Related papers: Logic Learning in Hopfield Networks

A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable $S_x = \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable…

We present an exact solution for the dynamics of on-line Hebbian learning in neural networks, with restricted and unrealizable training sets. In contrast to other studies on learning with restricted training sets, unrealizability is here…

The brain processes information through many layers of neurons. This deep architecture is representationally powerful, but it complicates learning by making it hard to identify the responsible neurons when a mistake is made. In machine…

Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could…

Recurrent neural networks in the chaotic regime exhibit complex dynamics reminiscent of high-level cortical activity during behavioral tasks. However, existing training methods for such networks are either biologically implausible, or…

Unifying probabilistic and logical learning is a key challenge in AI. We introduce a Bayesian inductive logic programming approach that learns minimum message length hypotheses from noisy data. Our approach balances hypothesis complexity…

Activity difference based learning algorithms-such as contrastive Hebbian learning and equilibrium propagation-have been proposed as biologically plausible alternatives to error back-propagation. However, on traditional digital chips these…

The brain performs unsupervised learning and (perhaps) simultaneous supervised learning. This raises the question as to whether a hybrid of supervised and unsupervised methods will produce better learning. Inspired by the rich space of…

Deep learning is very effective at jointly learning feature representations and classification models, especially when dealing with high dimensional input patterns. Probabilistic logic reasoning, on the other hand, is capable to take…

An increasing number of scientific experiments support the view of perception as Bayesian inference, which is rooted in Helmholtz's view of perception as unconscious inference. Recent study of logic presents a view of logical reasoning as…

Large Language Models (LLMs) typically have billions of parameters and are thus often difficult to interpret in their operation. In this work, we demonstrate that it is possible to decode neuron weights directly into token probabilities…

The plasticity property of biological neural networks allows them to perform learning and optimize their behavior by changing their configuration. Inspired by biology, plasticity can be modeled in artificial neural networks by using Hebbian…

We propose a novel framework seamlessly providing key properties of both neural nets (learning) and symbolic logic (knowledge and reasoning). Every neuron has a meaning as a component of a formula in a weighted real-valued logic, yielding a…

Modern data-driven machine learning system designs exploit inductive biases in architectural structure, invariance and equivariance requirements, task-specific loss functions, and computational optimization tools. Previous works have…

A general scheme to realize a perceptron for hardware neural networks is presented, where multiple interconnections are achieved by a superposition of Schrodinger waves. Spatially patterned potentials process information by coupling…

Combining machine learning with logic-based expert systems in order to get the best of both worlds are becoming increasingly popular. However, to what extent machine learning can already learn to reason over rule-based knowledge is still an…

The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological…

An essential goal in mechanistic interpretability to decode a network, i.e., to convert a neural network's raw weights to an interpretable algorithm. Given the difficulty of the decoding problem, progress has been made to understand the…

Large-scale deep neural networks consume expensive training costs, but the training results in less-interpretable weight matrices constructing the networks. Here, we propose a mode decomposition learning that can interpret the weight…

In this paper, we present a new supervised learning algorithm that is based on the Hebbian learning algorithm in an attempt to offer a substitute for back propagation along with the gradient descent for a more biologically plausible method.…