Alessio Ansuini

Lucrezia Valeriani, Diego Doimo, Francesca Cuturello et al.

Large transformers are powerful architectures used for self-supervised data analysis across various data types, including protein sequences, images, and text. In these models, the semantic structure of the dataset emerges from a sequence of transformations between one representation and the next. We characterize the geometric and statistical properties of these representations and how they change as we move through the layers. By analyzing the intrinsic dimension (ID) and neighbor composition, we find that the representations evolve similarly in transformers trained on protein language tasks and image reconstruction tasks. In the first layers, the data manifold expands, becoming high-dimensional, and then contracts significantly in the intermediate layers. In the last part of the model, the ID remains approximately constant or forms a second shallow peak. We show that the semantic information of the dataset is better expressed at the end of the first peak, and this phenomenon can be observed across many models trained on diverse datasets. Based on our findings, we point out an explicit strategy to identify, without supervision, the layers that maximize semantic content: representations at intermediate layers corresponding to a relative minimum of the ID profile are more suitable for downstream learning tasks.

Gonzalo Uribarri, Federico Barone, Alessio Ansuini et al.

Time Series Classification (TSC) is essential in fields like medicine, environmental science, and finance, enabling tasks such as disease diagnosis, anomaly detection, and stock price analysis. While machine learning models like Recurrent Neural Networks and InceptionTime are successful in numerous applications, they can face scalability issues due to computational requirements. Recently, ROCKET has emerged as an efficient alternative, achieving state-of-the-art performance and simplifying training by utilizing a large number of randomly generated features from the time series data. However, many of these features are redundant or non-informative, increasing computational load and compromising generalization. Here we introduce Sequential Feature Detachment (SFD) to identify and prune non-essential features in ROCKET-based models, such as ROCKET, MiniRocket, and MultiRocket. SFD estimates feature importance using model coefficients and can handle large feature sets without complex hyperparameter tuning. Testing on the UCR archive shows that SFD can produce models with better test accuracy using only 10\% of the original features. We named these pruned models Detach-ROCKET. We also present an end-to-end procedure for determining an optimal balance between the number of features and model accuracy. On the largest binary UCR dataset, Detach-ROCKET improves test accuracy by 0.6\% while reducing features by 98.9\%. By enabling a significant reduction in model size without sacrificing accuracy, our methodology improves computational efficiency and contributes to model interpretability. We believe that Detach-ROCKET will be a valuable tool for researchers and practitioners working with time series data, who can find a user-friendly implementation of the model at \url{https://github.com/gon-uri/detach_rocket}.

Diego Doimo, Alessandro Serra, Alessio Ansuini et al.

In-context learning (ICL) and supervised fine-tuning (SFT) are two common strategies for improving the performance of modern large language models (LLMs) on specific tasks. Despite their different natures, these strategies often lead to comparable performance gains. However, little is known about whether they induce similar representations inside LLMs. We approach this problem by analyzing the probability landscape of their hidden representations in the two cases. More specifically, we compare how LLMs solve the same question-answering task, finding that ICL and SFT create very different internal structures, in both cases undergoing a sharp transition in the middle of the network. In the first half of the network, ICL shapes interpretable representations hierarchically organized according to their semantic content. In contrast, the probability landscape obtained with SFT is fuzzier and semantically mixed. In the second half of the model, the fine-tuned representations develop probability modes that better encode the identity of answers, while the landscape of ICL representations is characterized by less defined peaks. Our approach reveals the diverse computational strategies developed inside LLMs to solve the same task across different conditions, allowing us to make a step towards designing optimal methods to extract information from language models.

Ludovica de Paolis, Fabio Anselmi, Alessio Ansuini et al.

Mathematical modeling of visual textures traces back to Julesz's intuition that texture perception in humans is based on local correlations between image features. An influential approach for texture analysis and generation generalizes this notion to linear correlations between the nonlinear features computed by convolutional neural networks (CNNs), compiled into Gram matrices. Given that CNNs are often used as models for the visual system, it is natural to ask whether such "texture representations" spontaneously align with the textures' perceptual content, and in particular whether those CNNs that are regarded as better models for the visual system also possess more human-like texture representations. Here we compare the perceptual content captured by feature correlations computed for a diverse pool of CNNs, and we compare it to the models' perceptual alignment with the mammalian visual system as measured by Brain-Score. Surprisingly, we find that there is no connection between conventional measures of CNN quality as a model of the visual system and its alignment with human texture perception. We conclude that texture perception involves mechanisms that are distinct from those that are commonly modeled using approaches based on CNNs trained on object recognition, possibly depending on the integration of contextual information.

