Bridging Silicon and the Hippocampus: Algebro-Deterministic Memory "VaCoAl" as a Substrate for Vector-HaSH and TEM

• URL: http://arxiv.org/abs/2605.15652v5
• Date: Fri, 22 May 2026 01:21:52 GMT
• Title: Bridging Silicon and the Hippocampus: Algebro-Deterministic Memory "VaCoAl" as a Substrate for Vector-HaSH and TEM
• Abstract summary: We introduce VaCoAl, an algebro-deterministic hyperdimensional memory architecture built on Galois-field linear-feedback shift registers.<n>Its deterministic Galois-field diffusion offers a substrate-level alternative to Vector-HaSH's random projections.<n>We derive testable iEEG predictions, uniting computational neuroscience, electrophysiology, and hyperdimensional computing.
• Score: 18.56157183294801
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Vector-HaSH and the Tolman-Eichenbaum Machine (TEM) propose the hippocampal-entorhinal circuit factorizes memory via a grid-cell scaffold for compositional replay. Concurrently, human iEEG shows sharp-wave ripples gate recall and multi-hop replay fidelity decays multiplicatively. Yet, these fields lack a shared algebraic foundation. We introduce VaCoAl, an algebro-deterministic hyperdimensional memory architecture built on Galois-field linear-feedback shift registers. Its deterministic Galois-field diffusion offers a substrate-level alternative to Vector-HaSH's random projections, matching quasi-orthogonality while ensuring bit-exact reproducibility. Furthermore, the path-integral Confidence Ratio CR2 provides an algebraically tractable model for the empirically observed multiplicative replay decay. Biologically, VaCoAl's two operating regimes align with the EC-CA3 direct and EC-DG-CA3 trisynaptic pathways, explaining their 520-Myr conservation. Independent cellular evidence supports that the DG-CA3 pathway implements a biophysical homologue of Galois-field arithmetic. We also link this framework to Judea Pearl's Ladder of Causation. Reversible GF(2) binding provides the surgical algebra for the do-operator (Rung 2), and VaCoAl's dual-orthogonalizer architecture supplies the parallel substrate required for counterfactual reasoning (Rung 3). Ultimately, we prove these formal correspondences and derive testable iEEG predictions, uniting computational neuroscience, electrophysiology, and hyperdimensional computing.

