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While classical in many theoretical settings-and in particular in statistical physics-inspired works-the assumption of Gaussian i.i.d. input data is often perceived as a strong limitation in the context of statistics and machine learning. In this study, we redeem this line of work in the case of generalized linear classification, also known as the perceptron model, with random labels. We argue that there is a large universality class of high-dimensional input data for which we obtain the same minimum training loss as for Gaussian data with corresponding data covariance. In the limit of vanishing regularization, we further demonstrate that the training loss is independent of the data covariance. On the theoretical side, we prove this universality for an arbitrary mixture of homogeneous Gaussian clouds. Empirically, we show that the universality holds also for a broad range of real data sets.

Objectives: Fibromyalgia (FM) is a musculoskeletal syndrome characterised by widespread chronic pain often associated with systemic manifestations such as mood disturbances, persistent fatigue, unrefreshed sleep, and cognitive impairment, substantially impacting patients' health-related quality of life. Based on this background, this study aimed to evaluate the prevalence of FM syndrome in patients referring to an outpatient clinic in a central orthopaedic institute for a painful shoulder. The demographic and clinical characteristics of patients fulfilling the criteria for FM syndrome were also correlated with the severity of symptoms., Methods: Consecutive adult patients referring to the shoulder orthopaedic outpatient clinic of the ASST Gaetano Pini-CTO, Milan, Italy, to undergo a clinical evaluation were assessed for eligibility in an observational, cross-sectional, monocentric study., Results: Two hundred-one patients were enrolled: 103 males (51.2%) and 98 females (48.8%). The mean age ± standard deviation (SD) of the patients was 55.3 ± 14.3 years in the whole population. Of all the patients, 12 (5.97%) fulfilled the 2016 FM syndrome criteria based on the FM severity scale (FSS). Of these, 11 were females (91.7%, p=0.002). The mean age (SD) was 61.3 (10.8) in the positive criteria sample. Patients with positive criteria had a mean FIQR of 57.3 ± 16.8 (range 21.6-81.5)., Conclusions: We found that FM syndrome is more frequent than expected in a cohort of patients referring to a shoulder orthopaedic outpatient clinic, with a prevalence rate (6%) more than double that of the general population (2%).

Stochastic neural networks are a prototypical computational device able to build a probabilistic representation of an ensemble of external stimuli. Building on the relationship between inference and learning, we derive a synaptic plasticity rule that relies only on delayed activity correlations, and that shows a number of remarkable features. Our delayed-correlations matching (DCM) rule satisfies some basic requirements for biological feasibility: finite and noisy afferent signals, Dale's principle and asymmetry of synaptic connections, locality of the weight update computations. Nevertheless, the DCM rule is capable of storing a large, extensive number of patterns as attractors in a stochastic recurrent neural network, under general scenarios without requiring any modification: it can deal with correlated patterns, a broad range of architectures (with or without hidden neuronal states), one-shot learning with the palimpsest property, all the while avoiding the proliferation of spurious attractors. When hidden units are present, our learning rule can be employed to construct Boltzmann machine-like generative models, exploiting the addition of hidden neurons in feature extraction and classification tasks., Competing Interests: We declare we have no competing interests.

Stochasticity and limited precision of synaptic weights in neural network models are key aspects of both biological and hardware modeling of learning processes. Here we show that a neural network model with stochastic binary weights naturally gives prominence to exponentially rare dense regions of solutions with a number of desirable properties such as robustness and good generalization performance, while typical solutions are isolated and hard to find. Binary solutions of the standard perceptron problem are obtained from a simple gradient descent procedure on a set of real values parametrizing a probability distribution over the binary synapses. Both analytical and numerical results are presented. An algorithmic extension that allows to train discrete deep neural networks is also investigated.

Learning in neural networks poses peculiar challenges when using discretized rather then continuous synaptic states. The choice of discrete synapses is motivated by biological reasoning and experiments, and possibly by hardware implementation considerations as well. In this paper we extend a previous large deviations analysis which unveiled the existence of peculiar dense regions in the space of synaptic states which accounts for the possibility of learning efficiently in networks with binary synapses. We extend the analysis to synapses with multiple states and generally more plausible biological features. The results clearly indicate that the overall qualitative picture is unchanged with respect to the binary case, and very robust to variation of the details of the model. We also provide quantitative results which suggest that the advantages of increasing the synaptic precision (i.e., the number of internal synaptic states) rapidly vanish after the first few bits, and therefore that, for practical applications, only few bits may be needed for near-optimal performance, consistent with recent biological findings. Finally, we demonstrate how the theoretical analysis can be exploited to design efficient algorithmic search strategies.