GRT-RNN-b0.7.0-20m (MatterWaveAI/grt-rnn-b0.7.0-20m)

GRT-RNN-b0.7.0-20m is the 20M (b0.7.0-20m) Compact Purely Rotational Gated Recurrent Neural Network (Rotational-RNN / Unitary-GRU / Rotational-minGRU), Unitary World Model & O(1) Constant-Memory Trajectory Judge (~26.4M stored parameters / ~66M dense-equivalent capacity, 0 dense linear matrices, 0 1D/2D convolutional layers, 0 bytes KV cache).

Built on MatterWaveAI/grt-20m as the 20M edge and scaling-ladder rung of GRT-RNN, GRT-RNN-b0.7.0-20m formulates gated recurrent state transitions through norm-preserving orthogonal transformations (det = +1.000000):

  • Dual Operating Modes — Parallel Geodesic minGRU Scan + Nonlinear State-Coupled Unitary-GRU: Trains via a parallel prefix scan (< 3.82e-6 numerical parity with O(1) step recurrence) and supports nonlinear hidden-state-coupled reset/transition gating in O(1) compute and O(1) memory per token (0 bytes of KV cache, 2.25 KB fixed recurrent state) across arbitrary sequence lengths (T = 128 -> 8,192+).
  • Zero Vanishing or Exploding Gradients by Construction: Homogeneous state magnitude drifts by < 5.0e-7 over 1,000+ recursive steps (< 1e-14 at T = 8,192 in float64).

Release Note (b0.7.0 Preview Card): This card reports 20M (b0.7.0-20m) held-out XL-smol verification (12,003 held-out XL-smol records / 29,609 questions and 17,130 12-domain XL-smol test records / 44,287 questions), SLM-Bench & GSM8K reasoning benchmarks (13,644 examples), parallel-scan parity, nonlinear Unitary-GRU stability, and O(1) memory scaling. Model weights, architectural implementation details, and source code are withheld during the staged world-model release cycle.


XL-smol Benchmark Results (GRT-RNN-b0.7.0-20m)

1. Rotational Gated Recurrent (GRT-RNN-b0.7.0-20m) & Unitary Invariants

Architectural Invariant / Benchmark Target Gate GRT-RNN-b0.7.0-20m Result Status
Dense Linear / 1D / 2D Convolutional Layers 0 / 0 / 0 0 / 0 / 0 (100% Orthogonal) PASS
Parallel Geodesic minGRU Scan vs. O(1) Step Parity < 1e-5 3.81e-6 (Exact Match) PASS
Unitary Recurrent Transition Determinant (Scan & Nonlinear GRU) +1.000000 +1.000000000000 PASS
8,192-Step Homogeneous State Norm Drift (Unitary Stability) < 1e-6 9.55e-15 f64 / < 5.0e-7 f32 PASS
KV-Cache Memory Growth (T = 128 -> 8,192, Pure RNN) 0 bytes 0 bytes (2.25 KB fixed state) PASS
Collapse-Free State Effective Rank Retention (0 Negatives) >= 90.0% >= 96.0% PASS

2. GRT-RNN-b0.7.0-20m: XL-smol System-1 Rotational RNN World-Model Judge & MPC Router (12,003 Held-Out Records / 29,609 Questions)

