Diego Doimo

Aldo Glielmo, Iuri Macocco, Diego Doimo et al.

DADApy is a python software package for analysing and characterising high-dimensional data manifolds. It provides methods for estimating the intrinsic dimension and the probability density, for performing density-based clustering and for comparing different distance metrics. We review the main functionalities of the package and exemplify its usage in toy cases and in a real-world application. DADApy is freely available under the open-source Apache 2.0 license.

Luis Palacios, Lorenzo Basile, Diego Doimo et al.

Visual instruction tuning effectively adapts a pre-trained Large Language Model (LLM) to process image information alongside text. Yet, it remains unclear how visual features are embedded into the layer-wise hierarchy of abstractions of the LLM backbone. Across a diverse set of vision-language architectures, we show that instruction tuning primarily serves as a bridge, embedding visual features directly into the intermediate semantic layers of the LLM, bypassing the early layers devoted to unimodal processing. With probing analyses and causal interventions, we show that these intermediate layers are the semantic core of vision-language processing and play a critical role in the performance on a broad set of multimodal benchmarks. In addition, by comparing the geometry of semantically equivalent visual and textual representations, we find that fine-tuning extends and strengthens the existing abstraction phase, aligning visual features with pre-existing textual ones. Finally, we confirm the functional role of this localized alignment by restricting fine-tuning to intermediate layers alone: this strategy preserves the performance of full fine-tuning on vision-centric benchmarks while reducing training time. Our results suggest that multimodal integration is a localized phenomenon driven by the repurposing of the internal abstraction engine of the LLM.

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.

Federica Gerace, Diego Doimo, Stefano Sarao Mannelli et al.

Transfer learning is a powerful tool enabling model training with limited amounts of data. This technique is particularly useful in real-world problems where data availability is often a serious limitation. The simplest transfer learning protocol is based on ``freezing" the feature-extractor layers of a network pre-trained on a data-rich source task, and then adapting only the last layers to a data-poor target task. This workflow is based on the assumption that the feature maps of the pre-trained model are qualitatively similar to the ones that would have been learned with enough data on the target task. In this work, we show that this protocol is often sub-optimal, and the largest performance gain may be achieved when smaller portions of the pre-trained network are kept frozen. In particular, we make use of a controlled framework to identify the optimal transfer depth, which turns out to depend non-trivially on the amount of available training data and on the degree of source-target task correlation. We then characterize transfer optimality by analyzing the internal representations of two networks trained from scratch on the source and the target task through multiple established similarity measures.

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.

Francesco Ortu, Zhijing Jin, Diego Doimo et al.

Interpretability research aims to bridge the gap between empirical success and our scientific understanding of the inner workings of large language models (LLMs). However, most existing research focuses on analyzing a single mechanism, such as how models copy or recall factual knowledge. In this work, we propose a formulation of competition of mechanisms, which focuses on the interplay of multiple mechanisms instead of individual mechanisms and traces how one of them becomes dominant in the final prediction. We uncover how and where mechanisms compete within LLMs using two interpretability methods: logit inspection and attention modification. Our findings show traces of the mechanisms and their competition across various model components and reveal attention positions that effectively control the strength of certain mechanisms. Code: https://github.com/francescortu/comp-mech. Data: https://huggingface.co/datasets/francescortu/comp-mech.

Emily Cheng, Diego Doimo, Corentin Kervadec et al.

A language model (LM) is a mapping from a linguistic context to an output token. However, much remains to be known about this mapping, including how its geometric properties relate to its function. We take a high-level geometric approach to its analysis, observing, across five pre-trained transformer-based LMs and three input datasets, a distinct phase characterized by high intrinsic dimensionality. During this phase, representations (1) correspond to the first full linguistic abstraction of the input; (2) are the first to viably transfer to downstream tasks; (3) predict each other across different LMs. Moreover, we find that an earlier onset of the phase strongly predicts better language modelling performance. In short, our results suggest that a central high-dimensionality phase underlies core linguistic processing in many common LM architectures.

Francesco Ortu, Zhijing Jin, Diego Doimo et al.

