Gianluigi Silvestri

Gianluigi Silvestri, Fabio Valerio Massoli, Tribhuvanesh Orekondy et al.

A promising way to mitigate the expensive process of obtaining a high-dimensional signal is to acquire a limited number of low-dimensional measurements and solve an under-determined inverse problem by utilizing the structural prior about the signal. In this paper, we focus on adaptive acquisition schemes to save further the number of measurements. To this end, we propose a reinforcement learning-based approach that sequentially collects measurements to better recover the underlying signal by acquiring fewer measurements. Our approach applies to general inverse problems with continuous action spaces and jointly learns the recovery algorithm. Using insights obtained from theoretical analysis, we also provide a probabilistic design for our methods using variational formulation. We evaluate our approach on multiple datasets and with two measurement spaces (Gaussian, Radon). Our results confirm the benefits of adaptive strategies in low-acquisition horizon settings.

Gianluigi Silvestri, Daan Roos, Luca Ambrogioni

In this work, we provide a deterministic alternative to the stochastic variational training of generative autoencoders. We refer to these new generative autoencoders as AutoEncoders within Flows (AEF), since the encoder and decoder are defined as affine layers of an overall invertible architecture. This results in a deterministic encoding of the data, as opposed to the stochastic encoding of VAEs. The paper introduces two related families of AEFs. The first family relies on a partition of the ambient space and is trained by exact maximum-likelihood. The second family exploits a deterministic expansion of the ambient space and is trained by maximizing the log-probability in this extended space. This latter case leaves complete freedom in the choice of encoder, decoder and prior architectures, making it a drop-in replacement for the training of existing VAEs and VAE-style models. We show that these AEFs can have strikingly higher performance than architecturally identical VAEs in terms of log-likelihood and sample quality, especially for low dimensional latent spaces. Importantly, we show that AEF samples are substantially sharper than VAE samples.

Gianluigi Silvestri, Luca Ambrogioni, Chieh-Hsin Lai et al.

Consistency Training (CT) has recently emerged as a strong alternative to diffusion models for image generation. However, non-distillation CT often suffers from high variance and instability, motivating ongoing research into its training dynamics. We propose Variational Consistency Training (VCT), a flexible and effective framework compatible with various forward kernels, including those in flow matching. Its key innovation is a learned noise-data coupling scheme inspired by Variational Autoencoders, where a data-dependent encoder models noise emission. This enables VCT to adaptively learn noise-todata pairings, reducing training variance relative to the fixed, unsorted pairings in classical CT. Experiments on multiple image datasets demonstrate significant improvements: our method surpasses baselines, achieves state-of-the-art FID among non-distillation CT approaches on CIFAR-10, and matches SoTA performance on ImageNet 64 x 64 with only two sampling steps. Code is available at https://github.com/sony/vct.

Gianluigi Silvestri, Luca Ambrogioni

Current state-of-the-art generative approaches frequently rely on a two-stage training procedure, where an autoencoder (often a VAE) first performs dimensionality reduction, followed by training a generative model on the learned latent space. While effective, this introduces computational overhead and increased sampling times. We challenge this paradigm by proposing Consistency Training of Variational AutoEncoders (CoVAE), a novel single-stage generative autoencoding framework that adopts techniques from consistency models to train a VAE architecture. The CoVAE encoder learns a progressive series of latent representations with increasing encoding noise levels, mirroring the forward processes of diffusion and flow matching models. This sequence of representations is regulated by a time dependent $β$ parameter that scales the KL loss. The decoder is trained using a consistency loss with variational regularization, which reduces to a conventional VAE loss at the earliest latent time. We show that CoVAE can generate high-quality samples in one or few steps without the use of a learned prior, significantly outperforming equivalent VAEs and other single-stage VAEs methods. Our approach provides a unified framework for autoencoding and diffusion-style generative modeling and provides a viable route for one-step generative high-performance autoencoding. Our code is publicly available at https://github.com/gisilvs/covae.