GRT-RNN-b0.7.0-20m XL-smol Evaluation Suite Held-Out Records (n) Test Questions Top-1 Accuracy pass@2 Accuracy Option-Order Consistency
Multi-Hop Relational Rollout Verification (2..3 Hops) 2,500 5,000 89.80% 95.80% 100.0% (PASS)
Causal Science & Physical Commonsense Verification 2,500 5,000 94.90% 98.40% 100.0% (PASS)
Single-Hop Factual World-Model Verification 2,500 5,000 87.10% 93.20% 100.0% (PASS)
4-Mode Socratic & Epistemic Verification (SEE/SAY/DO/KNOW) 2,500 5,000 64.00% 92.60% 100.0% (PASS)
2D Visual-Spatial Grid Rule Induction (ARC-AGI-2 XL-smol) 1,200 3,600 core (7,200 all) 55.83% 81.00% 100.0% (PASS)
Agent MPC Action Routing, Drift & Prompt-Injection Defense 803 2,409 66.50% 71.71% 100.0% (PASS)
6-Suite XL-smol Aggregate (Macro / Micro) 12,003 26,009 core (29,609 all) 76.36% / 79.01% 89.64% 100.0% (PASS)
Consolidated 12-Domain XL-smol Benchmark (data_master_v9_xl) 17,130 40,687 core (44,287 all) 73.28% Macro 75.82% Core Micro 100.0% (PASS)

3. 20M SLM-Bench Multiple-Choice & GSM8K Mathematical Verification (13,644 Examples)

Benchmark (20M Rung) Split (n) Random GRT-RNN-b0.7.0-20m (24h Curriculum) GRT-RNN-b0.7.0-20m (10C Horizon)
BoolQ (google/boolq) val (3,270) 50.00% 66.64% 73.39%
QNLI (nyu-mll/glue) val (1,000) 50.00% 78.60% 86.48%
ARC-Easy (allenai/ai2_arc) test (2,376) 25.00% 38.09% 55.80%
ARC-Challenge (allenai/ai2_arc) test (1,172) 25.00% 30.63% 40.78%
OpenBookQA (allenai/openbookqa) test (500) 25.00% 45.40% 55.04%
PIQA (baber/piqa) val (1,838) 50.00% 57.34% 65.72%
WinoGrande (allenai/winogrande) val (1,267) 50.00% 52.72% 63.34%
HellaSwag (Rowan/hellaswag) val (1,000) 25.00% 37.70% 51.08%
CommonsenseQA (tau/commonsense_qa) val (1,221) 20.00% 28.83% 41.58%
9-Task Macro Average 13,144 total 35.56% 48.44% 59.25%
GSM8K 4-Way Verification test (500) 25.00% 98.60% (PPL 7.54) 98.80% (PPL 2.15)

Coming Next: Scaled Unitary Rotational RNN Models (GRT-RNN-100M & GRT-RNN-350M)

Building directly on the 10M, 20M, and 30M GRT-RNN and S1-GRT-RNN scaling ladder, our next scaled releases expand O(1) constant-memory unitary gated rotational RNN (Rotational-minGRU / Unitary-GRU) modeling and stateful System-1 MPC verification:

  1. GRT-RNN-100M (~195M Dense-Equivalent Capacity — Scaled Unitary Rotational RNN World Model & Stateful S1 Judge):
    • Scales unitary gated rotational RNN recurrence (grt-rnn) and stateful MPC trajectory verification (s1-grt-rnn) in a deep 0-linear-layer architecture—projected on our empirical scaling ladder to reach 64.9% SLM-Bench macro accuracy, 89.2% structured knowledge accuracy, and >99% streaming cognitive routing accuracy with 0 bytes of KV cache in pure RNN mode (-66.7% in Hybrid mode).
  2. GRT-RNN-350M (~920M Dense-Equivalent Capacity — Flagship Unitary Rotational RNN Foundation Model):
    • Scales parallel geodesic minGRU scan training and nonlinear state-coupled Unitary-GRU execution across arbitrary sequence horizons (93.8% structured knowledge accuracy, 97.0% cognitive telemetry routing).

MatterWaveAI Unitary Rotational RNN (GRT-RNN / minGRU / GRU) Scaling Ladder (10M / 20M / 30M)


License & Citation

Released under the Apache 2.0 license.

@techreport{householter2026grt,
  title       = {The Geometric Rotation Transformer: A Purely Rotational Foundation Architecture},
  author      = {Householter, David},
  institution = {MatterWave AI},
  year        = {2026},
  url         = {https://matterwave.ai}
}
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