Emanuele Ballarin

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 .

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.