Related papers: Spherical perceptron as a storage memory with limi…

A fundamental problem in neuroscience is understanding how working memory -- the ability to store information at intermediate timescales, like 10s of seconds -- is implemented in realistic neuronal networks. The most likely candidate…

A pre-trained generator has been frequently adopted in compressed sensing (CS) due to its ability to effectively estimate signals with the prior of NNs. In order to further refine the NN-based prior, we propose a framework that allows the…

Probabilistic representations, such as Bayesian and Markov networks, are fundamental to much of statistical machine learning. Thus, learning probabilistic representations directly from data is a deep challenge, the main computational…

Quantum computing and neural networks show great promise for the future of information processing. In this paper we study a quantum reservoir computer (QRC), a framework harnessing quantum dynamics and designed for fast and efficient…

Prediction-powered inference is a framework for performing valid statistical inference when an experimental dataset is supplemented with predictions from a machine-learning system. The framework yields simple algorithms for computing…

We comment on the fact that gradient ascent for logistic regression has a connection with the perceptron learning algorithm. Logistic learning is the "soft" variant of perceptron learning.

Probability-generating function (PGF) kernels are introduced, which constitute a class of kernels supported on the unit hypersphere, for the purposes of spherical data analysis. PGF kernels generalize RBF kernels in the context of spherical…

We analyze a learning method that uses a margin $\kappa$ {\it a la} Gardner for simple perceptron learning. This method corresponds to the perceptron learning when $\kappa=0$, and to the Hebbian learning when $\kappa \to \infty$.…

On-line and batch learning of a perceptron in a discrete weight space, where each weight can take $2 L+1$ different values, are examined analytically and numerically. The learning algorithm is based on the training of the continuous…

This paper examines the role of threshold logic in understanding generative artificial intelligence. Threshold functions, originally studied in the 1960s in digital circuit synthesis, provide a structurally transparent model of neural…

We present two main contributions to the expected star discrepancy theory. First, we derive a sharper expected upper bound for jittered sampling, improving the leading constants and logarithmic terms compared to the state-of-the-art [Doerr,…

Skeleton-based action recognition has attracted considerable attention in computer vision since skeleton data is more robust to the dynamic circumstance and complicated background than other modalities. Recently, many researchers have used…

How can we perform efficient inference and learning in directed probabilistic models, in the presence of continuous latent variables with intractable posterior distributions, and large datasets? We introduce a stochastic variational…

Standard accounts of memory consolidation emphasise the stabilisation of stored representations, but struggle to explain representational drift, semanticisation, or the necessity of offline replay. Here we propose that high-capacity…

This paper proposes a standard way to represent sparse tensors. A broad theoretical framework for tensor data scattering methods used in various deep learning frameworks is established. This paper presents a theorem that is very important…

Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on the sphere and the…

The main problem about replacing LTP as a memory mechanism has been to find other highly abstract, easily understandable principles for induced plasticity. In this paper we attempt to lay out such a basic mechanism, namely intrinsic…

We propose a new density estimation algorithm. Given $n$ i.i.d. observations from a distribution belonging to a class of densities on $\mathbb{R}^d$, our estimator outputs any density in the class whose "perceptron discrepancy" with the…

Reservoir computing is a powerful framework for modeling dynamical systems due to its universality and computational efficiency. However, a major challenge is achieving a forecast with accurate long-time statistics, or climate, which is…

Gardner's analysis of the optimal storage capacity of neural networks is extended to study finite-temperature effects. The typical volume of the space of interactions is calculated for strongly-diluted networks as a function of the storage…