering-based approach on a dynamically updated finite pool of samples or gradients. We thereby successfully counteract catastrophic forgetting in one of the hardest settings, namely: domain-incremental learning, a setting for which the problem was previously unsolved. We showcase the benefits of our approach by applying these ideas to projection-based methods, such as A-GEM and OGD, which lead to task-agnostic versions of them. Experiments on real datasets demonstrate the effectiveness of the proposed strategy and its promising performance compared to state-of-the-art methods.

cs.LG↗

arXiv2023

Variational Information Pursuit with Large Language and Multimodal Models for Interpretable Predictions

Variational Information Pursuit (V-IP) is a framework for making interpretable predictions by design by sequentially selecting a short chain of task-relevant, user-defined and interpretable queries about the data that are most informative for the task. While this allows for built-in interpretability in predictive models, applying V-IP to any task requires data samples with dense concept-labeling by domain experts, limiting the application of V-IP to small-scale tasks where manual data annotation is feasible. In this work, we extend the V-IP framework with Foundational Models (FMs) to address this limitation. More specifically, we use a two-step process, by first leveraging Large Language Models (LLMs) to generate a sufficiently large candidate set of task-relevant interpretable concepts, then using Large Multimodal Models to annotate each data sample by semantic similarity with each concept in the generated concept set. While other interpretable-by-design frameworks such as Concept Bottleneck Models (CBMs) require an additional step of removing repetitive and non-discriminative concepts to have good interpretability and test performance, we mathematically and empirically justify that, with a sufficiently informative and task-relevant query (concept) set, the proposed FM+V-IP method does not require any type of concept filtering. In addition, we show that FM+V-IP with LLM generated concepts can achieve better test performance than V-IP with human annotated concepts, demonstrating the effectiveness of LLMs at generating efficient query sets. Finally, when compared to other interpretable-by-design frameworks such as CBMs, FM+V-IP can achieve competitive test performance using fewer number of concepts/queries in both cases with filtered or unfiltered concept sets.

cs.LG↗