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Stefano Peluchetti

Stefano Peluchetti contributes to research discovery and scholarly infrastructure.

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Machine Learning math.ST Statistics Theory Computer Vision math.PR Methodology

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preprint2026arXiv

Binomial flows: Denoising and flow matching for discrete ordinal data

Flow-based generative modeling in continuous spaces exploit Tweedie's formula to express the denoiser (learned in training) as a score function (used in sampling). In contrast, this relation has been largely missing in the discrete setting where common approaches focus on learning discrete scores and rates. In this work we close this gap for discrete non-negative ordinal data by introducing Binomial flows. Our framework provides a simple recipe for training a discrete diffusion model which simultaneously denoises, samples, and estimates exact likelihoods. We verify our methodology on synthetic examples and obtain competitive results on real-world data sets.

preprint2026arXiv

KamonBench: A Grammar-Based Dataset for Evaluating Compositional Factor Recovery in Vision-Language Models

Kamon (family crests) are an important part of Japanese culture and a natural test case for compositional visual recognition: each crest combines a small number of symbolic choices, but the space of possible descriptions is sparse. We introduce KamonBench, a grammar-based image-to-structure benchmark with 20,000 synthetic composite crests and auxiliary component examples. Each composite crest is paired with a formal kamon description language - "kamon yōgo" - description, a segmented Japanese analysis, an English translation, and a non-linguistic program code. Because each synthetic crest is generated from known factors, namely container, modifier, and motif, KamonBench supports evaluation beyond caption-level accuracy: direct program-code factor metrics, controlled factor-pair recombination splits, counterfactual motif-sensitivity groups under fixed container-modifier contexts, and linear probes of factor accessibility. We include baseline results for a ViT encoder/Transformer decoder and two VGG n-gram decoders, with and without learned positional masks. KamonBench therefore provides a controlled testbed for sparse compositional visual recognition and factor recovery in vision-language models.

preprint2023arXiv

Large-width asymptotics for ReLU neural networks with $α$-Stable initializations

There is a recent and growing literature on large-width asymptotic properties of Gaussian neural networks (NNs), namely NNs whose weights are initialized as Gaussian distributions. Two popular problems are: i) the study of the large-width distributions of NNs, which characterizes the infinitely wide limit of a rescaled NN in terms of a Gaussian stochastic process; ii) the study of the large-width training dynamics of NNs, which characterizes the infinitely wide dynamics in terms of a deterministic kernel, referred to as the neural tangent kernel (NTK), and shows that, for a sufficiently large width, the gradient descent achieves zero training error at a linear rate. In this paper, we consider these problems for $α$-Stable NNs, namely NNs whose weights are initialized as $α$-Stable distributions with $α\in(0,2]$. First, for $α$-Stable NNs with a ReLU activation function, we show that if the NN's width goes to infinity then a rescaled NN converges weakly to an $α$-Stable stochastic process. As a difference with respect to the Gaussian setting, our result shows that the choice of the activation function affects the scaling of the NN, that is: to achieve the infinitely wide $α$-Stable process, the ReLU activation requires an additional logarithmic term in the scaling with respect to sub-linear activations. Then, we study the large-width training dynamics of $α$-Stable ReLU-NNs, characterizing the infinitely wide dynamics in terms of a random kernel, referred to as the $α$-Stable NTK, and showing that, for a sufficiently large width, the gradient descent achieves zero training error at a linear rate. The randomness of the $α$-Stable NTK is a further difference with respect to the Gaussian setting, that is: within the $α$-Stable setting, the randomness of the NN at initialization does not vanish in the large-width regime of the training.

preprint2022arXiv

Deep Stable neural networks: large-width asymptotics and convergence rates

In modern deep learning, there is a recent and growing literature on the interplay between large-width asymptotic properties of deep Gaussian neural networks (NNs), i.e. deep NNs with Gaussian-distributed weights, and Gaussian stochastic processes (SPs). Such an interplay has proved to be critical in Bayesian inference under Gaussian SP priors, kernel regression for infinitely wide deep NNs trained via gradient descent, and information propagation within infinitely wide NNs. Motivated by empirical analyses that show the potential of replacing Gaussian distributions with Stable distributions for the NN's weights, in this paper we present a rigorous analysis of the large-width asymptotic behaviour of (fully connected) feed-forward deep Stable NNs, i.e. deep NNs with Stable-distributed weights. We show that as the width goes to infinity jointly over the NN's layers, i.e. the ``joint growth" setting, a rescaled deep Stable NN converges weakly to a Stable SP whose distribution is characterized recursively through the NN's layers. Because of the non-triangular structure of the NN, this is a non-standard asymptotic problem, to which we propose an inductive approach of independent interest. Then, we establish sup-norm convergence rates of the rescaled deep Stable NN to the Stable SP, under the ``joint growth" and a ``sequential growth" of the width over the NN's layers. Such a result provides the difference between the ``joint growth" and the ``sequential growth" settings, showing that the former leads to a slower rate than the latter, depending on the depth of the layer and the number of inputs of the NN. Our work extends some recent results on infinitely wide limits for deep Gaussian NNs to the more general deep Stable NNs, providing the first result on convergence rates in the ``joint growth" setting.