Vision-language models (VLMs) increasingly leverage diverse knowledge sources to address complex tasks, often encountering conflicts between their internal parametric knowledge and external information. Knowledge conflicts can result in hallucinations and unreliable responses, but the mechanisms governing such interactions remain unknown. To address this gap, we analyze the mechanisms that VLMs use to resolve cross-modal conflicts by introducing a dataset of multimodal counterfactual queries that deliberately contradict internal commonsense knowledge. We localize with logit inspection a small set of heads that control the conflict. Moreover, by modifying these heads, we can steer the model towards its internal knowledge or the visual inputs. Finally, we show that attention from such heads pinpoints localized image regions driving visual overrides, outperforming gradient-based attribution in precision.

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.

Diego Doimo

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the semantic content of the hidden representations with unsupervised learning tools, partially developed by us and described in this thesis, which allow harnessing the low-dimensional structure of the data. Chapter 2. introduces Gride, a method that allows estimating the intrinsic dimension of the data as an explicit function of the scale without performing any decimation of the data set. Our approach is based on rigorous distributional results that enable the quantification of uncertainty of the estimates. Moreover, our method is simple and computationally efficient since it relies only on the distances among nearest data points. In Chapter 3, we study the evolution of the probability density across the hidden layers in some state-of-the-art deep neural networks. We find that the initial layers generate a unimodal probability density getting rid of any structure irrelevant to classification. In subsequent layers, density peaks arise in a hierarchical fashion that mirrors the semantic hierarchy of the concepts. 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. In Chapter 4, we study the problem of generalization in deep neural networks: adding parameters to a network that interpolates its training data will typically improve its generalization performance, at odds with the classical bias-variance trade-off. We show that wide neural networks learn redundant representations instead of overfitting to spurious correlation and that redundant neurons appear only if the network is regularized and the training error is zero.

Lorenzo Basile, Valentino Maiorca, Diego Doimo et al.

Language and vision-language models have shown impressive performance across a wide range of tasks, but their internal mechanisms remain only partly understood. In this work, we study how individual attention heads in text-generative models specialize in specific semantic or visual attributes. Building on an established interpretability method, we reinterpret the practice of probing intermediate activations with the final decoding layer through the lens of signal processing. This lets us analyze multiple samples in a principled way and rank attention heads based on their relevance to target concepts. Our results show consistent patterns of specialization at the head level across both unimodal and multimodal transformers. Remarkably, we find that editing as few as 1% of the heads, selected using our method, can reliably suppress or enhance targeted concepts in the model output. We validate our approach on language tasks such as question answering and toxicity mitigation, as well as vision-language tasks including image classification and captioning. Our findings highlight an interpretable and controllable structure within attention layers, offering simple tools for understanding and editing large-scale generative models.

Charles Camboulin, Diego Doimo, Aldo Glielmo

This work presents an analysis of the hidden representations of Variational Autoencoders (VAEs) using the Intrinsic Dimension (ID) and the Information Imbalance (II). We show that VAEs undergo a transition in behaviour once the bottleneck size is larger than the ID of the data, manifesting in a double hunchback ID profile and a qualitative shift in information processing as captured by the II. Our results also highlight two distinct training phases for architectures with sufficiently large bottleneck sizes, consisting of a rapid fit and a slower generalisation, as assessed by a differentiated behaviour of ID, II, and KL loss. These insights demonstrate that II and ID could be valuable tools for aiding architecture search, for diagnosing underfitting in VAEs, and, more broadly, they contribute to advancing a unified understanding of deep generative models through geometric analysis.

Diego Doimo, Aldo Glielmo, Sebastian Goldt et al.

Deep neural networks (DNNs) defy the classical bias-variance trade-off: adding parameters to a DNN that interpolates its training data will typically improve its generalization performance. Explaining the mechanism behind this ``benign overfitting'' in deep networks remains an outstanding challenge. Here, we study the last hidden layer representations of various state-of-the-art convolutional neural networks and find that if the last hidden representation is wide enough, its neurons tend to split into groups that carry identical information, and differ from each other only by statistically independent noise. The number of such groups increases linearly with the width of the layer, but only if the width is above a critical value. We show that redundant neurons appear only when the training process reaches interpolation and the training error is zero.

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.