Michele Alessi, Alessio Ansuini, Alex Rodriguez

We introduce Density-Informed VAE (DiVAE), a lightweight, data-driven regularizer that aligns the VAE log-prior probability $\log p_Z(z)$ with a log-density estimated from data. Standard VAEs match latents to a simple prior, overlooking density structure in the data-space. DiVAE encourages the encoder to allocate posterior mass in proportion to data-space density and, when the prior is learnable, nudges the prior toward high-density regions. This is realized by adding a robust, precision-weighted penalty to the ELBO, incurring negligible computational overhead. On synthetic datasets, DiVAE (i) improves distributional alignment of latent log-densities to its ground truth counterpart, (ii) improves prior coverage, and (iii) yields better OOD uncertainty calibration. On MNIST, DiVAE improves alignment of the prior with external estimates of the density, providing better interpretability, and improves OOD detection for learnable priors.

Nicola Aladrah, Emanuele Ballarin, Matteo Biagetti et al.

A key challenge in machine learning is to explain how learning dynamics select among the many solutions that achieve identical loss values in overparameterized models - a phenomenon known as implicit bias. Controlling this bias provides a direct mechanism on learned representations, which are central to interpretability, robustness, and reasoning in modern AI systems. Yet, despite its importance, existing explanations remain largely ad hoc and lack a unifying mechanism. We develop a theoretical and constructive framework in which implicit bias emerges as a geometric correction induced by the interplay between gradient noise and continuous symmetries of the loss. We compute the induced bias across a range of architectures, predicting new behaviors and explaining known ones. The approach also enables inverse design: by engineering predictor - preserving parameterizations, it is possible to shape the bias, with sparsity and spectral sparsity emerging as canonical instances. Numerical experiments support the theory and validate the inverse - design framework in controlled settings.

Emanuele Ballarin, Alessio Ansuini, Luca Bortolussi

In this work, we propose a novel adversarial defence mechanism for image classification - CARSO - blending the paradigms of adversarial training and adversarial purification in a synergistic robustness-enhancing way. The method builds upon an adversarially-trained classifier, and learns to map its internal representation associated with a potentially perturbed input onto a distribution of tentative clean reconstructions. Multiple samples from such distribution are classified by the same adversarially-trained model, and a carefully chosen aggregation of its outputs finally constitutes the robust prediction of interest. Experimental evaluation by a well-established benchmark of strong adaptive attacks, across different image datasets, shows that CARSO is able to defend itself against adaptive end-to-end white-box attacks devised for stochastic defences. Paying a modest clean accuracy toll, our method improves by a significant margin the state-of-the-art for Cifar-10, Cifar-100, and TinyImageNet-200 $\ell_\infty$ robust classification accuracy against AutoAttack. Code, and instructions to obtain pre-trained models are available at: https://github.com/emaballarin/CARSO .

Edith Natalia Villegas Garcia, Alessio Ansuini

The rapid advancements in transformer-based language models have revolutionized natural language processing, yet understanding the internal mechanisms of these models remains a significant challenge. This paper explores the application of sparse autoencoders (SAE) to interpret the internal representations of protein language models, specifically focusing on the ESM-2 8M parameter model. By performing a statistical analysis on each latent component's relevance to distinct protein annotations, we identify potential interpretations linked to various protein characteristics, including transmembrane regions, binding sites, and specialized motifs. We then leverage these insights to guide sequence generation, shortlisting the relevant latent components that can steer the model towards desired targets such as zinc finger domains. This work contributes to the emerging field of mechanistic interpretability in biological sequence models, offering new perspectives on model steering for sequence design.

Yuri Gardinazzi, Karthik Viswanathan, Giada Panerai et al.

Understanding the decision-making processes of large language models is critical given their widespread applications. To achieve this, we aim to connect a formal mathematical framework - zigzag persistence from topological data analysis - with practical and easily applicable algorithms. Zigzag persistence is particularly effective for characterizing data as it dynamically transforms across model layers. Within this framework, we introduce topological descriptors that measure how topological features, $p$-dimensional holes, persist and evolve throughout the layers. Unlike methods that assess each layer individually and then aggregate the results, our approach directly tracks the full evolutionary path of these features. This offers a statistical perspective on how prompts are rearranged and their relative positions changed in the representation space, providing insights into the system's operation as an integrated whole. To demonstrate the expressivity and applicability of our framework, we highlight how sensitive these descriptors are to different models and a variety of datasets. As a showcase application to a downstream task, we use zigzag persistence to establish a criterion for layer pruning, achieving results comparable to state-of-the-art methods while preserving the system-level perspective.