preprint2022arXiv

Learning-augmented count-min sketches via Bayesian nonparametrics

The count-min sketch (CMS) is a time and memory efficient randomized data structure that provides estimates of tokens' frequencies in a data stream of tokens, i.e. point queries, based on random hashed data. A learning-augmented version of the CMS, referred to as CMS-DP, has been proposed by Cai, Mitzenmacher and Adams (\textit{NeurIPS} 2018), and it relies on Bayesian nonparametric (BNP) modeling of the data stream of tokens via a Dirichlet process (DP) prior, with estimates of a point query being obtained as suitable mean functionals of the posterior distribution of the point query, given the hashed data. While the CMS-DP has proved to improve on some aspects of CMS, it has the major drawback of arising from a ``constructive" proof that builds upon arguments tailored to the DP prior, namely arguments that are not usable for other nonparametric priors. In this paper, we present a ``Bayesian" proof of the CMS-DP that has the main advantage of building upon arguments that are usable, in principle, within a broad class of nonparametric priors arising from normalized completely random measures. This result leads to develop a novel learning-augmented CMS under power-law data streams, referred to as CMS-PYP, which relies on BNP modeling of the data stream of tokens via a Pitman-Yor process (PYP) prior. Under this more general framework, we apply the arguments of the ``Bayesian" proof of the CMS-DP, suitably adapted to the PYP prior, in order to compute the posterior distribution of a point query, given the hashed data. Applications to synthetic data and real textual data show that the CMS-PYP outperforms the CMS and the CMS-DP in estimating low-frequency tokens, which are known to be of critical interest in textual data, and it is competitive with respect to a variation of the CMS designed for low-frequency tokens. An extension of our BNP approach to more general queries is also discussed.

preprint2021arXiv

A Bayesian nonparametric approach to count-min sketch under power-law data streams

The count-min sketch (CMS) is a randomized data structure that provides estimates of tokens' frequencies in a large data stream using a compressed representation of the data by random hashing. In this paper, we rely on a recent Bayesian nonparametric (BNP) view on the CMS to develop a novel learning-augmented CMS under power-law data streams. We assume that tokens in the stream are drawn from an unknown discrete distribution, which is endowed with a normalized inverse Gaussian process (NIGP) prior. Then, using distributional properties of the NIGP, we compute the posterior distribution of a token's frequency in the stream, given the hashed data, and in turn corresponding BNP estimates. Applications to synthetic and real data show that our approach achieves a remarkable performance in the estimation of low-frequency tokens. This is known to be a desirable feature in the context of natural language processing, where it is indeed common in the context of the power-law behaviour of the data.

preprint2020arXiv

Infinitely deep neural networks as diffusion processes

When the parameters are independently and identically distributed (initialized) neural networks exhibit undesirable properties that emerge as the number of layers increases, e.g. a vanishing dependency on the input and a concentration on restrictive families of functions including constant functions. We consider parameter distributions that shrink as the number of layers increases in order to recover well-behaved stochastic processes in the limit of infinite depth. This leads to set forth a link between infinitely deep residual networks and solutions to stochastic differential equations, i.e. diffusion processes. We show that these limiting processes do not suffer from the aforementioned issues and investigate their properties.

preprint2020arXiv

Stable behaviour of infinitely wide deep neural networks

We consider fully connected feed-forward deep neural networks (NNs) where weights and biases are independent and identically distributed as symmetric centered stable distributions. Then, we show that the infinite wide limit of the NN, under suitable scaling on the weights, is a stochastic process whose finite-dimensional distributions are multivariate stable distributions. The limiting process is referred to as the stable process, and it generalizes the class of Gaussian processes recently obtained as infinite wide limits of NNs (Matthews at al., 2018b). Parameters of the stable process can be computed via an explicit recursion over the layers of the network. Our result contributes to the theory of fully connected feed-forward deep NNs, and it paves the way to expand recent lines of research that rely on Gaussian infinite wide limits.

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