Romain Cosentino

Romain Cosentino, Sarath Shekkizhar, Mahdi Soltanolkotabi et al.

Self-supervised learning (SSL) has emerged as a desirable paradigm in computer vision due to the inability of supervised models to learn representations that can generalize in domains with limited labels. The recent popularity of SSL has led to the development of several models that make use of diverse training strategies, architectures, and data augmentation policies with no existing unified framework to study or assess their effectiveness in transfer learning. We propose a data-driven geometric strategy to analyze different SSL models using local neighborhoods in the feature space induced by each. Unlike existing approaches that consider mathematical approximations of the parameters, individual components, or optimization landscape, our work aims to explore the geometric properties of the representation manifolds learned by SSL models. Our proposed manifold graph metrics (MGMs) provide insights into the geometric similarities and differences between available SSL models, their invariances with respect to specific augmentations, and their performances on transfer learning tasks. Our key findings are two fold: (i) contrary to popular belief, the geometry of SSL models is not tied to its training paradigm (contrastive, non-contrastive, and cluster-based); (ii) we can predict the transfer learning capability for a specific model based on the geometric properties of its semantic and augmentation manifolds.

Romain Cosentino, Anirvan Sengupta, Salman Avestimehr et al.

Self-supervised learning (SSL) is currently one of the premier techniques to create data representations that are actionable for transfer learning in the absence of human annotations. Despite their success, the underlying geometry of these representations remains elusive, which obfuscates the quest for more robust, trustworthy, and interpretable models. In particular, mainstream SSL techniques rely on a specific deep neural network architecture with two cascaded neural networks: the encoder and the projector. When used for transfer learning, the projector is discarded since empirical results show that its representation generalizes more poorly than the encoder's. In this paper, we investigate this curious phenomenon and analyze how the strength of the data augmentation policies affects the data embedding. We discover a non-trivial relation between the encoder, the projector, and the data augmentation strength: with increasingly larger augmentation policies, the projector, rather than the encoder, is more strongly driven to become invariant to the augmentations. It does so by eliminating crucial information about the data by learning to project it into a low-dimensional space, a noisy estimate of the data manifold tangent plane in the encoder representation. This analysis is substantiated through a geometrical perspective with theoretical and empirical results.

Romain Cosentino, Sarath Shekkizhar

The advancement of large language models (LLMs) for real-world applications hinges critically on enhancing their reasoning capabilities. In this work, we explore the reasoning abilities of large language models (LLMs) through their geometrical understanding. We establish a connection between the expressive power of LLMs and the density of their self-attention graphs. Our analysis demonstrates that the density of these graphs defines the intrinsic dimension of the inputs to the MLP blocks. We demonstrate through theoretical analysis and toy examples that a higher intrinsic dimension implies a greater expressive capacity of the LLM. We further provide empirical evidence linking this geometric framework to recent advancements in methods aimed at enhancing the reasoning capabilities of LLMs.

Randall Balestriero, Romain Cosentino, Sarath Shekkizhar

Large Language Models (LLMs) drive current AI breakthroughs despite very little being known about their internal representations. In this work, we propose to shed the light on LLMs inner mechanisms through the lens of geometry. In particular, we develop in closed form $(i)$ the intrinsic dimension in which the Multi-Head Attention embeddings are constrained to exist and $(ii)$ the partition and per-region affine mappings of the feedforward (MLP) network of LLMs' layers. Our theoretical findings further enable the design of novel principled solutions applicable to state-of-the-art LLMs. First, we show that, through our geometric understanding, we can bypass LLMs' RLHF protection by controlling the embedding's intrinsic dimension through informed prompt manipulation. Second, we derive interpretable geometrical features that can be extracted from any (pre-trained) LLM, providing a rich abstract representation of their inputs. We observe that these features are sufficient to help solve toxicity detection, and even allow the identification of various types of toxicity. Our results demonstrate how, even in large-scale regimes, exact theoretical results can answer practical questions in LLMs. Code: https://github.com/RandallBalestriero/SplineLLM

Romain Cosentino, Sarath Shekkizhar, Adam Earle et al.

Negotiation requires more than inferring what the other side wants: it requires using that information to make advantageous offers and counteroffers over multiple turns. We study whether large language model (LLM) agents do this in a controlled multi-attribute bargaining environment. We find that current LLM agents can model a counterparty's preferences, but do not reliably turn that knowledge into strategic bargaining. When given negotiating partner preference information, agents model it accurately and early in their reasoning traces, yet this does not reliably improve outcomes for the informed side. Turn-level analyses show why: agents often respond to what they believe the counterparty values, but do not consistently pair those moves with gains on their own high-value attributes. Sellers are more accommodating overall, and in asymmetric-information conditions, the informed side often makes the more weakly compensated concessions. Because agents fail to leverage this underlying utility structure for strategic advantage, their final agreements are heavily dictated by surface-level opening anchors rather than actual utility weights. Finally, requiring agents to explicitly state concession-for-reciprocity trades before making an offer makes individual turns look more strategic, but ultimately fails to improve the efficiency of the final agreements.

