HypercubeHopfield

HypercubeHopfield — modern Hopfield associative memory on a Boolean hypercube. Neurons sit on the vertices of a dim-dimensional cube (N = 2^dim). Patterns are stored explicitly and retrieved by softmax attention over a sparse neighborhood — not collapsed into a Hebbian weight matrix, and not full all-to-all modern-Hopfield attention either.

A topology you don't store. Connectivity is the mask table of the Hamming ball — one XOR per neighbor, no adjacency list, at any size. Each vertex attends only inside that ball; cost scales with connections, not with the full cube.

HypercubeAI ecosystem

HypercubeESN · HypercubeCNN · HypercubeHopfield · HypercubeWTF · HypercubeEtalon · HypercubeCascade · HypercubeLCN

📄 Foundational paper: Boolean Hypercubes as a Neural Substrate (D. C. Liptak, 2026)

HypercubeHopfield is an experiment in the HypercubeAI project — our quest to systematically re-implement classical neural architectures on a Boolean hypercube topology instead of Euclidean grids or random graphs. The central thesis is “topology-native intelligence”: the hypercube’s algebraic structure (vertex-transitive symmetry, Hamming geometry, bitwise addressing) can serve as a first-class computational substrate.

A topology you don’t store — the graph is specified: connectivity is implicit in the vertex indices; with a seed and a few config scalars the whole reservoir reconstructs mathematically.
Perfect homogeneity — every vertex has the same degree and the same local world, so local dynamics mean the same thing everywhere — no structural favorites baked in by a random graph.
Cheap navigation — each neighbor is a few bit operations on the vertex index, not a pointer chase through a stored edge list, so walks stay arithmetic and cache-friendly.
Topology-native pairing — the readout consumes the reservoir’s output with zero geometric distortion, and the learned kernels exploit the same locality that generated the dynamics. The data never leaves the hypercube it was born on.

Each product in the family is a different architecture on that same foundation.

Installation

pip install hypercube-hopfield

Pre-built wheels for Python 3.10–3.13 on Windows, Linux, and macOS. NumPy is the only runtime dependency.

Build from source (C++23 + CMake): see the Python SDK guide.

Quick Start

import numpy as np
import hypercube_hopfield as hh

# 256 neurons (dim=8, N=2^8)
net = hh.HopfieldNetwork(dim=8, seed=42)

patterns = np.random.randn(10, net.num_vertices).astype(np.float32)
net.store_patterns(patterns)

cue = patterns[0] + np.random.randn(net.num_vertices).astype(np.float32) * 0.3
result = net.recall(cue)
print(f"Converged: {result.converged}, steps: {result.steps}")
# result.state is the cleaned recall; input cue is not modified

Features

Explicit pattern storage — modern Hopfield retrieval without a Hebbian weight matrix
Sparse Hamming-ball attention — reach and neighbor_fraction control connectivity and cost
Two update modes — Sync (default, deterministic) and Async (guaranteed energy descent)
Pickle / save / load — persist config and all stored patterns
NumPy integration — automatic float32 conversion; recall does not mutate the cue

Documentation

Python SDK Reference — full API, persistence, errors
Project README — architecture framing, C++ quick start, build
HopfieldNetwork architecture — connectivity, energy, parameters

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hypercube-hopfield 1.0.3

HypercubeHopfield

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Quick Start

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