Daily Papers

Vector Symbolic Architectures (VSAs) have emerged as a novel framework for enabling interpretable machine learning algorithms equipped with the ability to reason and explain their decision processes. The basic idea is to represent discrete information through high dimensional random vectors. Complex data structures can be built up with operations over vectors such as the "binding" operation involving element-wise vector multiplication, which associates data together. The reverse task of decomposing the associated elements is a combinatorially hard task, with an exponentially large search space. The main algorithm for performing this search is the resonator network, inspired by Hopfield network-based memory search operations. In this work, we introduce a new variant of the resonator network, based on self-attention based update rules in the iterative search problem. This update rule, based on the Hopfield network with log-sum-exp energy function and norm-bounded states, is shown to substantially improve the performance and rate of convergence. As a result, our algorithm enables a larger capacity for associative memory, enabling applications in many tasks like perception based pattern recognition, scene decomposition, and object reasoning. We substantiate our algorithm with a thorough evaluation and comparisons to baselines.

Vector Symbolic Architectures (VSAs) give a way to represent a complex object as a single fixed-length vector, so that similar objects have similar vector representations. These vector representations then become easy to use for machine learning or nearest-neighbor search. We review a previously proposed VSA method, MBAT (Matrix Binding of Additive Terms), which uses multiplication by random matrices for binding related terms. However, multiplying by such matrices introduces instabilities which can harm performance. Making the random matrices be orthogonal matrices provably fixes this problem. With respect to larger scale applications, we see how to apply MBAT vector representations for any data expressed in JSON. JSON is used in numerous programming languages to express complex data, but its native format appears highly unsuited for machine learning. Expressing JSON as a fixed-length vector makes it readily usable for machine learning and nearest-neighbor search. Creating such JSON vectors also shows that a VSA needs to employ binding operations that are non-commutative. VSAs are now ready to try with full-scale practical applications, including healthcare, pharmaceuticals, and genomics. Keywords: MBAT (Matrix Binding of Additive Terms), VSA (Vector Symbolic Architecture), HDC (Hyperdimensional Computing), Distributed Representations, Binding, Orthogonal Matrices, Recurrent Connections, Machine Learning, Search, JSON, VSA Applications

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership i in S and estimating set intersection sizes |X cap Y| for two sets of symbols X and Y, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

Despite their capabilities, Large Language Models (LLMs) remain opaque with limited understanding of their internal representations. Current interpretability methods, such as direct logit attribution (DLA) and sparse autoencoders (SAEs), provide restricted insight due to limitations such as the model's output vocabulary or unclear feature names. This work introduces Hyperdimensional Probe, a novel paradigm for decoding information from the LLM vector space. It combines ideas from symbolic representations and neural probing to project the model's residual stream into interpretable concepts via Vector Symbolic Architectures (VSAs). This probe combines the strengths of SAEs and conventional probes while overcoming their key limitations. We validate our decoding paradigm with controlled input-completion tasks, probing the model's final state before next-token prediction on inputs spanning syntactic pattern recognition, key-value associations, and abstract inference. We further assess it in a question-answering setting, examining the state of the model both before and after text generation. Our experiments show that our probe reliably extracts meaningful concepts across varied LLMs, embedding sizes, and input domains, also helping identify LLM failures. Our work advances information decoding in LLM vector space, enabling extracting more informative, interpretable, and structured features from neural representations.

Hyperdimensional computing (HD), also known as vector symbolic architectures (VSA), is a framework for computing with distributed representations by exploiting properties of random high-dimensional vector spaces. The commitment of the scientific community to aggregate and disseminate research in this particularly multidisciplinary area has been fundamental for its advancement. Joining these efforts, we present Torchhd, a high-performance open source Python library for HD/VSA. Torchhd seeks to make HD/VSA more accessible and serves as an efficient foundation for further research and application development. The easy-to-use library builds on top of PyTorch and features state-of-the-art HD/VSA functionality, clear documentation, and implementation examples from well-known publications. Comparing publicly available code with their corresponding Torchhd implementation shows that experiments can run up to 100x faster. Torchhd is available at: https://github.com/hyperdimensional-computing/torchhd.

