Equipping large language models (LLMs) with latent-space memory has attracted increasing attention as they can extend the context window of existing language models. However, retaining information from the distant past remains a challenge. For example, MemoryLLM (Wang et al., 2024a), as a representative work with latent-space memory, compresses past information into hidden states across all layers, forming a memory pool of 1B parameters. While effective for sequence lengths up to 16k tokens, it struggles to retain knowledge beyond 20k tokens. In this work, we address this limitation by introducing M+, a memory-augmented model based on MemoryLLM that significantly enhances long-term information retention. M+ integrates a long-term memory mechanism with a co-trained retriever, dynamically retrieving relevant information during text generation. We evaluate M+ on diverse benchmarks, including long-context understanding and knowledge retention tasks. Experimental results show that M+ significantly outperforms MemoryLLM and recent strong baselines, extending knowledge retention from under 20k to over 160k tokens with similar GPU memory overhead.

We propose a novel energy function for Dense Associative Memory (DenseAM) networks, the log-sum-ReLU (LSR), inspired by optimal kernel density estimation. Unlike the common log-sum-exponential (LSE) function, LSR is based on the Epanechnikov kernel and enables exact memory retrieval with exponential capacity without requiring exponential separation functions. Uniquely, it introduces abundant additional emergent local minima while preserving perfect pattern recovery --- a characteristic previously unseen in DenseAM literature. Empirical results show that LSR energy has significantly more local minima (memories) that have comparable log-likelihood to LSE-based models. Analysis of LSR's emergent memories on image datasets reveals a degree of creativity and novelty, hinting at this method's potential for both large-scale memory storage and generative tasks.

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.

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been integrated with various deep learning architectures. We uncover a novel connection between the AM dynamics and the inherent discrete assignment necessary in clustering to propose a novel unconstrained continuous relaxation of the discrete clustering problem, enabling end-to-end differentiable clustering with AM, dubbed ClAM. Leveraging the pattern completion ability of AMs, we further develop a novel self-supervised clustering loss. Our evaluations on varied datasets demonstrate that ClAM benefits from the self-supervision, and significantly improves upon both the traditional Lloyd's k-means algorithm, and more recent continuous clustering relaxations (by upto 60% in terms of the Silhouette Coefficient).

Sequence memory is an essential attribute of natural and artificial intelligence that enables agents to encode, store, and retrieve complex sequences of stimuli and actions. Computational models of sequence memory have been proposed where recurrent Hopfield-like neural networks are trained with temporally asymmetric Hebbian rules. However, these networks suffer from limited sequence capacity (maximal length of the stored sequence) due to interference between the memories. Inspired by recent work on Dense Associative Memories, we expand the sequence capacity of these models by introducing a nonlinear interaction term, enhancing separation between the patterns. We derive novel scaling laws for sequence capacity with respect to network size, significantly outperforming existing scaling laws for models based on traditional Hopfield networks, and verify these theoretical results with numerical simulation. Moreover, we introduce a generalized pseudoinverse rule to recall sequences of highly correlated patterns. Finally, we extend this model to store sequences with variable timing between states' transitions and describe a biologically-plausible implementation, with connections to motor neuroscience.

Our work combines aspects of three promising paradigms in machine learning, namely, attention mechanism, energy-based models, and associative memory. Attention is the power-house driving modern deep learning successes, but it lacks clear theoretical foundations. Energy-based models allow a principled approach to discriminative and generative tasks, but the design of the energy functional is not straightforward. At the same time, Dense Associative Memory models or Modern Hopfield Networks have a well-established theoretical foundation, and allow an intuitive design of the energy function. We propose a novel architecture, called the Energy Transformer (or ET for short), that uses a sequence of attention layers that are purposely designed to minimize a specifically engineered energy function, which is responsible for representing the relationships between the tokens. In this work, we introduce the theoretical foundations of ET, explore its empirical capabilities using the image completion task, and obtain strong quantitative results on the graph anomaly detection and graph classification tasks.

The fruit fly Drosophila’s olfactory circuit has inspired a new locality sensitive hashing (LSH) algorithm, FlyHash. In contrast with classical LSH algorithms that produce low dimensional hash codes, FlyHash produces sparse high-dimensional hash codes and has also been shown to have superior empirical performance compared to classical LSH algorithms in similarity search. However, FlyHash uses random projections and cannot learn from data. Building on inspiration from FlyHash and the ubiquity of sparse expansive representations in neurobiology, our work proposes a novel hashing algorithm BioHash that produces sparse high dimensional hash codes in a data-driven manner. We show that BioHash outperforms previously published benchmarks for various hashing methods. Since our learning algorithm is based on a local and biologically plausible synaptic plasticity rule, our work provides evidence for the proposal that LSH might be a computational reason for the abundance of sparse expansive motifs in a variety of biological systems. We also propose a convolutional variant BioConvHash that further improves performance. From the perspective of computer science, BioHash and BioConvHash are fast, scalable and yield compressed binary representations that are useful for similarity search.

Deep neural networks (DNNs) trained in a supervised way suffer from two known problems. First, the minima of the objective function used in learning correspond to data points (also known as rubbish examples or fooling images) that lack semantic similarity with the training data. Second, a clean input can be changed by a small, and often imperceptible for human vision, perturbation so that the resulting deformed input is misclassified by the network. These findings emphasize the differences between the ways DNNs and humans classify patterns and raise a question of designing learning algorithms that more accurately mimic human perception compared to the existing methods. Our article examines these questions within the framework of dense associative memory (DAM) models. These models are defined by the energy function, with higher-order (higher than quadratic) interactions between the neurons. We show that in the limit when the power of the interaction vertex in the energy function is sufficiently large, these models have the following three properties. First, the minima of the objective function are free from rubbish images, so that each minimum is a semantically meaningful pattern. Second, artificial patterns poised precisely at the decision boundary look ambiguous to human subjects and share aspects of both classes that are separated by that decision boundary. Third, adversarial images constructed by models with small power of the interaction vertex, which are equivalent to DNN with rectified linear units, fail to transfer to and fool the models with higher-order interactions. This opens up the possibility of using higher-order models for detecting and stopping malicious adversarial attacks. The results we present suggest that DAMs with higher-order energy functions are more robust to adversarial and rubbish inputs than DNNs with rectified linear units.

A model of associative memory is studied, which stores and reliably retrieves many more patterns than the number of neurons in the network. We propose a simple duality between this dense associative memory and neural networks commonly used in deep learning. On the associative memory side of this duality, a family of models that smoothly interpolates between two limiting cases can be constructed. One limit is referred to as the feature-matching mode of pattern recognition, and the other one as the prototype regime. On the deep learning side of the duality, this family corresponds to feedforward neural networks with one hidden layer and various activation functions, which transmit the activities of the visible neurons to the hidden layer. This family of activation functions includes logistics, rectified linear units, and rectified polynomials of higher degrees. The proposed duality makes it possible to apply energy-based intuition from associative memory to analyze computational properties of neural networks with unusual activation functions - the higher rectified polynomials which until now have not been used in deep learning. The utility of the dense memories is illustrated for two test cases: the logical gate XOR and the recognition of handwritten digits from the MNIST data set.