Recurrent predictive coding models for associative memory employing covariance learning

PrediRep: Modeling hierarchical predictive coding with an unsupervised deep learning network

Hierarchical predictive coding (hPC) provides a compelling framework for understanding how the cortex predicts future sensory inputs by minimizing prediction errors through an internal generative model of the external world. Existing deep learning models inspired by hPC incorporate architectural choices that deviate from core hPC principles, potentially limiting their utility for neuroscientific investigations. We introduce PrediRep (Predicting Representations), a novel deep learning network that adheres more closely to architectural principles of hPC. We validate PrediRep by comparing its functional alignment with hPC to that of existing models after being trained on a next-frame prediction task. Our findings demonstrate that PrediRep, particularly when trained with an all-level loss function (PrediRepAll), exhibits high functional alignment with hPC. In contrast to other contemporary deep learning networks inspired by hPC, it consistently processes input-relevant information at higher hierarchical levels and maintains active representations and accurate predictions across all hierarchical levels. Although PrediRep was designed primarily to serve as a model suitable for neuroscientific research rather than to optimize performance, it nevertheless achieves competitive performance in next-frame prediction while utilizing significantly fewer trainable parameters than alternative models. Our results underscore that even minor architectural deviations from neuroscientific theories like hPC can lead to significant functional discrepancies. By faithfully adhering to hPC principles, PrediRep provides a more accurate tool for in silico exploration of cortical phenomena. PrediRep's lightweight and biologically plausible design makes it well-suited for future studies aiming to investigate the neural underpinnings of predictive coding and to derive empirically testable predictions.

Toward a Biologically Plausible SNN-Based Associative Memory with Context-Dependent Hebbian Connectivity

In this paper, we propose a spiking neural network model with Hebbian connectivity for implementing energy-efficient associative memory, whose activity is determined by input stimuli. The model consists of three interacting layers of Hodgkin-Huxley-Mainen spiking neurons with excitatory and inhibitory synaptic connections. Information patterns are stored in memory using a symmetric Hebbian matrix and can be retrieved in response to a specific stimulus pattern. Binary images are encoded using in-phase and anti-phase oscillations relative to a global clock signal. Utilizing the phase-locking effect allows for cluster synchronization of neurons (both on the input and output layers). Interneurons in the intermediate layer filter signal propagation pathways depending on the context of the input layer, effectively engaging only a portion of the synaptic connections within the Hebbian matrix for recognition. The stability of the oscillation phase is investigated for both in-phase and anti-phase synchronization modes when recognizing direct and inverse images. This context-dependent effect opens promising avenues for the development of analog hardware circuits for energy-efficient neurocomputing applications, potentially leading to breakthroughs in artificial intelligence and cognitive computing.

Learning probability distributions of sensory inputs with Monte Carlo predictive coding

It has been suggested that the brain employs probabilistic generative models to optimally interpret sensory information. This hypothesis has been formalised in distinct frameworks, focusing on explaining separate phenomena. On one hand, classic predictive coding theory proposed how the probabilistic models can be learned by networks of neurons employing local synaptic plasticity. On the other hand, neural sampling theories have demonstrated how stochastic dynamics enable neural circuits to represent the posterior distributions of latent states of the environment. These frameworks were brought together by variational filtering that introduced neural sampling to predictive coding. Here, we consider a variant of variational filtering for static inputs, to which we refer as Monte Carlo predictive coding (MCPC). We demonstrate that the integration of predictive coding with neural sampling results in a neural network that learns precise generative models using local computation and plasticity. The neural dynamics of MCPC infer the posterior distributions of the latent states in the presence of sensory inputs, and can generate likely inputs in their absence. Furthermore, MCPC captures the experimental observations on the variability of neural activity during perceptual tasks. By combining predictive coding and neural sampling, MCPC can account for both sets of neural data that previously had been explained by these individual frameworks.

Spiking representation learning for associative memories

Networks of interconnected neurons communicating through spiking signals offer the bedrock of neural computations. Our brain's spiking neural networks have the computational capacity to achieve complex pattern recognition and cognitive functions effortlessly. However, solving real-world problems with artificial spiking neural networks (SNNs) has proved to be difficult for a variety of reasons. Crucially, scaling SNNs to large networks and processing large-scale real-world datasets have been challenging, especially when compared to their non-spiking deep learning counterparts. The critical operation that is needed of SNNs is the ability to learn distributed representations from data and use these representations for perceptual, cognitive and memory operations. In this work, we introduce a novel SNN that performs unsupervised representation learning and associative memory operations leveraging Hebbian synaptic and activity-dependent structural plasticity coupled with neuron-units modelled as Poisson spike generators with sparse firing (~1 Hz mean and ~100 Hz maximum firing rate). Crucially, the architecture of our model derives from the neocortical columnar organization and combines feedforward projections for learning hidden representations and recurrent projections for forming associative memories. We evaluated the model on properties relevant for attractor-based associative memories such as pattern completion, perceptual rivalry, distortion resistance, and prototype extraction.