Classification of time series data is an important task for many application domains. One of the best existing methods for this task, in terms of accuracy and computation time, is MiniROCKET. In this work, we extend this approach to provide better global temporal encodings using hyperdimensional computing (HDC) mechanisms. HDC (also known as Vector Symbolic Architectures, VSA) is a general method to explicitly represent and process information in high-dimensional vectors. It has previously been used successfully in combination with deep neural networks and other signal processing algorithms. We argue that the internal high-dimensional representation of MiniROCKET is well suited to be complemented by the algebra of HDC. This leads to a more general formulation, HDC-MiniROCKET, where the original algorithm is only a special case. We will discuss and demonstrate that HDC-MiniROCKET can systematically overcome catastrophic failures of MiniROCKET on simple synthetic datasets. These results are confirmed by experiments on the 128 datasets from the UCR time series classification benchmark. The extension with HDC can achieve considerably better results on datasets with high temporal dependence without increasing the computational effort for inference.

We present HyperSeg, a hyperdimensional computing (HDC) approach to unsupervised dialogue topic segmentation. HDC is a class of vector symbolic architectures that leverages the probabilistic orthogonality of randomly drawn vectors at extremely high dimensions (typically over 10,000). HDC generates rich token representations through its low-cost initialization of many unrelated vectors. This is especially beneficial in topic segmentation, which often operates as a resource-constrained pre-processing step for downstream transcript understanding tasks. HyperSeg outperforms the current state-of-the-art in 4 out of 5 segmentation benchmarks -- even when baselines are given partial access to the ground truth -- and is 10 times faster on average. We show that HyperSeg also improves downstream summarization accuracy. With HyperSeg, we demonstrate the viability of HDC in a major language task. We open-source HyperSeg to provide a strong baseline for unsupervised topic segmentation.

We present the COGnitive Neural GENerative system (CogNGen), a cognitive architecture that combines two neurobiologically-plausible, computational models: predictive processing and hyperdimensional/vector-symbolic models. We draw inspiration from architectures such as ACT-R and Spaun/Nengo. CogNGen is in broad agreement with these, providing a level of detail between ACT-R's high-level symbolic description of human cognition and Spaun's low-level neurobiological description, furthermore creating the groundwork for designing agents that learn continually from diverse tasks and model human performance at larger scales than what is possible with current systems. We test CogNGen on four maze-learning tasks, including those that test memory and planning, and find that CogNGen matches performance of deep reinforcement learning models and exceeds on a task designed to test memory.

Existing work in language grounding typically study single environments. How do we build unified models that apply across multiple environments? We propose the multi-environment Symbolic Interactive Language Grounding benchmark (SILG), which unifies a collection of diverse grounded language learning environments under a common interface. SILG consists of grid-world environments that require generalization to new dynamics, entities, and partially observed worlds (RTFM, Messenger, NetHack), as well as symbolic counterparts of visual worlds that require interpreting rich natural language with respect to complex scenes (ALFWorld, Touchdown). Together, these environments provide diverse grounding challenges in richness of observation space, action space, language specification, and plan complexity. In addition, we propose the first shared model architecture for RL on these environments, and evaluate recent advances such as egocentric local convolution, recurrent state-tracking, entity-centric attention, and pretrained LM using SILG. Our shared architecture achieves comparable performance to environment-specific architectures. Moreover, we find that many recent modelling advances do not result in significant gains on environments other than the one they were designed for. This highlights the need for a multi-environment benchmark. Finally, the best models significantly underperform humans on SILG, which suggests ample room for future work. We hope SILG enables the community to quickly identify new methodologies for language grounding that generalize to a diverse set of environments and their associated challenges.