In this article, we propose a variational inference formulation of auto-associative memories, allowing us to combine perceptual inference and memory retrieval into the same mathematical framework. In this formulation, the prior probability distribution onto latent representations is made memory dependent, thus pulling the inference process towards previously stored representations. We then study how different neural network approaches to variational inference can be applied in this framework. We compare methods relying on amortized inference such as Variational Auto Encoders and methods relying on iterative inference such as Predictive Coding and suggest combining both approaches to design new auto-associative memory models. We evaluate the obtained algorithms on the CIFAR10 and CLEVR image datasets and compare them with other associative memory models such as Hopfield Networks, End-to-End Memory Networks and Neural Turing Machines.

Associative memory plays an important role in human intelligence and its mechanisms have been linked to attention in machine learning. While the machine learning community's interest in associative memories has recently been rekindled, most work has focused on memory recall ( read) over memory learning ( write). In this paper, we present BayesPCN, a hierarchical associative memory capable of performing continual one-shot memory writes without meta-learning. Moreover, BayesPCN is able to gradually forget past observations ( forget) to free its memory. Experiments show that BayesPCN can recall corrupted i.i.d.

Large language models have demonstrated an impressive ability to perform factual recall. Prior work has found that transformers trained on factual recall tasks can store information at a rate proportional to their parameter count. In our work, we show that shallow transformers can use a combination of associative memories to obtain such near optimal storage capacity. We begin by proving that the storage capacities of both linear and MLP associative memories scale linearly with parameter count. We next introduce a synthetic factual recall task, and prove that a transformer with a single layer of self-attention followed by an MLP can obtain 100% accuracy on the task whenever either the total number of self-attention parameters or MLP parameters scales (up to log factors) linearly with the number of facts. In particular, the transformer can trade off between using the value matrices or the MLP as an associative memory to store the dataset of facts. We complement these expressivity results with an analysis of the gradient flow trajectory of a simplified linear attention model trained on our factual recall task, where we show that the model exhibits sequential learning behavior.

Associative memory architectures such as the Hopfield network have long been important conceptual and theoretical models for neuroscience and artificial intelligence. However, translating these abstract models into spiking neural networks has been surprisingly difficult. Indeed, much previous work has been restricted to storing a small number of primarily non-overlapping memories in large networks, thereby limiting their scalability. Here, we revisit the associative memory problem in light of recent advances in understanding spike-based computation. Using a recently-established geometric framework, we show that the spiking activity for a large class of all-inhibitory networks is situated on a low-dimensional, convex, and piecewise-linear manifold, with dynamics that move along the manifold. We then map the associative memory problem onto these dynamics, and demonstrate how the vertices of a hypercubic manifold can be used to store stable, overlapping activity patterns with a direct correspondence to the original Hopfield model. We propose several learning rules, and demonstrate a linear scaling of the storage capacity with the number of neurons, as well as robust pattern completion abilities. Overall, this work serves as a case study to demonstrate the effectiveness of using a geometrical perspective to design dynamics on neural manifolds, with implications for neuroscience and machine learning.

Firing rate models are dynamical systems widely used in applied and theoretical neuroscience to describe local cortical dynamics in neuronal populations. By providing a macroscopic perspective of neuronal activity, these models are essential for investigating oscillatory phenomena, chaotic behavior, and associative memory processes. Despite their widespread use, the application of firing rate models to associative memory networks has received limited mathematical exploration, and most existing studies are focused on specific models. Conversely, well-established associative memory designs, such as Hopfield networks, lack key biologically-relevant features intrinsic to firing rate models, including positivity and interpretable synaptic matrices that reflect excitatory and inhibitory interactions. To address this gap, we propose a general framework that ensures the emergence of re-scaled memory patterns as stable equilibria in the firing rate dynamics. Furthermore, we analyze the conditions under which the memories are locally and globally asymptotically stable, providing insights into constructing biologically-plausible and robust systems for associative memory retrieval.