A sparse quantized hopfield network for online-continual memory

An important difference between brains and deep neural networks is the way they learn. Nervous systems learn online where a stream of noisy data points are presented in a non-independent, identically distributed way. Further, synaptic plasticity in the brain depends only on information local to synapses. Deep networks, on the other hand, typically use non-local learning algorithms and are trained in an offline, non-noisy, independent, identically distributed setting. Understanding how neural networks learn under the same constraints as the brain is an open problem for neuroscience and neuromorphic computing. A standard approach to this problem has yet to be established. In this paper, we propose that discrete graphical models that learn via an online maximum a posteriori learning algorithm could provide such an approach. We implement this kind of model in a neural network called the Sparse Quantized Hopfield Network. We show our model outperforms state-of-the-art neural networks on associative memory tasks, outperforms these networks in online, continual settings, learns efficiently with noisy inputs, and is better than baselines on an episodic memory task.

Predictive coding networks for temporal prediction

One of the key problems the brain faces is inferring the state of the world from a sequence of dynamically changing stimuli, and it is not yet clear how the sensory system achieves this task. A well-established computational framework for describing perceptual processes in the brain is provided by the theory of predictive coding. Although the original proposals of predictive coding have discussed temporal prediction, later work developing this theory mostly focused on static stimuli, and key questions on neural implementation and computational properties of temporal predictive coding networks remain open. Here, we address these questions and present a formulation of the temporal predictive coding model that can be naturally implemented in recurrent networks, in which activity dynamics rely only on local inputs to the neurons, and learning only utilises local Hebbian plasticity. Additionally, we show that temporal predictive coding networks can approximate the performance of the Kalman filter in predicting behaviour of linear systems, and behave as a variant of a Kalman filter which does not track its own subjective posterior variance. Importantly, temporal predictive coding networks can achieve similar accuracy as the Kalman filter without performing complex mathematical operations, but just employing simple computations that can be implemented by biological networks. Moreover, when trained with natural dynamic inputs, we found that temporal predictive coding can produce Gabor-like, motion-sensitive receptive fields resembling those observed in real neurons in visual areas. In addition, we demonstrate how the model can be effectively generalized to nonlinear systems. Overall, models presented in this paper show how biologically plausible circuits can predict future stimuli and may guide research on understanding specific neural circuits in brain areas involved in temporal prediction.

Competitive learning to generate sparse representations for associative memory

One of the most well established brain principles, Hebbian learning, has led to the theoretical concept of neural assemblies. Based on it, many interesting brain theories have spawned. Palm's work implements this concept through multiple binary Willshaw associative memories, in a model that not only has a wide cognitive explanatory power but also makes neuroscientific predictions. Yet, Willshaw's associative memory can only achieve top capacity when the stored vectors are extremely sparse (number of active bits can grow logarithmically with the vector's length). This strict requirement makes it difficult to apply any model that uses this associative memory, like Palm's, to real data. Hence the fact that most works apply the memory to optimal randomly generated codes that do not represent any information. This issue creates the need for encoders that can take real data, and produce sparse representations - a problem which is also raised following Barlow's efficient coding principle. In this work, we propose a biologically-constrained network that encodes images into codes that are suitable for Willshaw's associative memory. The network is organized into groups of neurons that specialize on local receptive fields, and learn through a competitive scheme. After conducting auto- and hetero-association experiments on two visual data sets, we can conclude that our network not only beats sparse coding baselines, but also that it comes close to the performance achieved using optimal random codes.

Sequential Memory with Temporal Predictive Coding

Forming accurate memory of sequential stimuli is a fundamental function of biological agents. However, the computational mechanism underlying sequential memory in the brain remains unclear. Inspired by neuroscience theories and recent successes in applying predictive coding (PC) to static memory tasks, in this work we propose a novel PC-based model for sequential memory, called temporal predictive coding (tPC). We show that our tPC models can memorize and retrieve sequential inputs accurately with a biologically plausible neural implementation. Importantly, our analytical study reveals that tPC can be viewed as a classical Asymmetric Hopfield Network (AHN) with an implicit statistical whitening process, which leads to more stable performance in sequential memory tasks of structured inputs. Moreover, we find that tPC exhibits properties consistent with behavioral observations and theories in neuroscience, thereby strengthening its biological relevance. Our work establishes a possible computational mechanism underlying sequential memory in the brain that can also be theoretically interpreted using existing memory model frameworks.