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Davide Buffelli

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4 papers

1 author row

NeurIPS Conference 2024 Conference Paper

Deep Equilibrium Algorithmic Reasoning

Dobrik Georgiev
JJ Wilson
Davide Buffelli
Pietro Liò

Neural Algorithmic Reasoning (NAR) research has demonstrated that graph neural networks (GNNs) could learn to execute classical algorithms. However, most previous approaches have always used a recurrent architecture, where each iteration of the GNN matches an iteration of the algorithm. In this paper we study neurally solving algorithms from a different perspective: since the algorithm’s solution is often an equilibrium, it is possible to find the solution directly by solving an equilibrium equation. Our approach requires no information on the ground-truth number of steps of the algorithm, both during train and test time. Furthermore, the proposed method improves the performance of GNNs on executing algorithms and is a step towards speeding up existing NAR models. Our empirical evidence, leveraging algorithms from the CLRS-30 benchmark, validates that one can train a network to solve algorithmic problems by directly finding the equilibrium. We discuss the practical implementation of such models and propose regularisations to improve the performance of these equilibrium reasoners.

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NeurIPS Conference 2024 Conference Paper

Exact, Tractable Gauss-Newton Optimization in Deep Reversible Architectures Reveal Poor Generalization

Davide Buffelli
Jamie McGowan
Wangkun Xu
Alexandru Cioba
Da-shan Shiu
Guillaume Hennequin
Alberto Bernacchia

Second-order optimization has been shown to accelerate the training of deep neural networks in many applications, often yielding faster progress per iteration on the training loss compared to first-order optimizers. However, the generalization properties of second-order methods are still being debated. Theoretical investigations have proved difficult to carry out outside the tractable settings of heavily simplified model classes - thus, the relevance of existing theories to practical deep learning applications remains unclear. Similarly, empirical studies in large-scale models and real datasets are significantly confounded by the necessity to approximate second-order updates in practice. It is often unclear whether the observed generalization behaviour arises specifically from the second-order nature of the parameter updates, or instead reflects the specific structured (e. g. Kronecker) approximations used or any damping-based interpolation towards first-order updates. Here, we show for the first time that exact Gauss-Newton (GN) updates take on a tractable form in a class of deep reversible architectures that are sufficiently expressive to be meaningfully applied to common benchmark datasets. We exploit this novel setting to study the training and generalization properties of the GN optimizer. We find that exact GN generalizes poorly. In the mini-batch training setting, this manifests as rapidly saturating progress even on the training loss, with parameter updates found to overfit each mini-batch without producing the features that would support generalization to other mini-batches. In contrast to previous work, we show that our experiments run in the feature learning regime, in which the neural tangent kernel (NTK) changes during the course of training. However, changes in the NTK are not associated with any significant change in neural representations, explaining the lack of generalization.

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AAAI Conference 2023 Conference Paper

Scalable Theory-Driven Regularization of Scene Graph Generation Models

Davide Buffelli
Efthymia Tsamoura

Several techniques have recently aimed to improve the performance of deep learning models for Scene Graph Generation (SGG) by incorporating background knowledge. State-of-the-art techniques can be divided into two families: one where the background knowledge is incorporated into the model in a subsymbolic fashion, and another in which the background knowledge is maintained in symbolic form. Despite promising results, both families of techniques face several shortcomings: the first one requires ad-hoc, more complex neural architectures increasing the training or inference cost; the second one suffers from limited scalability w.r.t. the size of the background knowledge. Our work introduces a regularization technique for injecting symbolic background knowledge into neural SGG models that overcomes the limitations of prior art. Our technique is model-agnostic, does not incur any cost at inference time, and scales to previously unmanageable background knowledge sizes. We demonstrate that our technique can improve the accuracy of state-of-the-art SGG models, by up to 33%.

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NeurIPS Conference 2022 Conference Paper

SizeShiftReg: a Regularization Method for Improving Size-Generalization in Graph Neural Networks

Davide Buffelli
Pietro Lió
Fabio Vandin

In the past few years, graph neural networks (GNNs) have become the de facto model of choice for graph classification. While, from the theoretical viewpoint, most GNNs can operate on graphs of any size, it is empirically observed that their classification performance degrades when they are applied on graphs with sizes that differ from those in the training data. Previous works have tried to tackle this issue in graph classification by providing the model with inductive biases derived from assumptions on the generative process of the graphs, or by requiring access to graphs from the test domain. The first strategy is tied to the quality of the assumptions made for the generative process, and requires the use of specific models designed after the explicit definition of the generative process of the data, leaving open the question of how to improve the performance of generic GNN models in general settings. On the other hand, the second strategy can be applied to any GNN, but requires access to information that is not always easy to obtain. In this work we consider the scenario in which we only have access to the training data, and we propose a regularization strategy that can be applied to any GNN to improve its generalization capabilities from smaller to larger graphs without requiring access to the test data. Our regularization is based on the idea of simulating a shift in the size of the training graphs using coarsening techniques, and enforcing the model to be robust to such a shift. Experimental results on standard datasets show that popular GNN models, trained on the 50% smallest graphs in the dataset and tested on the 10% largest graphs, obtain performance improvements of up to 30% when trained with our regularization strategy.

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