Alessandro Serra, Francesco Ortu, Emanuele Panizon et al.

Recent advances in multimodal training have significantly improved the integration of image understanding and generation within a unified model. This study investigates how vision-language models (VLMs) handle image-understanding tasks, focusing on how visual information is processed and transferred to the textual domain. We compare native multimodal VLMs, models trained from scratch on multimodal data to generate both text and images, and non-native multimodal VLMs, models adapted from pre-trained large language models or capable of generating only text, highlighting key differences in information flow. We find that in native multimodal VLMs, image and text embeddings are more separated within the residual stream. Moreover, VLMs differ in how visual information reaches text: non-native multimodal VLMs exhibit a distributed communication pattern, where information is exchanged through multiple image tokens, whereas models trained natively for joint image and text generation tend to rely on a single post-image token that acts as a narrow gate for visual information. We show that ablating this single token significantly deteriorates image-understanding performance, whereas targeted, token-level interventions reliably steer image semantics and downstream text with fine-grained control.

Niccolò Tosato, Lorenzo Basile, Emanuele Ballarin et al.

The Backpropagation algorithm has often been criticised for its lack of biological realism. In an attempt to find a more biologically plausible alternative, the recently introduced Forward-Forward algorithm replaces the forward and backward passes of Backpropagation with two forward passes. In this work, we show that the internal representations obtained by the Forward-Forward algorithm can organise into category-specific ensembles exhibiting high sparsity -- composed of a low number of active units. This situation is reminiscent of what has been observed in cortical sensory areas, where neuronal ensembles are suggested to serve as the functional building blocks for perception and action. Interestingly, while this sparse pattern does not typically arise in models trained with standard Backpropagation, it can emerge in networks trained with Backpropagation on the same objective proposed for the Forward-Forward algorithm.

Diego Doimo, Aldo Glielmo, Alessio Ansuini et al.

Deep convolutional networks (DCNs) learn meaningful representations where data that share the same abstract characteristics are positioned closer and closer. Understanding these representations and how they are generated is of unquestioned practical and theoretical interest. In this work we study the evolution of the probability density of the ImageNet dataset across the hidden layers in some state-of-the-art DCNs. We find that the initial layers generate a unimodal probability density getting rid of any structure irrelevant for classification. In subsequent layers density peaks arise in a hierarchical fashion that mirrors the semantic hierarchy of the concepts. Density peaks corresponding to single categories appear only close to the output and via a very sharp transition which resembles the nucleation process of a heterogeneous liquid. This process leaves a footprint in the probability density of the output layer where the topography of the peaks allows reconstructing the semantic relationships of the categories.

Alessio Ansuini, Alessandro Laio, Jakob H. Macke et al.

Deep neural networks progressively transform their inputs across multiple processing layers. What are the geometrical properties of the representations learned by these networks? Here we study the intrinsic dimensionality (ID) of data-representations, i.e. the minimal number of parameters needed to describe a representation. We find that, in a trained network, the ID is orders of magnitude smaller than the number of units in each layer. Across layers, the ID first increases and then progressively decreases in the final layers. Remarkably, the ID of the last hidden layer predicts classification accuracy on the test set. These results can neither be found by linear dimensionality estimates (e.g., with principal component analysis), nor in representations that had been artificially linearized. They are neither found in untrained networks, nor in networks that are trained on randomized labels. This suggests that neural networks that can generalize are those that transform the data into low-dimensional, but not necessarily flat manifolds.

Eric Medvet, Alberto Bartoli, Alessio Ansuini et al.

We explore the use of Intrinsic Dimension (ID) for gaining insights in how populations evolve in Evolutionary Algorithms. ID measures the minimum number of dimensions needed to accurately describe a dataset and its estimators are being used more and more in Machine Learning to cope with large datasets. We postulate that ID can provide information about population which is complimentary w.r.t.\ what (a simple measure of) diversity tells. We experimented with the application of ID to populations evolved with a recent variant of Grammatical Evolution. The preliminary results suggest that diversity and ID constitute two different points of view on the population dynamics.