Related papers: A Noise Sensitivity Exponent Controls Large Statis…

Neural networks are known to develop latent representations that are $aligned$, namely structurally similar across networks trained with different architectures, training protocols, or training datasets. We study this phenomenon in a…

Modern neural networks are undeniably successful. Numerous studies have investigated how the curvature of loss landscapes can affect the quality of solutions. In this work we consider the Hessian matrix during network training. We reiterate…

For three decades statistical mechanics has been providing a framework to analyse neural networks. However, the theoretically tractable models, e.g., perceptrons, random features models and kernel machines, or multi-index models and…

We propose a deep learning framework for modeling complex high-dimensional densities called Non-linear Independent Component Estimation (NICE). It is based on the idea that a good representation is one in which the data has a distribution…

The noise sensitivity of a Boolean function describes its likelihood to flip under small perturbations of its input. Introduced in the seminal work of Benjamini, Kalai and Schramm [Inst. Hautes \'{E}tudes Sci. Publ. Math. 90 (1999) 5-43],…

Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…

The expressive capacity of quantum systems for machine learning is limited by quantum sampling noise incurred during measurement. Although it is generally believed that noise limits the resolvable capacity of quantum systems, the precise…

Spikes are the currency in central nervous systems for information transmission and processing. They are also believed to play an essential role in low-power consumption of the biological systems, whose efficiency attracts increasing…

Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and nonlinearity and differential equations with varying…

Bayesian neural networks with latent variables are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, can capture complex noise patterns…

We consider the problem of mixed sparse linear regression with two components, where two real $k$-sparse signals $\beta_1, \beta_2$ are to be recovered from $n$ unlabelled noisy linear measurements. The sparsity is allowed to be sublinear…

Noise robustness is critical when applying automatic speech recognition (ASR) in real-world scenarios. One solution involves the used of speech enhancement (SE) models as the front end of ASR. However, neural network-based (NN-based) SE…

Representation learning is fundamental to modern machine learning, powering applications such as text retrieval and multimodal understanding. However, learning robust and generalizable representations remains challenging. While prior work…

We explore the sequential decision making problem where the goal is to estimate uniformly well a number of linear models, given a shared budget of random contexts independently sampled from a known distribution. The decision maker must…

We consider the class of noisy multi-layered sigmoid recurrent neural networks with $w$ (unbounded) weights for classification of sequences of length $T$, where independent noise distributed according to $\mathcal{N}(0,\sigma^2)$ is added…

Learning and decision-making in domains with naturally high noise-to-signal ratio, such as Finance or Healthcare, is often challenging, while the stakes are very high. In this paper, we study the problem of learning and acting under a…

We present a theoretical analysis of the training process for a single-layer GAN fed by high-dimensional input data. The training dynamics of the proposed model at both microscopic and macroscopic scales can be exactly analyzed in the…

Cortical sensory neurons are known to be highly variable, in the sense that responses evoked by identical stimuli often change dramatically from trial to trial. The origin of this variability is uncertain, but it is usually interpreted as…

We provide a new robust convergence analysis of the well-known power method for computing the dominant singular vectors of a matrix that we call the noisy power method. Our result characterizes the convergence behavior of the algorithm when…

When feedback is absorbed faster than task structure can be evaluated, the learner will favor feedback over truth. A two-timescale model shows this feedback-truth gap is inevitable whenever the two rates differ and vanishes only when they…