Recent works have derived neural networks with online correlation-based learning rules to perform \textit{kernel similarity matching}. These works applied existing linear similarity matching algorithms to nonlinear features generated with random Fourier methods. In this paper attempt to perform kernel similarity matching by directly learning the nonlinear features. Our algorithm proceeds by deriving and then minimizing an upper bound for the sum of squared errors between output and input kernel similarities. The construction of our upper bound leads to online correlation-based learning rules which can be implemented with a 1 layer recurrent neural network. In addition to generating high-dimensional linearly separable representations, we show that our upper bound naturally yields representations which are sparse and selective for specific input patterns. We compare the approximation quality of our method to neural random Fourier method and variants of the popular but non-biological ``Nystr{\o}m'' method for approximating the kernel matrix. Our method appears to be comparable or better than randomly sampled Nystr{\o}m methods when the outputs are relatively low dimensional (although still potentially higher dimensional than the inputs) but less faithful when the outputs are very high dimensional.

Abstract-- Artificial neural networks can be used to solve a variety of robotic tasks. However, they risk failing catastrophically when faced with out-of-distribution (OOD) situations. Several approaches have employed a type of synaptic plasticity known as Hebbian learning that can dynamically adjust weights based on local neural activities. Research has shown that synaptic plasticity can make policies more robust and help them adapt to unforeseen changes in the environment. In this work, we improve the Hebbian network with a weight normalization mechanism for preventing weight divergence, analyze the principal components of the Hebbian's weights, The disadvantages of these In the field of machine learning research, deep neural types of solutions are that they extend the necessary training networks (DNNs) have been shown to be useful across a time or risk, resulting in an architecture that is overly specific wide range of tasks [1], [2], including robotics [3], [4], [5]. to the task for which it was designed [11], [12]. However, policies for agent control based on deep neural Animals, on the other hand, demonstrate remarkable networks tend to be brittle [6], meaning that they are at risk adaptability in adjusting their motor patterns to accomplish of catastrophic failure when faced with out-of-distribution various tasks. Synaptic plasticity is thought to play (OOD) situations [7], [8].

Recent works have derived neural networks with online correlation-based learning rules to perform \textit{kernel similarity matching}. These works applied existing linear similarity matching algorithms to nonlinear features generated with random Fourier methods. In this paper attempt to perform kernel similarity matching by directly learning the nonlinear features. Our algorithm proceeds by deriving and then minimizing an upper bound for the sum of squared errors between output and input kernel similarities. The construction of our upper bound leads to online correlation-based learning rules which can be implemented with a 1 layer recurrent neural network.

A modern challenge of Artificial Intelligence is learning multiple patterns at once (i.e.parallel learning). While this can not be accomplished by standard Hebbian associative neural networks, in this paper we show how the Multitasking Hebbian Network (a variation on theme of the Hopfield model working on sparse data-sets) is naturally able to perform this complex task. We focus on systems processing in parallel a finite (up to logarithmic growth in the size of the network) amount of patterns, mirroring the low-storage level of standard associative neural networks at work with pattern recognition. For mild dilution in the patterns, the network handles them hierarchically, distributing the amplitudes of their signals as power-laws w.r.t. their information content (hierarchical regime), while, for strong dilution, all the signals pertaining to all the patterns are raised with the same strength (parallel regime). Further, confined to the low-storage setting (i.e., far from the spin glass limit), the presence of a teacher neither alters the multitasking performances nor changes the thresholds for learning: the latter are the same whatever the training protocol is supervised or unsupervised. Results obtained through statistical mechanics, signal-to-noise technique and Monte Carlo simulations are overall in perfect agreement and carry interesting insights on multiple learning at once: for instance, whenever the cost-function of the model is minimized in parallel on several patterns (in its description via Statistical Mechanics), the same happens to the standard sum-squared error Loss function (typically used in Machine Learning).

We consider dense, associative neural-networks trained by a teacher (i.e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as quality and quantity of the training dataset, network storage and noise, that is valid in the limit of large network size and structureless datasets: these networks may work in a ultra-storage regime (where they can handle a huge amount of patterns, if compared with shallow neural networks) or in a ultra-detection regime (where they can perform pattern recognition at prohibitive signal-to-noise ratios, if compared with shallow neural networks). Guided by the random theory as a reference framework, we also test numerically learning, storing and retrieval capabilities shown by these networks on structured datasets as MNist and Fashion MNist. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate supervised learning in neural networks, beyond the shallow limit, in general.

This work studies how brain-inspired neural ensembles equipped with local Hebbian plasticity can perform active inference (AIF) in order to control dynamical agents. A generative model capturing the environment dynamics is learned by a network composed of two distinct Hebbian ensembles: a posterior network, which infers latent states given the observations, and a state transition network, which predicts the next expected latent state given current state-action pairs. Experimental studies are conducted using the Mountain Car environment from the OpenAI gym suite, to study the effect of the various Hebbian network parameters on the task performance. It is shown that the proposed Hebbian AIF approach outperforms the use of Q-learning, while not requiring any replay buffer, as in typical reinforcement learning systems. These results motivate further investigations of Hebbian learning for the design of AIF networks that can learn environment dynamics without the need for revisiting past buffered experiences.

This paper introduces the modulated Hebbian plus Q network architecture (MOHQA) for solving challenging partially observable Markov decision processes (POMDPs) deep reinforcement learning problems with sparse rewards and confounding observations. The proposed architecture combines a deep Q-network (DQN), and a modulated Hebbian network with neural eligibility traces (MOHN). Bio-inspired neural traces are used to bridge temporal delays between actions and rewards. The purpose is to discover distal cause-effect relationships where confounding observations and sparse rewards cause standard RL algorithms to fail. Each of the two modules of the network (DQN and MOHN) is responsible for different aspects of learning. DQN learns low level features and control, while MOHN contributes to the high-level decisions by bridging rewards with past actions. The strength of the approach is to support a DQN standard framework when temporal difference errors are difficult to compute due to non-observable states. The system is tested on a set of generalized decision making problems encoded as decision tree graphs that deliver delayed rewards after key decision points and confounding observations. The simulations show that the proposed approach helps solve problems that are currently challenging for state-of-the-art deep reinforcement learning algorithms.