Alessandro Favero

Francesco Cagnetta, Leonardo Petrini, Umberto M. Tomasini et al. · cambridge

Deep learning algorithms demonstrate a surprising ability to learn high-dimensional tasks from limited examples. This is commonly attributed to the depth of neural networks, enabling them to build a hierarchy of abstract, low-dimensional data representations. However, how many training examples are required to learn such representations remains unknown. To quantitatively study this question, we introduce the Random Hierarchy Model: a family of synthetic tasks inspired by the hierarchical structure of language and images. The model is a classification task where each class corresponds to a group of high-level features, chosen among several equivalent groups associated with the same class. In turn, each feature corresponds to a group of sub-features chosen among several equivalent ones and so on, following a hierarchy of composition rules. We find that deep networks learn the task by developing internal representations invariant to exchanging equivalent groups. Moreover, the number of data required corresponds to the point where correlations between low-level features and classes become detectable. Overall, our results indicate how deep networks overcome the curse of dimensionality by building invariant representations, and provide an estimate of the number of data required to learn a hierarchical task.

Francesco Cagnetta, Alessandro Favero, Matthieu Wyart · cambridge

Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such as images. Yet, we lack a quantitative understanding of how such structure affects performance, e.g., the rate of decay of the generalisation error with the number of training samples. In this paper, we study infinitely-wide deep CNNs in the kernel regime. First, we show that the spectrum of the corresponding kernel inherits the hierarchical structure of the network, and we characterise its asymptotics. Then, we use this result together with generalisation bounds to prove that deep CNNs adapt to the spatial scale of the target function. In particular, we find that if the target function depends on low-dimensional subsets of adjacent input variables, then the decay of the error is controlled by the effective dimensionality of these subsets. Conversely, if the target function depends on the full set of input variables, then the error decay is controlled by the input dimension. We conclude by computing the generalisation error of a deep CNN trained on the output of another deep CNN with randomly-initialised parameters. Interestingly, we find that, despite their hierarchical structure, the functions generated by infinitely-wide deep CNNs are too rich to be efficiently learnable in high dimension.

Ke Wang, Nikolaos Dimitriadis, Alessandro Favero et al. · cambridge

Fine-tuning pre-trained models has become the standard approach to endow them with specialized knowledge, but it poses fundamental challenges. In particular, \textit{(i)} fine-tuning often leads to catastrophic forgetting, where improvements on a target domain degrade generalization on other tasks, and \textit{(ii)} merging fine-tuned checkpoints from disparate tasks can lead to significant performance loss. To address these challenges, we introduce LiNeS, Layer-increasing Network Scaling, a post-training editing technique designed to preserve pre-trained generalization while enhancing fine-tuned task performance. LiNeS scales parameter updates linearly based on their layer depth within the network, maintaining shallow layers close to their pre-trained values to preserve general features while allowing deeper layers to retain task-specific representations. In multi-task model merging scenarios, layer-wise scaling of merged parameters reduces negative task interference. LiNeS demonstrates significant improvements in both single-task and multi-task settings across various benchmarks in vision and natural language processing. It mitigates forgetting, enhances out-of-distribution generalization, integrates seamlessly with existing multi-task model merging baselines improving their performance across benchmarks and model sizes, and can boost generalization when merging LLM policies aligned with different rewards via RLHF. Our method is simple to implement, computationally efficient and complementary to many existing techniques. Our source code is available at https://github.com/wang-kee/LiNeS

Alessandro Favero, Luca Zancato, Matthew Trager et al. · cambridge

Generative Vision-Language Models (VLMs) are prone to generate plausible-sounding textual answers that, however, are not always grounded in the input image. We investigate this phenomenon, usually referred to as "hallucination" and show that it stems from an excessive reliance on the language prior. In particular, we show that as more tokens are generated, the reliance on the visual prompt decreases, and this behavior strongly correlates with the emergence of hallucinations. To reduce hallucinations, we introduce Multi-Modal Mutual-Information Decoding (M3ID), a new sampling method for prompt amplification. M3ID amplifies the influence of the reference image over the language prior, hence favoring the generation of tokens with higher mutual information with the visual prompt. M3ID can be applied to any pre-trained autoregressive VLM at inference time without necessitating further training and with minimal computational overhead. If training is an option, we show that M3ID can be paired with Direct Preference Optimization (DPO) to improve the model's reliance on the prompt image without requiring any labels. Our empirical findings show that our algorithms maintain the fluency and linguistic capabilities of pre-trained VLMs while reducing hallucinations by mitigating visually ungrounded answers. Specifically, for the LLaVA 13B model, M3ID and M3ID+DPO reduce the percentage of hallucinated objects in captioning tasks by 25% and 28%, respectively, and improve the accuracy on VQA benchmarks such as POPE by 21% and 24%.

Alessandro Favero, Antonio Sclocchi, Matthieu Wyart · cambridge

Diffusion probabilistic models have become a cornerstone of modern generative AI, yet the mechanisms underlying their generalization remain poorly understood. In fact, if these models were perfectly minimizing their training loss, they would just generate data belonging to their training set, i.e., memorize, as empirically found in the overparameterized regime. We revisit this view by showing that, in highly overparameterized diffusion models, generalization in natural data domains is progressively achieved during training before the onset of memorization. Our results, ranging from image to language diffusion models, systematically support the empirical law that memorization time is proportional to the dataset size. Generalization vs. memorization is then best understood as a competition between time scales. We show that this phenomenology is recovered in diffusion models learning a simple probabilistic context-free grammar with random rules, where generalization corresponds to the hierarchical acquisition of deeper grammar rules as training time grows, and the generalization cost of early stopping can be characterized. We summarize these results in a phase diagram. Overall, our results support that a principled early-stopping criterion - scaling with dataset size - can effectively optimize generalization while avoiding memorization, with direct implications for hyperparameter transfer and privacy-sensitive applications.

Guillermo Ortiz-Jimenez, Alessandro Favero, Pascal Frossard

Task arithmetic has recently emerged as a cost-effective and scalable approach to edit pre-trained models directly in weight space: By adding the fine-tuned weights of different tasks, the model's performance can be improved on these tasks, while negating them leads to task forgetting. Yet, our understanding of the effectiveness of task arithmetic and its underlying principles remains limited. We present a comprehensive study of task arithmetic in vision-language models and show that weight disentanglement is the crucial factor that makes it effective. This property arises during pre-training and manifests when distinct directions in weight space govern separate, localized regions in function space associated with the tasks. Notably, we show that fine-tuning models in their tangent space by linearizing them amplifies weight disentanglement. This leads to substantial performance improvements across multiple task arithmetic benchmarks and diverse models. Building on these findings, we provide theoretical and empirical analyses of the neural tangent kernel (NTK) of these models and establish a compelling link between task arithmetic and the spatial localization of the NTK eigenfunctions. Overall, our work uncovers novel insights into the fundamental mechanisms of task arithmetic and offers a more reliable and effective approach to edit pre-trained models through the NTK linearization.