We answer this question with Vector-Symbolic Policy Gradient (VSPG), a discrete-action actor that represents each action by a unit-norm hypervector and scores it by similarity to the encoded state. Under the standard softmax policy-gradient surrogate, we prove that its update is exactly advantage-weighted hypervector bundling followed by normalization, and therefore supports standard advantage estimators. We further show that each trained action hypervector is a fixed-size compressed kernel memory, storing an advantage-weighted kernel expansion over visited states and transferring evidence according to the encoder-induced similarity. This provides a concrete mechanism that can support sample-efficient learning without increasing inference-time memory. Finally, for bipolar action memories, we prove that greedy action selection is stable under random bit flips, with failure probability decaying exponentially in the hypervector dimension. VSPG thus connects VSA action memories, log-linear policy gradients, and kernel policy search while providing a quantitative robustness guarantee.
Quanling Zhao, Anthony Hitchcock Thomas, Ari Brin +2cs.LG cs.AI
Hyperdimensional computing (HDC) is an approach from the cognitive science literature for solving information processing tasks using data represented as high-dimensional random vectors. The technique has a rigorous mathematical backing, and is easy to implement in energy-efficient and highly parallel hardware like FPGAs and "processing-in-memory" architectures. The effectiveness of HDC in machine learning largely depends on how raw data is mapped to high-dimensional space. In this work, we propose NysHD, a new method for constructing this mapping that is based on the Nyström method from the literature on kernel approximation. Our approach provides a simple recipe to turn any user-defined positive-semidefinite similarity function into an equivalent mapping in HDC. There is a vast literature on the design of such functions for learning problems. Our approach provides a mechanism to import them into the HDC setting, expanding the types of problems that can be tackled using HDC. Empirical evaluation against existing HDC encoding methods shows that NysHD can achieve, on average, 11% and 17% better classification accuracy on graph and string datasets respectively.
Hyperdimensional Computing (HDC) represents symbols using high-dimensional hypervectors of dimension $D$. In hypervector decomposition, the objective is to recover $F$ constituent hypervectors, each drawn from a codebook of size $N$, from a bound target hypervector. This requires searching over $N^F$ candidate tuples, making the task computationally prohibitive at scale. Recent quantum approach provides a quadratic search advantage, but typically rely on qubit-inefficient $O(D)$-qubit hypervector representations. We propose a qubit-efficient quantum framework for HDC decomposition that reduces the representation cost to $O(\log D)$. The framework introduces logarithmic hypervector and binding encodings, together with a reversible hypervector lookup operator for circuit-level manipulation of dense hypervectors. Combined with a modified Dürr-Høyer search procedure, the method preserves $O(\sqrt{N^F})$ search complexity while substantially reducing qubit usage. Experimental results validate correct similarity computation, accurate decomposition in executable regimes, and significantly improved qubit scaling over baselines based on explicit $D$-qubit hypervector encodings, achieving up to $2{,}000\times$ fewer qubits.
Zhiling Chen, David Gorsich, Matthew P. Castanier +3cs.RO cs.CV
Robotic inspection relies on accurate sensing to acquire high-fidelity geometric measurements for defect detection and metrology. While prior work has focused on robot motion and viewpoint planning, how to configure sensing parameters remains largely underexplored, despite their decisive impact on measurement quality. We propose SenseHD, a robotic sensing system that formulates scanner configuration as an instruction-conditioned sensing decision. Instead of predicting precise parameter values, SenseHD treats sensing parameters as discrete sensing actions and selects stable sensing regimes through hyperdimensional associative memory. Experiments on a real robotic inspection platform demonstrate that SenseHD robustly selects appropriate sensing configurations and significantly improves inspection reliability, while remaining lightweight and efficient compared to baseline methods.
Tabular data embeddings have become a cornerstone of data profiling and data integration pipelines, enabling tasks such as entity annotation and resolution; schema matching; column type detection; and table search, among others. Existing approaches embed rows, columns, or entire tables into a vector space and rely on nearest-neighbor search to retrieve candidate matches. A fundamental limitation of current embedding methods is the lack of interpretable similarity scores: the concrete similarity value between a query and its nearest neighbour carries no intrinsic meaning, making it impossible to determine whether that neighbour is a true match or simply the least-dissimilar item in a corpus that contains no valid answer. This inability to set principled thresholds for retrieval undermines practical deployment, particularly for zero-match detection. We investigate the use of HyperDimensional Computing (HDC), specifically the Holographic Reduced Representations (HRR) model, as a framework for tabular row embeddings when the retrieval task corresponds to answering structured select-project queries in vector space. Exploiting the algebraic properties of HDC operations, we derive closed-form expected similarity values for both equality and non-equality retrieval predicates, which converge to interpretable values as dimensionality increases, and use these to identify suitable retrieval thresholds. We evaluate HDC against EmbDI, a graph-based baseline, on two real-world datasets across varying table sizes and predicate lengths. Our results show that HDC matches or outperforms EmbDI for row retrieval across all configurations, handles non-equality predicates more robustly, and achieves perfect attribute projection accuracy at sufficient dimensionality -- while uniquely enabling reliable identification of zero-match predicates through its principled thresholds.
Hiroyuki Chuma, Kanji Otsuk, Yoichi Satocs.NE cs.AI
In The Algebraic Mind, Gary Marcus identified three components essential for any adequate cognitive architecture: operations over variables, recursively structured representations, and a distinction between mental representations of individuals and kinds. He argued that standard multilayer perceptrons supported none of these, acknowledging that a neural implementation using registers and treelets, constructed via developmental programs rather than gradient descent, remained a programmatic conjecture. Twenty-five years later, the required substrate is now available. Our newly developed PyVaCoAl/VaCoAl is a hyperdimensional computing architecture organized end-to-end around a single algebraic primitive: XOR-and-shift over GF(2), implemented by primitive-polynomial linear-feedback shift registers. The architecture supports reversible variable binding via Bind(R,F) = R XOR shift(F), non-commutative compositional bundling that distinguishes "the dog bites the man" from "the man bites the dog," and address-space individual/kind separation under the same algebra. A companion perspective argues that the dentate gyrus-CA3 circuit is a biological homologue of this same engine, with developmentally specified mossy-fiber targeting supplying the innate microcircuitry Marcus anticipated. In this paper, we map the correspondence between Marcus's three pillars and the operational commitments of PyVaCoAl/VaCoAl. We reinterpret the treelet as an algebraic register set indexed by a primitive generator polynomial, arguing that this architecture provides a functional neural substrate meeting Marcus's specifications far more closely than the tensor products, circular convolution, or temporal synchrony available in 2001. We also demonstrate how this substrate naturally extends to Pearl's rung-3 counterfactual reasoning, a capability the original treelet program did not directly target.