Echoloc

Geometric Gossip Equilibrium Network (GGEN) -- a novel sequence model architecture combining projective geometric algebra G(3,0,1), local-only neighbor communication, and deep equilibrium fixed-point iteration.

A Lumis-2 research track by Eptesicus Laboratories.

Architecture

Each token is represented as a multivector (16 components) in G(3,0,1). Tokens communicate only with radius R neighbors through a Geometric Gossip Cell (GGC). The network iterates the GGC until hidden states converge to a fixed point.

• Grade 0 (scalar): continuous activations
• Grade 2 (bivector): ternary spikes from the Gerhard/ASNN-Goose lineage
• Equivariance to E(3) by construction

Target model sizes: 50M (Tiny), 350M (Base), 900M (Large).

Project Structure

echoloc/
  config.py              configuration dataclasses
  src/
    algebra/             G(3,0,1) geometric algebra primitives
    model/               GGEN model components (GGC cell, embedding, decode)
    spikes/              ternary spike function, spiking brain validator
    training/            equilibrium solver, loss functions, distillation
    utils/               convergence monitoring, Lipschitz estimation, ERF measurement
  tests/                 Phase 0 mathematical validation tests
  scripts/               run registration, gate evaluation, dossier generation
  notebooks/             Colab/Kaggle execution notebooks
  docs/                  living documentation
  state/                 machine-readable project state
  reports/               generated reports and evidence bundles
  knowledge/             reference material on core concepts

Phase Plan

• Phase 0: Mathematical validation (CPU, $0)
• Phase 1: Toy tasks + ERF stress test (Kaggle T4, $0)
• Phase 2: Language modeling at 50M scale (Kaggle T4, $0)
• Phase 3: Spatial/3D tasks (Kaggle/Colab, $0-20)
• Phase 4: Multimodal fusion (RunPod, $20-50)
• Phase 5: Scale-up (RunPod/Hetzner, $200-500)

License

MIT License. Copyright (c) 2026 Deyan Todorov.