Sarath Shekkizhar, Romain Cosentino, Adam Earle et al.

As large language model (LLM) based agents interact autonomously with one another, a new class of failures emerges that cannot be predicted from single agent performance: behavioral drifts in agent-agent conversations (AxA). Unlike human-agent interactions, where humans ground and steer conversations, AxA lacks such stabilizing signals, making these failures unique. We investigate one such failure, echoing, where agents abandon their assigned roles and instead mirror their conversational partners, undermining their intended objectives. Through experiments across $60$ AxA configurations, $3$ domains, and $2000+$ conversations, we demonstrate that echoing occurs across three major LLM providers, with echoing rates from $5\%$ to $70\%$ depending on the model and domain. Moreover, we find that echoing is persistent even in advanced reasoning models with substantial rates ($32.8\%$) that are not reduced by increased reasoning efforts. We analyze prompt impacts, conversation dynamics, showing that echoing arises as interaction grows longer ($7+$ turns in experiments) and is not merely an artifact of sub-optimal prompting. Finally, we introduce a protocol-level mitigation in which targeted use of structured responses reduces echoing to $9\%$.

Romain Cosentino, Sarath Shekkizhar, Adam Earle

We develop a theoretical framework for agent-to-agent interactions in multi-agent scenarios. We consider the setup in which two language model based agents perform iterative gradient updates toward their respective objectives in-context, using the output of the other agent as input. We characterize the generation dynamics associated with the interaction when the agents have misaligned objectives, and show that this results in a biased equilibrium where neither agent reaches its target - with the residual errors predictable from the objective gap and the geometry induced by the prompt of each agent. We establish the conditions for asymmetric convergence and provide an algorithm that provably achieves an adversarial result, producing one-sided success. Experiments with trained transformer models as well as GPT$5$ for the task of in-context linear regression validate the theory. Our framework presents a setup to study, predict, and defend multi-agent systems; explicitly linking prompt design and interaction setup to stability, bias, and robustness.

Romain Cosentino

We develop a continual learning method for pretrained models that \emph{requires no access to old-task data}, addressing a practical barrier in foundation model adaptation where pretraining distributions are often unavailable. Our key observation is that pretrained networks exhibit substantial \emph{geometric redundancy}, and that this redundancy can be exploited in two complementary ways. First, redundant neurons provide a proxy for dominant pretraining-era feature directions, enabling the construction of approximately protected update subspaces directly from pretrained weights. Second, redundancy offers a natural bias for \emph{where} to place plasticity: by restricting updates to a subset of redundant neurons and constraining the remaining degrees of freedom, we obtain update families with reduced functional drift on the old-data distribution and improved worst-case retention guarantees. These insights lead to \textsc{PLATE} (\textbf{Pla}sticity-\textbf{T}unable \textbf{E}fficient Adapters), a continual learning method requiring no past-task data that provides explicit control over the plasticity-retention trade-off. PLATE parameterizes each layer with a structured low-rank update $ΔW = B A Q^\top$, where $B$ and $Q$ are computed once from pretrained weights and kept frozen, and only $A$ is trained on the new task. The code is available at https://github.com/SalesforceAIResearch/PLATE.

Sarath Shekkizhar, Romain Cosentino, Adam Earle

Standard LLM benchmarks evaluate the assistant turn: the model generates a response to an input, a verifier scores correctness, and the analysis ends. This paradigm leaves unmeasured whether the LLM encodes any awareness of what follows the assistant response. We propose user-turn generation as a probe of this gap: given a conversation context of user query and assistant response, we let a model generate under the user role. If the model's weights encode interaction awareness, the generated user turn will be a grounded follow-up that reacts to the preceding context. Through experiments across $11$ open-weight LLMs (Qwen3.5, gpt-oss, GLM) and $5$ datasets (math reasoning, instruction following, conversation), we show that interaction awareness is decoupled from task accuracy. In particular, within the Qwen3.5 family, GSM8K accuracy scales from $41\%$ ($0.8$B) to $96.8\%$ ($397$B-A$17$B), yet genuine follow-up rates under deterministic generation remain near zero. In contrast, higher temperature sampling reveals interaction awareness is latent with follow up rates reaching $22\%$. Controlled perturbations validate that the proposed probe measures a real property of the model, and collaboration-oriented post-training on Qwen3.5-2B demonstrates an increase in follow-up rates. Our results show that user-turn generation captures a dimension of LLM behavior, interaction awareness, that is unexplored and invisible with current assistant-only benchmarks.

Sarath Shekkizhar, Romain Cosentino

This paper investigates multimodal agents, in particular, OpenAI's Computer-User Agent (CUA), trained to control and complete tasks through a standard computer interface, similar to humans. We evaluated the agent's performance on the New York Times Wordle game to elicit model behaviors and identify shortcomings. Our findings revealed a significant discrepancy in the model's ability to recognize colors correctly depending on the context. The model had a $5.36\%$ success rate over several hundred runs across a week of Wordle. Despite the immense enthusiasm surrounding AI agents and their potential to usher in Artificial General Intelligence (AGI), our findings reinforce the fact that even simple tasks present substantial challenges for today's frontier AI models. We conclude with a discussion of the potential underlying causes, implications for future development, and research directions to improve these AI systems.

