arXiv subjects

Jerome Garnier-Brun

Publications and source records attributed to Jerome Garnier-Brun.

9 recordsLinked to original sources

arXiv2026

Replication and Information Extraction in a Minimal Agent-Environment Model

How can information be extracted from data without explicit guidance or rewards? We investigate this question in a minimal setting where a classifying agent is exposed to a stream of structured data produced by a generative environment, and evolves by seeking consistency of its own labels in time. We find that imposing a simplicity bias on the classification rule can drive the dynamics toward label-coherent steady states, which we coin functional replicators. Remarkably, these persistent labeling rules align with the latent structure of the data. Using analytical tools from statistical mechanics, we characterize this spontaneous learning phase transition. Extending the analysis to a population of agents that pool labels from one another, we show that interaction reshapes the learning phase boundary, in some regimes enabling spontaneous learning that no isolated agent can achieve, while suppressing it in others. Our minimal framework thus opens a route to decentralized learning through label exchange alone, requiring no access to the internal weights of other agents.

cond-mat.dis-nn↗

arXiv2026

Biased Generalization in Diffusion Models

Generalization in generative modeling is defined as the ability to learn an underlying distribution from a finite dataset and produce novel samples, with evaluation largely driven by held-out performance and perceived sample quality. In practice, training is often stopped at the minimum of the test loss, taken as an operational indicator of generalization. We challenge this viewpoint by identifying a phase of biased generalization during training, in which the model continues to decrease the test loss while favoring samples with anomalously high proximity to training data. By training the same network on two disjoint datasets and comparing the mutual distances of generated samples and their similarity to training data, we introduce a quantitative measure of bias and demonstrate its presence on real images. We then study the mechanism of bias, using a controlled hierarchical data model where access to exact scores and ground-truth statistics allows us to precisely characterize its onset. We attribute this phenomenon to the sequential nature of feature learning in deep networks, where coarse structure is learned early in a data-independent manner, while finer features are resolved later in a way that increasingly depends on individual training samples. Our results show that early stopping at the test loss minimum, while optimal under standard generalization criteria, may be insufficient for privacy-critical applications.

cs.LG↗

arXiv2025

Hydrodynamics of Cooperation and Self-Interest in a Two-Population Occupation Model

We study the hydrodynamics of a system of agents who optimize either their individual utility (self-interest) or the collective welfare (cooperation). When agents act selfishly, their interactions are non-reciprocal, driving the system out of equilibrium; by contrast, purely altruistic dynamics restore reciprocity and yield an equilibrium-like description. We investigate how mixtures of these two behaviors shape the macroscopic properties of the liquid of agents. For highly rational agents, we find that introducing a small fraction of altruists can suppress the sub-optimal clustering induced by selfish dynamics. This phenomenon can be attributed to altruists localizing at interfaces and acting as effective surfactants, shedding a new light on earlier findings in fixed neighborhood-based models [Phys. Rev. Lett. \textbf{120}, 208301 (2018)]. When agents are boundedly rational, we introduce a well-mixed approximation that reduces the two-population model to a single effective scalar field theory. This allows us to leverage state-of-the-art tools from active matter to analytically characterize how altruism modifies surface tension and nucleation dynamics.

cond-mat.stat-mech↗

arXiv2025

How transformers learn structured data: insights from hierarchical filtering

Understanding the learning process and the embedded computation in transformers is becoming a central goal for the development of interpretable AI. In the present study, we introduce a hierarchical filtering procedure for data models of sequences on trees, allowing us to hand-tune the range of positional correlations in the data. Leveraging this controlled setting, we provide evidence that vanilla encoder-only transformers can approximate the exact inference algorithm when trained on root classification and masked language modeling tasks, and study how this computation is discovered and implemented. We find that correlations at larger distances, corresponding to increasing layers of the hierarchy, are sequentially included by the network during training. By comparing attention maps from models trained with varying degrees of filtering and by probing the different encoder levels, we find clear evidence of a reconstruction of correlations on successive length scales corresponding to the various levels of the hierarchy, which we relate to a plausible implementation of the exact inference algorithm within the same architecture.

cs.LG↗

arXiv2024

Socioeconomic agents as active matter in nonequilibrium Sakoda-Schelling models

How robust are socioeconomic agent-based models with respect to the details of the agents' decision rule? We tackle this question by considering an occupation model in the spirit of the Sakoda-Schelling model, historically introduced to shed light on segregation dynamics among human groups. For a large class of utility functions and decision rules, we pinpoint the nonequilibrium nature of the agent dynamics, while recovering the equilibrium-like phase separation phenomenology. Within the mean field approximation we show how the model can be mapped, to some extent, onto an active matter field description. Finally, we consider non-reciprocal interactions between two populations, and show how they can lead to non-steady macroscopic behavior. We believe our approach provides a unifying framework to further study geography-dependent agent-based models, notably paving the way for joint consideration of population and price dynamics within a field theoretic approach.