Related papers

• ProgFormer: Hierarchical Voxel Diffusion Transformer for Longitudinal Brain MRI Prediction [81.07048249760953]
  longitudinal changes are often subtle and confined to specific anatomical regions.<n>Most subject-specific brain structure remains stable over time.<n>ProgFormer is a hierarchical voxel-space Diffusion Transformer for longitudinal brain MRI prediction.
  arXiv  Detail & Related papers  (2026-07-30T00:13:42Z)
• How to Build Marcus's Algebraic Mind: From Thagard's Brain--Mind Viewpoint [18.56157183294801]
  Two critiques of connectionist cognition converge on one missing capacity.<n>We argue one substrate answers both.<n>VaCoAl is a hyperdimensional architecture built on one primitive, XOR-and-shift over GF(2), on primitive-polynomial linear-feedback shift registers.
  arXiv  Detail & Related papers  (2026-07-18T01:12:54Z)
• MambaADv2: Evolving Duality-enhanced State Space Model for Unsupervised Anomaly Detection [108.36437360254605]
  This paper proposes MambaADv2, a framework tailored for multi-class unsupervised anomaly detection.<n>MambaADv2 comprises a pre-trained encoder and a Mamba-inspired decoder, equipped with Duality-enhanced State Space (DSS) modules across multiple scales.<n>The structure of the Hybrid State Space (HSS) block is tailored by following the SSD-based Mamba lineage and incorporating Mamba3-style position-aware state-space modeling.
  arXiv  Detail & Related papers  (2026-06-22T10:14:06Z)
• Shattering the Symmetry Trap in Fixed-Ansatz VQE: An Accelerated ADAPT-VQE Study of Three Pillar Molecules under Bravyi-Kitaev Mapping [0.0]
  We show how ADAPT-VQE framework shatters structural limitations across three distinct electronic and geometric molecular pillars.<n>Our numerical results show that the accelerated ADAPT-VQE framework achieves instant, exact Full Configuration Interaction.<n>This study establishes a robust, hardware-efficient path for simulating strongly correlated, highly polarized triatomic chemical environments.
  arXiv  Detail & Related papers  (2026-06-04T10:13:23Z)
• How to Build Marcus's Algebraic Mind: Algebro-Deterministic Substrate over Galois Fields [18.56157183294801]
  PyVaCoAl/VaCoAl is a hyperdimensional computing architecture organized end-to-end around a single algebraic primitive.<n>In this paper, we map the correspondence between Marcus's three pillars and the operational commitments of PyVaCoAl/VaCoAl.
  arXiv  Detail & Related papers  (2026-05-20T16:40:27Z)
• NOETHER: A Constructive Framework for Metamorphic Pattern Discovery from Operator Algebras [6.691613382732758]
  Metamorphic Testing is recognised in IEEE/ISO software-testing standards and increasingly recommended for AI systems.<n>Existing approaches share an inductive grounding that leaves three foundational questions open.<n>We propose a framework whose downstream step from operator algebra to MetaPattern set is mechanical and provable.
  arXiv  Detail & Related papers  (2026-05-17T11:18:35Z)
• Geometric Factual Recall in Transformers [57.48371649045765]
  A common view casts internal weight matrices as associative memories over pairs of embeddings, requiring memorization counts that scale linearly with the number of facts.<n>We develop a theoretical and empirical account of an alternative, emphgeometric form of memorization in which learned embeddings encode structure directly.<n>In a controlled setting where a single-layer transformer must memorize random vectors from subjects to a shared attribute set, we prove that a logarithmic embedding dimension suffices.<n>We extend these results to the multi-hop setting, providing constructions with and without chain-of-thought that exhibit a provable
  arXiv  Detail & Related papers  (2026-05-12T17:22:22Z)
• Beyond LLMs, Sparse Distributed Memory, and Neuromorphics <A Hyper-Dimensional SRAM-CAM "VaCoAl" for Ultra-High Speed, Ultra-Low Power, and Low Cost> [18.56157183294801]
  We propose VaCoAl on ultra-high-dimensional binary spaces on ultra-high-dimensional RAM/DRAM-CAM.<n>It embeds a cognitive bound -- the Frontier Size -- into its architecture, ranking candidates by path-integral confidence.<n>We evaluate multi-hop reasoning on about 470k mentor-student relations from Wikidata, tracing up to 57 generations.
  arXiv  Detail & Related papers  (2026-04-13T16:13:17Z)
• ReCALL: Recalibrating Capability Degradation for MLLM-based Composed Image Retrieval [64.14282916266998]
  Composed Image Retrieval aims to retrieve target images based on a hybrid query comprising a reference image and a modification text.<n>We propose ReCALL, a model-agnostic framework that follows a diagnose-generate-refine pipeline.<n>Experiments on CIRR and FashionIQ show that ReCALL consistently recalibrates degraded capabilities and achieves state-of-the-art performance.
  arXiv  Detail & Related papers  (2026-02-02T04:52:54Z)
• GSPN-2: Efficient Parallel Sequence Modeling [101.33780567131716]
  Generalized Spatial Propagation Network (GSPN) addresses this by replacing quadratic self-attention with a line-scan propagation scheme.<n>GSPN-2 establishes a new efficiency frontier for modeling global spatial context in vision applications.
  arXiv  Detail & Related papers  (2025-11-28T07:26:45Z)
• Triangle Multiplication Is All You Need For Biomolecular Structure Representations [56.26342479807906]
  We introduce Pairmixer, a streamlined alternative that eliminates triangle attention while preserving higher-order geometric reasoning capabilities.<n>Pairmixer substantially improves computational efficiency, matching state-of-the-art structure predictors across folding and docking benchmarks.<n>Within BoltzDesign, for example, Pairmixer delivers over 2x faster sampling and scales to sequences 30% longer than the memory limits of Pairformer.
  arXiv  Detail & Related papers  (2025-10-21T17:59:02Z)
• Bidirectional Representations Augmented Autoregressive Biological Sequence Generation:Application in De Novo Peptide Sequencing [51.12821379640881]
  Autoregressive (AR) models offer holistic, bidirectional representations but face challenges with generative coherence and scalability.<n>We propose a hybrid framework enhancing AR generation by dynamically integrating rich contextual information from non-autoregressive mechanisms.<n>A novel cross-decoder attention module enables the AR decoder to iteratively query and integrate these bidirectional features.
  arXiv  Detail & Related papers  (2025-10-09T12:52:55Z)
• Cycle-Consistent Helmholtz Machine: Goal-Seeded Simulation via Inverted Inference [5.234742752529437]
  We introduce the emphCycle-Consistent Helmholtz Machine (C$2$HM)<n>C$2$HM reframes inference as a emphgoal-seeded, emphasymmetric process grounded in structured internal priors.<n>By offering a biologically inspired alternative to classical amortized inference, $C2$HM reconceives generative modeling as intentional simulation.
  arXiv  Detail & Related papers  (2025-07-03T17:24:27Z)
• Geometric Algebra Planes: Convex Implicit Neural Volumes [70.12234371845445]
  We show that GA-Planes is equivalent to a sparse low-rank factor plus low-resolution matrix. We also show that GA-Planes can be adapted for many existing representations.
  arXiv  Detail & Related papers  (2024-11-20T18:21:58Z)
• Laughing Hyena Distillery: Extracting Compact Recurrences From Convolutions [101.08706223326928]
  Recent advances in attention-free sequence models rely on convolutions as alternatives to the attention operator at the core of Transformers. In this paper, we seek to enable $mathcal O(1)$ compute and memory cost per token in any pre-trained long convolution architecture.
  arXiv  Detail & Related papers  (2023-10-28T18:40:03Z)
• 3D Mitochondria Instance Segmentation with Spatio-Temporal Transformers [101.44668514239959]
  We propose a hybrid encoder-decoder framework that efficiently computes spatial and temporal attentions in parallel. We also introduce a semantic clutter-background adversarial loss during training that aids in the region of mitochondria instances from the background.
  arXiv  Detail & Related papers  (2023-03-21T17:58:49Z)
• Three-fold way of entanglement dynamics in monitored quantum circuits [68.8204255655161]
  We investigate the measurement-induced entanglement transition in quantum circuits built upon Dyson's three circular ensembles. We obtain insights into the interplay between the local entanglement generation by the gates and the entanglement reduction by the measurements.
  arXiv  Detail & Related papers  (2022-01-28T17:21:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.