The Entropic Associative Memory holds objects in a 2D relation or ``memory plane'' using a finite table as the medium. Memory objects are stored by reinforcing simultaneously the cells used by the cue, implementing a form of Hebb's learning rule. Stored objects are ``overlapped'' on the medium, hence the memory is indeterminate and has an entropy value at each state. The retrieval operation constructs an object from the cue and such indeterminate content. In this paper we present the extension to the hetero-associative case in which these properties are preserved. Pairs of hetero-associated objects, possibly of different domain and/or modalities, are held in a 4D relation. The memory retrieval operation selects a largely indeterminate 2D memory plane that is specific to the input cue; however, there is no cue left to retrieve an object from such latter plane. We propose three incremental methods to address such missing cue problem, which we call random, sample and test, and search and test. The model is assessed with composite recollections consisting of manuscripts digits and letters selected from the MNIST and the EMNIST corpora, respectively, such that cue digits retrieve their associated letters and vice versa. We show the memory performance and illustrate the memory retrieval operation using all three methods. The system shows promise for storing, recognizing and retrieving very large sets of object with very limited computing resources.

We study the optimal memorization capacity of modern Hopfield models and Kernelized Hopfield Models (KHMs), a transformer-compatible class of Dense Associative Memories. We present a tight analysis by establishing a connection between the memory configuration of KHMs and spherical codes from information theory. Specifically, we treat the stored memory set as a specialized spherical code. This enables us to cast the memorization problem in KHMs into a point arrangement problem on a hypersphere. We show that the optimal capacity of KHMs occurs when the feature space allows memories to form an optimal spherical code. This unique perspective leads to: (i) An analysis of how KHMs achieve optimal memory capacity, and identify corresponding necessary conditions. Importantly, we establish an upper capacity bound that matches the well-known exponential lower bound in the literature. This provides the first tight and optimal asymptotic memory capacity for modern Hopfield models. (ii) A sub-linear time algorithm $\mathtt{U}\text{-}\mathtt{Hop}$+ to reach KHMs' optimal capacity. (iii) An analysis of the scaling behavior of the required feature dimension relative to the number of stored memories. These efforts improve both the retrieval capability of KHMs and the representation learning of corresponding transformers. Experimentally, we provide thorough numerical results to back up theoretical findings.

Dense Associative Memories are high storage capacity variants of the Hopfield networks that are capable of storing a large number of memory patterns in the weights of the network of a given size. Their common formulations typically require storing each pattern in a separate set of synaptic weights, which leads to the increase of the number of synaptic weights when new patterns are introduced. In this work we propose an alternative formulation of this class of models using random features, commonly used in kernel methods. In this formulation the number of network's parameters remains fixed. At the same time, new memories can be added to the network by modifying existing weights. We show that this novel network closely approximates the energy function and dynamics of conventional Dense Associative Memories and shares their desirable computational properties.

An associative memory is a structure learned from a dataset \mathcal{M} of vectors (signals) in a way such that, given a noisy version of one of the vectors as input, the nearest valid vector from \mathcal{M} (nearest neighbor) is provided as output, preferably via a fast iterative algorithm. Traditionally, binary (or q -ary) Hopfield neural networks are used to model the above structure. In this paper, for the first time, we propose a model of associative memory based on sparse recovery of signals. Our basic premise is simple. For a dataset, we learn a set of linear constraints that every vector in the dataset must satisfy.

Associative memories in the brain receive and store patterns of activity registered by the sensory neurons, and are able to retrieve them when necessary. Due to their importance in human intelligence, computational models of associative memories have been developed for several decades now. In this paper, we present a novel neural model for realizing associative memories, which is based on a hierarchical generative network that receives external stimuli via sensory neurons. It is trained using predictive coding, an error-based learning algorithm inspired by information processing in the cortex. To test the model's capabilities, we perform multiple retrieval experiments from both corrupted and incomplete data points. In an extensive comparison, we show that this new model outperforms in retrieval accuracy and robustness popular associative memory models, such as autoencoders trained via backpropagation, and modern Hopfield networks.