arXiv subjects

Davide Straziota

Publications and source records attributed to Davide Straziota.

3 recordsLinked to original sources

arXiv2025

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↗

arXiv2025

Generative diffusion for perceptron problems: statistical physics analysis and efficient algorithms

We consider random instances of non-convex perceptron problems in the high-dimensional limit of a large number of examples $M$ and weights $N$, with finite load $\alpha = M/N$. We develop a formalism based on replica theory to predict the fundamental limits of efficiently sampling the solution space using generative diffusion algorithms, conjectured to be saturated when the score function is provided by Approximate Message Passing. For the spherical perceptron with negative margin $\kappa$, we find that the uniform distribution over solutions can be efficiently sampled in most of the Replica Symmetric region of the $\alpha$-$\kappa$ plane. In contrast, for binary weights, sampling from the uniform distribution remains intractable. A theoretical analysis of this obstruction leads us to identify a potential $U(s) = -\log(s)$, under which the corresponding tilted distribution becomes efficiently samplable via diffusion. Moreover, we show numerically that an annealing procedure over the shape of this potential yields a fast and robust Markov Chain Monte Carlo algorithm for sampling the solution space of the binary perceptron.

cond-mat.dis-nn↗

arXiv2025

Isolating the hard core of phaseless inference: the Phase selection formulation

Real-valued Phase retrieval is a non-convex continuous inference problem, where a high-dimensional signal is to be reconstructed from a dataset of signless linear measurements. Focusing on the noiseless case, we aim to disentangle the two distinct sub-tasks entailed in the Phase retrieval problem: the hard combinatorial problem of retrieving the missing signs of the measurements, and the nested convex problem of regressing the input-output observations to recover the hidden signal. To this end, we introduce and analytically characterize a two-level formulation of the problem, called ``Phase selection''. Within the Replica Theory framework, we perform a large deviation analysis to characterize the minimum mean squared error achievable with different guesses for the hidden signs. Moreover, we study the free-energy landscape of the problem when both levels are optimized simultaneously, as a function of the dataset size. At low temperatures, in proximity to the Bayes-optimal threshold -- previously derived in the context of Phase retrieval -- we detect the coexistence of two free-energy branches, one connected to the random initialization condition and a second to the signal. We derive the phase diagram for a first-order transition after which the two branches merge. Interestingly, introducing an $L_2$ regularization in the regression sub-task can anticipate the transition to lower dataset sizes, at the cost of a bias in the signal reconstructions which can be removed by annealing the regularization intensity. Finally, we study the inference performance of three meta-heuristics in the context of Phase selection: Simulated Annealing, Approximate Message Passing, and Langevin Dynamics on the continuous relaxation of the sign variables. With simultaneous annealing of the temperature and the $L_2$ regularization, they are shown to approach the Bayes-optimal sample efficiency.

cond-mat.dis-nn↗