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Fabrizio Pittorino

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Machine Learning cond-mat.dis-nn Computation and Language Computer Vision gr-qc Hardware Architecture Neural and Evolutionary Computing

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preprint2026arXiv

HERCULES: Hardware-Efficient, Robust, Continual Learning Neural Architecture Search

Neural Architecture Search (NAS) has emerged as a powerful framework for automatically discovering neural architectures that balance accuracy and efficiency. However, as AI transitions from static benchmarks to real-world deployment, the traditional focus on hardware-aware efficiency is no longer sufficient. We observe that modern NAS methods, especially those that target edge AI, are evolving to address a triple objective: Efficiency, Robustness, and Continual Learning. While efficiency ensures feasibility in resource-constrained environments, robustness guarantees reliability under environmental variabilities, and continual learning enables adaptation to sequential tasks without catastrophic forgetting. We propose a taxonomy of NAS approaches through this triple lens, distinguishing between methods targeting resource optimization, environmental resilience, and architectural plasticity. This unified perspective reveals that these axes, though often studied in isolation, are mutually reinforcing. Building on this taxonomy, we map the current landscape of these NAS methods into a new framework called Hardware-Efficient, Robust, and ContinUal LEarning Search (HERCULES). We define the desiderata, the twelve labours of HERCULES, addressing the non-trivial challenge of balancing an adequate search-space exploration with the immense computational costs of a multi-objective NAS, accounting for these crucial objectives of current AI systems. By identifying critical gaps in existing research, this survey outlines a roadmap toward integrated algorithmic, architectural, and hardware-software co-design for truly deployable, lifelong-learning AI systems.

preprint2022arXiv

Deep learning via message passing algorithms based on belief propagation

Message-passing algorithms based on the Belief Propagation (BP) equations constitute a well-known distributed computational scheme. It is exact on tree-like graphical models and has also proven to be effective in many problems defined on graphs with loops (from inference to optimization, from signal processing to clustering). The BP-based scheme is fundamentally different from stochastic gradient descent (SGD), on which the current success of deep networks is based. In this paper, we present and adapt to mini-batch training on GPUs a family of BP-based message-passing algorithms with a reinforcement field that biases distributions towards locally entropic solutions. These algorithms are capable of training multi-layer neural networks with discrete weights and activations with performance comparable to SGD-inspired heuristics (BinaryNet) and are naturally well-adapted to continual learning. Furthermore, using these algorithms to estimate the marginals of the weights allows us to make approximate Bayesian predictions that have higher accuracy than point-wise solutions.

preprint2021arXiv

Entropic gradient descent algorithms and wide flat minima

The properties of flat minima in the empirical risk landscape of neural networks have been debated for some time. Increasing evidence suggests they possess better generalization capabilities with respect to sharp ones. First, we discuss Gaussian mixture classification models and show analytically that there exist Bayes optimal pointwise estimators which correspond to minimizers belonging to wide flat regions. These estimators can be found by applying maximum flatness algorithms either directly on the classifier (which is norm independent) or on the differentiable loss function used in learning. Next, we extend the analysis to the deep learning scenario by extensive numerical validations. Using two algorithms, Entropy-SGD and Replicated-SGD, that explicitly include in the optimization objective a non-local flatness measure known as local entropy, we consistently improve the generalization error for common architectures (e.g. ResNet, EfficientNet). An easy to compute flatness measure shows a clear correlation with test accuracy.

preprint2020arXiv

Shaping the learning landscape in neural networks around wide flat minima

Learning in Deep Neural Networks (DNN) takes place by minimizing a non-convex high-dimensional loss function, typically by a stochastic gradient descent (SGD) strategy. The learning process is observed to be able to find good minimizers without getting stuck in local critical points, and that such minimizers are often satisfactory at avoiding overfitting. How these two features can be kept under control in nonlinear devices composed of millions of tunable connections is a profound and far reaching open question. In this paper we study basic non-convex one- and two-layer neural network models which learn random patterns, and derive a number of basic geometrical and algorithmic features which suggest some answers. We first show that the error loss function presents few extremely wide flat minima (WFM) which coexist with narrower minima and critical points. We then show that the minimizers of the cross-entropy loss function overlap with the WFM of the error loss. We also show examples of learning devices for which WFM do not exist. From the algorithmic perspective we derive entropy driven greedy and message passing algorithms which focus their search on wide flat regions of minimizers. In the case of SGD and cross-entropy loss, we show that a slow reduction of the norm of the weights along the learning process also leads to WFM. We corroborate the results by a numerical study of the correlations between the volumes of the minimizers, their Hessian and their generalization performance on real data.

preprint2014arXiv

Nonsingular cosmology from evolutionary quantum gravity

We provide a cosmological implementation of the evolutionary quantum gravity, describing an isotropic Universe, in the presence of a negative cosmological constant and a massive (preinflationary) scalar field. We demonstrate that the considered Universe has a nonsingular quantum behavior, associated to a primordial bounce, whose ground state has a high occupation number. Furthermore, in such a vacuum state, the super-Hamiltonian eigenvalue is negative, corresponding to a positive emerging dust energy density. The regularization of the model is performed via a polymer quantum approach to the Universe scale factor and the proper classical limit is then recovered, in agreement with a preinflationary state of the Universe. Since the dust energy density is redshifted by the Universe deSitter phase and the cosmological constant does not enter the ground state eigenvalue, we get a late-time cosmology, compatible with the present observations, endowed with a turning point in the far future.