Romain Cosentino, Randall Balestriero, Yanis Bahroun et al.

K-means defines one of the most employed centroid-based clustering algorithms with performances tied to the data's embedding. Intricate data embeddings have been designed to push $K$-means performances at the cost of reduced theoretical guarantees and interpretability of the results. Instead, we propose preserving the intrinsic data space and augment K-means with a similarity measure invariant to non-rigid transformations. This enables (i) the reduction of intrinsic nuisances associated with the data, reducing the complexity of the clustering task and increasing performances and producing state-of-the-art results, (ii) clustering in the input space of the data, leading to a fully interpretable clustering algorithm, and (iii) the benefit of convergence guarantees.

Romain Cosentino, Randall Balestriero, Yanis Bahroun et al.

We design an interpretable clustering algorithm aware of the nonlinear structure of image manifolds. Our approach leverages the interpretability of $K$-means applied in the image space while addressing its clustering performance issues. Specifically, we develop a measure of similarity between images and centroids that encompasses a general class of deformations: diffeomorphisms, rendering the clustering invariant to them. Our work leverages the Thin-Plate Spline interpolation technique to efficiently learn diffeomorphisms best characterizing the image manifolds. Extensive numerical simulations show that our approach competes with state-of-the-art methods on various datasets.

Romain Cosentino, Randall Balestriero

In this work, we propose the Sparse Multi-Family Deep Scattering Network (SMF-DSN), a novel architecture exploiting the interpretability of the Deep Scattering Network (DSN) and improving its expressive power. The DSN extracts salient and interpretable features in signals by cascading wavelet transforms, complex modulus and extract the representation of the data via a translation-invariant operator. First, leveraging the development of highly specialized wavelet filters over the last decades, we propose a multi-family approach to DSN. In particular, we propose to cross multiple wavelet transforms at each layer of the network, thus increasing the feature diversity and removing the need for an expert to select the appropriate filter. Secondly, we develop an optimal thresholding strategy adequate for the DSN that regularizes the network and controls possible instabilities induced by the signals, such as non-stationary noise. Our systematic and principled solution sparsifies the network's latent representation by acting as a local mask distinguishing between activity and noise. The SMF-DSN enhances the DSN by (i) increasing the diversity of the scattering coefficients and (ii) improves its robustness with respect to non-stationary noise.

Romain Cosentino, Randall Balestriero, Richard Baraniuk et al.

A big mystery in deep learning continues to be the ability of methods to generalize when the number of model parameters is larger than the number of training examples. In this work, we take a step towards a better understanding of the underlying phenomena of Deep Autoencoders (AEs), a mainstream deep learning solution for learning compressed, interpretable, and structured data representations. In particular, we interpret how AEs approximate the data manifold by exploiting their continuous piecewise affine structure. Our reformulation of AEs provides new insights into their mapping, reconstruction guarantees, as well as an interpretation of commonly used regularization techniques. We leverage these findings to derive two new regularizations that enable AEs to capture the inherent symmetry in the data. Our regularizations leverage recent advances in the group of transformation learning to enable AEs to better approximate the data manifold without explicitly defining the group underlying the manifold. Under the assumption that the symmetry of the data can be explained by a Lie group, we prove that the regularizations ensure the generalization of the corresponding AEs. A range of experimental evaluations demonstrate that our methods outperform other state-of-the-art regularization techniques.

Randall Balestriero, Romain Cosentino, Behnaam Aazhang et al.

We study the geometry of deep (neural) networks (DNs) with piecewise affine and convex nonlinearities. The layers of such DNs have been shown to be {\em max-affine spline operators} (MASOs) that partition their input space and apply a region-dependent affine mapping to their input to produce their output. We demonstrate that each MASO layer's input space partitioning corresponds to a {\em power diagram} (an extension of the classical Voronoi tiling) with a number of regions that grows exponentially with respect to the number of units (neurons). We further show that a composition of MASO layers (e.g., the entire DN) produces a progressively subdivided power diagram and provide its analytical form. The subdivision process constrains the affine maps on the (exponentially many) power diagram regions to greatly reduce their complexity. For classification problems, we obtain a formula for a MASO DN's decision boundary in the input space plus a measure of its curvature that depends on the DN's nonlinearities, weights, and architecture. Numerous numerical experiments support and extend our theoretical results.

Romain Cosentino, Randall Balestriero, Richard Baraniuk et al.

In this work, we derive a generic overcomplete frame thresholding scheme based on risk minimization. Overcomplete frames being favored for analysis tasks such as classification, regression or anomaly detection, we provide a way to leverage those optimal representations in real-world applications through the use of thresholding. We validate the method on a large scale bird activity detection task via the scattering network architecture performed by means of continuous wavelets, known for being an adequate dictionary in audio environments.