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Elizaveta Demyanenko

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3 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

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

Davide Straziota
Elizaveta Demyanenko
Carlo Baldassi
Carlo Lucibello

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.

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NeurIPS Conference 2025 Conference Paper

On the Bias of Next-Token Predictors Toward Systematically Inefficient Reasoning: A Shortest-Path Case Study

Riccardo Alberghi
Elizaveta Demyanenko
Luca Biggio
Luca Saglietti

Recent advances in natural language processing highlight two key factors for improving reasoning in large language models (LLMs): (i) allocating more test-time compute tends to help on harder problems but often introduces redundancy in the reasoning trace, and (ii) compute is most effective when reasoning is systematic and incremental, forming structured chains of thought (CoTs) akin to human problem-solving. To study these factors in isolation, we introduce a controlled setting based on shortest-path tasks in layered graphs. We train decoder-only transformers on question–trace–answer triples using a custom tokenizer, comparing models trained on optimal bottom-up dynamic programming traces with those trained on longer, valid traces involving backtracking. Surprisingly, under the same training-token budget, the latter models generalize better to unseen graphs. This benefit is not due to length alone—injecting arbitrary redundancy into reasoning traces fails to help and can even hurt performance. Instead, we find that generalization correlates with the model's confidence in next-token prediction, suggesting that long, coherent, and locally incremental traces make the training signal easier to optimize.

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ICLR Conference 2021 Conference Paper

Entropic gradient descent algorithms and wide flat minima

Fabrizio Pittorino
Carlo Lucibello
Christoph Feinauer
Gabriele Perugini
Carlo Baldassi
Elizaveta Demyanenko
Riccardo Zecchina

The properties of flat minima in the empirical risk landscape of neural networks have been debated for some time. Increasing evidence suggests they possess better generalization capabilities with respect to sharp ones. In this work we first discuss the relationship between alternative measures of flatness: The local entropy, which is useful for analysis and algorithm development, and the local energy, which is easier to compute and was shown empirically in extensive tests on state-of-the-art networks to be the best predictor of generalization capabilities. We show semi-analytically in simple controlled scenarios that these two measures correlate strongly with each other and with generalization. Then, we extend the analysis to the deep learning scenario by extensive numerical validations. We study two algorithms, Entropy-SGD and Replicated-SGD, that explicitly include the local entropy in the optimization objective. We devise a training schedule by which we consistently find flatter minima (using both flatness measures), and improve the generalization error for common architectures (e.g. ResNet, EfficientNet).

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