cond-mat.stat-mech↗

arXiv2024

Unlearnable Games and "Satisficing'' Decisions: A Simple Model for a Complex World

As a schematic model of the complexity economic agents are confronted with, we introduce the ``SK-game'', a discrete time binary choice model inspired from mean-field spin-glasses. We show that even in a completely static environment, agents are unable to learn collectively-optimal strategies. This is either because the learning process gets trapped in a sub-optimal fixed point, or because learning never converges and leads to a never ending evolution of agents intentions. Contrarily to the hope that learning might save the standard ``rational expectation'' framework in economics, we argue that complex situations are generically unlearnable and agents must do with satisficing solutions, as argued long ago by Herbert Simon (Simon 1955). Only a centralized, omniscient agent endowed with enormous computing power could qualify to determine the optimal strategy of all agents. Using a mix of analytical arguments and numerical simulations, we find that (i) long memory of past rewards is beneficial to learning whereas over-reaction to recent past is detrimental and leads to cycles or chaos; (ii) increased competition destabilizes fixed points and leads first to chaos and, in the high competition limit, to quasi-cycles; (iii) some amount of randomness in the learning process, perhaps paradoxically, allows the system to reach better collective decisions; (iv) non-stationary, ``aging'' behaviour spontaneously emerge in a large swath of parameter space of our complex but static world. On the positive side, we find that the learning process allows cooperative systems to coordinate around satisficing solutions with rather high (but markedly sub-optimal) average reward. However, hyper-sensitivity to the game parameters makes it impossible to predict ex ante who will be better or worse off in our stylized economy.

cond-mat.stat-mech↗

arXiv2023

Thermodynamic bounds on correlation times

We derive a variational expression for the correlation time of physical observables in steady-state diffusive systems. As a consequence of this variational expression, we obtain lower bounds on the correlation time, which provide speed limits on the self-averaging of observables. In equilibrium, the bound takes the form of a tradeoff relation between the long- and short-time fluctuations of an observable. Out of equilibrium, the tradeoff can be violated, leading to an acceleration of self-averaging. We relate this violation to the steady-state entropy production rate, as well as the geometric structure of the irreversible currents, giving rise to two complementary speed limits. One of these can be formulated as a lower estimate on the entropy production from the measurement of time-symmetric observables. Using an illustrating example, we show the intricate behavior of the correlation time out of equilibrium for different classes of observables and how this can be used to partially infer dissipation even if no time-reversal symmetry breaking can be observed in the trajectories of the observable.

cond-mat.stat-mech↗

arXiv2022

Bounded Rationality and Animal Spirits: A Fluctuation-Response Approach to Slutsky Matrices

The Slutsky equation, central in consumer choice theory, is derived from the usual hypotheses underlying most standard models in Economics, such as full rationality, homogeneity, and absence of interactions. We present a statistical physics framework that allows us to relax such assumptions. We first derive a general fluctuation-response formula that relates the Slutsky matrix to spontaneous fluctuations of consumption rather than to response to changing prices and budget. We then show that, within our hypotheses, the symmetry of the Slutsky matrix remains valid even when agents are only boundedly rational but non-interacting. We then propose a model where agents are influenced by the choice of others, leading to a phase transition beyond which consumption is dominated by herding (or `"fashion") effects. In this case, the individual Slutsky matrix is no longer symmetric, even for fully rational agents. The vicinity of the transition features a peak in asymmetry.

econ.TH↗

arXiv2021

A new spin on optimal portfolios and ecological equilibria

We consider the classical problem of optimal portfolio construction with the constraint that no short position is allowed, or equivalently the valid equilibria of multispecies Lotka-Volterra equations with self-regulation in the special case where the interaction matrix is of unit rank, corresponding to species competing for a common resource. We compute the average number of solutions and show that its logarithm grows as $N^α$, where $N$ is the number of assets or species and $α\leq 2/3$ depends on the interaction matrix distribution. We conjecture that the most likely number of solutions is much smaller and related to the typical sparsity $m(N)$ of the solutions, which we compute explicitly. We also find that the solution landscape is similar to that of spin-glasses, i.e. very different configurations are quasi-degenerate. Correspondingly, "disorder chaos" is also present in our problem. We discuss the consequence of such a property for portfolio construction and ecologies, and question the meaning of rational decisions when there is a very large number "satisficing" solutions.

cond-mat.stat-mech↗