Marco Nurisso

Guillermo Bernárdez, Lev Telyatnikov, Marco Montagna et al.

This paper describes the 2nd edition of the ICML Topological Deep Learning Challenge that was hosted within the ICML 2024 ELLIS Workshop on Geometry-grounded Representation Learning and Generative Modeling (GRaM). The challenge focused on the problem of representing data in different discrete topological domains in order to bridge the gap between Topological Deep Learning (TDL) and other types of structured datasets (e.g. point clouds, graphs). Specifically, participants were asked to design and implement topological liftings, i.e. mappings between different data structures and topological domains --like hypergraphs, or simplicial/cell/combinatorial complexes. The challenge received 52 submissions satisfying all the requirements. This paper introduces the main scope of the challenge, and summarizes the main results and findings.

Pierrick Leroy, Antonio Mastropietro, Marco Nurisso et al.

Face Recognition (FR) tasks have made significant progress with the advent of Deep Neural Networks, particularly through margin-based triplet losses that embed facial images into high-dimensional feature spaces. During training, these contrastive losses focus exclusively on identity information as labels. However, we observe a multiscale geometric structure emerging in the embedding space, influenced by interpretable facial (e.g., hair color) and image attributes (e.g., contrast). We propose a geometric approach to describe the dependence or invariance of FR models to these attributes and introduce a physics-inspired alignment metric. We evaluate the proposed metric on controlled, simplified models and widely used FR models fine-tuned with synthetic data for targeted attribute augmentation. Our findings reveal that the models exhibit varying degrees of invariance across different attributes, providing insight into their strengths and weaknesses and enabling deeper interpretability. Code available here: https://github.com/mantonios107/attrs-fr-embs}{https://github.com/mantonios107/attrs-fr-embs

Simone Azeglio, Simone Poetto, Luca Savant Aira et al.

Computational models of vision have traditionally been developed in a bottom-up fashion, by hierarchically composing a series of straightforward operations - i.e. convolution and pooling - with the aim of emulating simple and complex cells in the visual cortex, resulting in the introduction of deep convolutional neural networks (CNNs). Nevertheless, data obtained with recent neuronal recording techniques support that the nature of the computations carried out in the ventral visual stream is not completely captured by current deep CNN models. To fill the gap between the ventral visual stream and deep models, several benchmarks have been designed and organized into the Brain-Score platform, granting a way to perform multi-layer (V1, V2, V4, IT) and behavioral comparisons between the two counterparts. In our work, we aim to shift the focus on architectures that take into account lateral recurrent connections, a ubiquitous feature of the ventral visual stream, to devise adaptive receptive fields. Through recurrent connections, the input s long-range spatial dependencies can be captured in a local multi-step fashion and, as introduced with Gated Recurrent CNNs (GRCNN), the unbounded expansion of the neuron s receptive fields can be modulated through the use of gates. In order to increase the robustness of our approach and the biological fidelity of the activations, we employ specific data augmentation techniques in line with several of the scoring benchmarks. Enforcing some form of invariance, through heuristics, was found to be beneficial for better neural predictivity.

Marco Nurisso, Pierrick Leroy, Francesco Vaccarino

Studying the interplay between the geometry of the loss landscape and the optimization trajectories of simple neural networks is a fundamental step for understanding their behavior in more complex settings. This paper reveals the presence of topological obstruction in the loss landscape of shallow ReLU neural networks trained using gradient flow. We discuss how the homogeneous nature of the ReLU activation function constrains the training trajectories to lie on a product of quadric hypersurfaces whose shape depends on the particular initialization of the network's parameters. When the neural network's output is a single scalar, we prove that these quadrics can have multiple connected components, limiting the set of reachable parameters during training. We analytically compute the number of these components and discuss the possibility of mapping one to the other through neuron rescaling and permutation. In this simple setting, we find that the non-connectedness results in a topological obstruction, which, depending on the initialization, can make the global optimum unreachable. We validate this result with numerical experiments.

Enrico Cassano, Riccardo Renzulli, Marco Nurisso et al.

Effective concept unlearning in text-to-image diffusion models requires precise localization of concept representations within the model's latent space. While sparse autoencoders successfully reduce neuron polysemanticity (i.e., multiple concepts per neuron) compared to the original network, individual concept representations can still be distributed across multiple latent features, requiring extensive search procedures for concept unlearning. We introduce SAEmnesia, a supervised sparse autoencoder training method that promotes one-to-one concept-neuron mappings through systematic concept labeling, mitigating feature splitting and promoting feature centralization. Our approach learns specialized neurons with significantly stronger concept associations compared to unsupervised baselines. The only computational overhead introduced by SAEmnesia is limited to cross-entropy computation during training. At inference time, this interpretable representation reduces hyperparameter search by 96.67% with respect to current approaches. On the UnlearnCanvas benchmark, SAEmnesia achieves a 9.22% improvement over the state-of-the-art. In sequential unlearning tasks, we demonstrate superior scalability with a 28.4% improvement in unlearning accuracy for 9-object removal.

Marco Nurisso, Jesseba Fernando, Raj Deshpande et al.

Intelligent systems must deploy internal representations that are simultaneously structured -- to support broad generalization -- and selective -- to preserve input identity. We expose a fundamental limit on this tradeoff. For any model whose representational similarity between inputs decays with finite semantic resolution $\varepsilon$, we derive closed-form expressions that pin its probability of correct generalization $p_S$ and identification $p_I$ to a universal Pareto front independent of input space geometry. Extending the analysis to noisy, heterogeneous spaces and to $n>2$ inputs predicts a sharp $1/n$ collapse of multi-input processing capacity and a non-monotonic optimum for $p_S$. A minimal ReLU network trained end-to-end reproduces these laws: during learning a resolution boundary self-organizes and empirical $(p_S,p_I)$ trajectories closely follow theoretical curves for linearly decaying similarity. Finally, we demonstrate that the same limits persist in two markedly more complex settings -- a convolutional neural network and state-of-the-art vision-language models -- confirming that finite-resolution similarity is a fundamental emergent informational constraint, not merely a toy-model artifact. Together, these results provide an exact theory of the generalization-identification trade-off and clarify how semantic resolution shapes the representational capacity of deep networks and brains alike.