Gianluigi Silvestri, Edoardo Cetin

Reasoning-oriented language models achieve strong performance by generating long chain-of-thought traces at inference time. However, this capability comes with substantial and often excessive computational cost, which can materialize in redundant or inefficient reasoning. We study this setting and introduce Truncated-Reasoning Self-Distillation (TRSD), a lightweight post-training procedure that encourages models to produce correct predictions from partial reasoning traces. In TRSD, a frozen teacher model first generates a full reasoning trace and evaluates the corresponding answer distribution conditioned on the prompt and the complete reasoning to construct a synthetic training target. A student model with the same architecture is then trained to match the teacher's answer distribution while being conditioned only on a truncated prefix of its reasoning trace. Across multiple reasoning benchmarks and token budgets, we demonstrate that TRSD improves robustness to truncated inference, with far reduced accuracy tradeoffs when applied to a diverse set of reasoning models. Moreover, although never explicitly regularized for shorter generation during training, we also find that TRSD-trained models inherently output shorter reasoning traces without truncation, significantly reducing inference-time costs even without artificial interventions.

Beatrice Achilli, Enrico Ventura, Gianluigi Silvestri et al.

Generative diffusion processes are state-of-the-art machine learning models deeply connected with fundamental concepts in statistical physics. Depending on the dataset size and the capacity of the network, their behavior is known to transition from an associative memory regime to a generalization phase in a phenomenon that has been described as a glassy phase transition. Here, using statistical physics techniques, we extend the theory of memorization in generative diffusion to manifold-supported data. Our theoretical and experimental findings indicate that different tangent subspaces are lost due to memorization effects at different critical times and dataset sizes, which depend on the local variance of the data along their directions. Perhaps counterintuitively, we find that, under some conditions, subspaces of higher variance are lost first due to memorization effects. This leads to a selective loss of dimensionality where some prominent features of the data are memorized without a full collapse on any individual training point. We validate our theory with a comprehensive set of experiments on networks trained both in image datasets and on linear manifolds, which result in a remarkable qualitative agreement with the theoretical predictions.

Guido Klein, Pierre Guetschel, Gianluigi Silvestri et al.

Data scarcity in the brain-computer interface field can be alleviated through the use of generative models, specifically diffusion models. While diffusion models have previously been successfully applied to electroencephalogram (EEG) data, existing models lack flexibility w.r.t.~sampling or require alternative representations of the EEG data. To overcome these limitations, we introduce a novel approach to conditional diffusion models that utilizes classifier-free guidance to directly generate subject-, session-, and class-specific EEG data. In addition to commonly used metrics, domain-specific metrics are employed to evaluate the specificity of the generated samples. The results indicate that the proposed model can generate EEG data that resembles real data for each subject, session, and class.

Gianluigi Silvestri, Emily Fertig, Dave Moore et al.

Normalizing flows have shown great success as general-purpose density estimators. However, many real world applications require the use of domain-specific knowledge, which normalizing flows cannot readily incorporate. We propose embedded-model flows (EMF), which alternate general-purpose transformations with structured layers that embed domain-specific inductive biases. These layers are automatically constructed by converting user-specified differentiable probabilistic models into equivalent bijective transformations. We also introduce gated structured layers, which allow bypassing the parts of the models that fail to capture the statistics of the data. We demonstrate that EMFs can be used to induce desirable properties such as multimodality, hierarchical coupling and continuity. Furthermore, we show that EMFs enable a high performance form of variational inference where the structure of the prior model is embedded in the variational architecture. In our experiments, we show that this approach outperforms state-of-the-art methods in common structured inference problems.

Luca Ambrogioni, Gianluigi Silvestri, Marcel van Gerven

The automation of probabilistic reasoning is one of the primary aims of machine learning. Recently, the confluence of variational inference and deep learning has led to powerful and flexible automatic inference methods that can be trained by stochastic gradient descent. In particular, normalizing flows are highly parameterized deep models that can fit arbitrarily complex posterior densities. However, normalizing flows struggle in highly structured probabilistic programs as they need to relearn the forward-pass of the program. Automatic structured variational inference (ASVI) remedies this problem by constructing variational programs that embed the forward-pass. Here, we combine the flexibility of normalizing flows and the prior-embedding property of ASVI in a new family of variational programs, which we named cascading flows. A cascading flows program interposes a newly designed highway flow architecture in between the conditional distributions of the prior program such as to steer it toward the observed data. These programs can be constructed automatically from an input probabilistic program and can also be amortized automatically. We evaluate the performance of the new variational programs in a series of structured inference problems. We find that cascading flows have much higher performance than both normalizing flows and ASVI in a large set of structured inference problems.