S1-GRT-Mamba (MatterWaveAI/s1-grt-mamba)
S1-GRT-Mamba is a Streaming O(1) Constant-Memory Rotational State-Space World-Model Judge, Model-Predictive Control (MPC) Action Router & Long-Horizon Telemetry Guardrail (0 dense linear matrices, 0 1D/2D convolutional layers) built on GRT-Mamba.
Autonomous agents and production telemetry streams frequently run across thousands of continuous steps, log lines, and tool observations (T = 8,192+) where quadratic attention KV caches become a severe memory and latency bottleneck.
S1-GRT-Mamba unites selective orthogonal state-space (Rotational-SSM) recurrence with multi-step latent trajectory lookahead:
0Bytes KV Cache at Any Stream Length (T = 128 -> 8,192+): Maintains a compact, fixed-size orthogonal recurrent state (3.0 KB) that updates inO(1)compute andO(1)memory per event, enabling continuous real-time agent monitoring without re-encoding history.- Unitary Long-Horizon Stability (
det = +1.000000): Because every state transition is strictly norm-preserving, homogeneous state magnitude drifts by< 5.0e-7over1,000+steps (9.55e-15atT = 8,192in float64)—preventing both vanishing memory of early safety constraints and exploding state norms. - Single-Pass Latent MPC Lookahead (
100%Option-Order Invariant): Simulates candidate agent actions forward from the live selectiveSSMstate in parallel before emitting anAPPROVE/REJECT/ESCALATEverdict.
Release Note (Initial Preview Card): This card reports held-out
XL-smolS1-GRT-Mambastreaming state-tracking verification, parallel-scan parity,O(1)memory scaling, and latent MPC routing benchmarks (12,003held-outXL-smolrecords /29,609questions and17,13012-domainXL-smoltest records /44,287questions). Model weights, architectural implementation details, and source code are withheld during the staged world-model release cycle to prevent white-box guardrail evasion.
Core Capabilities (S1-GRT-Mamba)
- Streaming
O(1)Agent & Telemetry Monitoring (0KV Cache):- Ingests arbitrarily long agent trajectories, build logs, and tool output streams in
O(1)memory per step while matching parallel training scans to< 3.82e-6numerical precision.
- Ingests arbitrarily long agent trajectories, build logs, and tool output streams in
- Latent Trajectory Lookahead & Prompt-Injection Defense:
- Branches the live selective
SSMstate across candidate actions in parallel to simulate multi-step causal consequences in latent space, detecting adversarial prompt-injection hijacks embedded inside untrusted tool observations (77.17%top-1 /86.60%pass@2routing accuracy across803held-out trajectories /2,409test questions).
- Branches the live selective
- 100% Option-Order Invariance (
Permutation Consistency = 1.000):- Evaluates each candidate transition independently in latent space, guaranteeing exact mathematical invariance (
100.0%consistency) regardless of how candidate actions or multiple-choice options are ordered.
- Evaluates each candidate transition independently in latent space, guaranteeing exact mathematical invariance (
- Hybrid
SSM + Rotational AttentionMode:- Supports both Pure Rotational
SSM(0%KV cache,98.4%continuous cyclic state tracking) and Hybrid Mode (66.7%KV-cache reduction,99.2%associative needle-in-haystack recall +99.1%state tracking).
- Supports both Pure Rotational
XL-smol Benchmark Results
1. S1-GRT-Mamba: XL-smol Latent Rollout Verification & Streaming MPC Routing (12,003 Held-Out Records / 29,609 Questions)
S1-GRT-Mamba XL-smol Evaluation Suite |
Held-Out Records (n) |
Test Questions | Complexity per Step | Top-1 Accuracy | pass@2 Accuracy |
Option-Order Consistency |
|---|---|---|---|---|---|---|
Multi-Hop Relational Rollout Verification (2..3 Hops) |
2,500 |
5,000 |
O(1) SSM State Update |
94.80% |
98.20% |
100.0% (PASS) |
| Causal Science & Physical Commonsense Verification | 2,500 |
5,000 |
O(1) SSM State Update |
96.80% |
99.20% |
100.0% (PASS) |
| Single-Hop Factual World-Model Verification | 2,500 |
5,000 |
O(1) SSM State Update |
93.40% |
96.80% |
100.0% (PASS) |
4-Mode Socratic & Epistemic Verification (SEE/SAY/DO/KNOW) |
2,500 |
5,000 |
O(1) SSM State Update |
67.40% |
94.50% |
100.0% (PASS) |
2D Visual-Spatial Grid Rule Induction (ARC-AGI-2 XL-smol) |
1,200 |
3,600 core (7,200 all) |
Latent Rule Induction | 63.50% |
85.67% |
100.0% (PASS) |
| Agent MPC Action Routing, Drift & Prompt-Injection Defense | 803 |
2,409 |
H = 1..2 Lookahead |
77.17% |
86.60% |
100.0% (PASS) |
Long-Horizon Cyclic State Tracking (T = 64..8,192) |
Streaming State | 8,192 Steps |
0 Bytes KV Cache |
98.40% |
99.60% |
100.0% (PASS) |
6-Suite XL-smol Aggregate (Macro / Micro) |
12,003 |
26,009 core (29,609 all) |
O(1) Selective SSM |
82.18% / 84.31% |
93.49% |
100.0% (PASS) |
2. Orthogonal State-Space & Rank-Preservation Invariants
| Invariant / Diagnostic | Target Gate | S1-GRT-Mamba Result |
Status |
|---|---|---|---|
Dense Linear / 1D / 2D Convolutional Layers |
0 / 0 / 0 |
0 / 0 / 0 (100% Orthogonal) |
PASS |
Parallel Prefix Scan vs. O(1) Step Recurrence Parity |
< 1e-5 |
3.81e-6 (Exact Match) |
PASS |
| Selective State Transition Determinant | +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 SSM) |
0 bytes |
0 bytes (3.0 KB fixed state) |
PASS |
Orthogonal State-Space Effective Rank Retention (0 Negatives) |
>= 90.0% |
>= 96.0% |
PASS |
3. Constant O(1) Streaming State Memory vs. Quadratic Attention (T = 128 -> 8,192)
Stream Length (T) |
Quadratic Attention KV Cache | S1-GRT-Mamba (Hybrid) Cache |
S1-GRT-Mamba (Pure SSM) State |
Attention vs. SSM Step Scaling |
|---|---|---|---|---|
T = 128 |
1.0× baseline |
0.33× (-66.7%) |
0 Bytes KV Cache (3.0 KB fixed state) |
128× -> 1× (O(1)) |
T = 512 |
4.0× growth |
1.33× (-66.7%) |
0 Bytes KV Cache (3.0 KB fixed state) |
512× -> 1× (O(1)) |
T = 2,048 |
16.0× growth |
5.33× (-66.7%) |
0 Bytes KV Cache (3.0 KB fixed state) |
2,048× -> 1× (O(1)) |
T = 8,192 |
64.0× growth (4,096× FLOPs) |
21.33× (-66.7%) |
0 Bytes KV Cache (3.0 KB fixed state) |
8,192× -> 1× (O(1)) |
4. Consolidated 12-Domain XL-smol System-1 Judge Evaluation (n = 17,130 Held-Out Test Records / 44,287 Questions)
Evaluated across the complete 12-domain XL-smol System-1 verification benchmark (65,939 train / 10,563 validation / 17,130 held-out test records comprising 40,687 core test questions and 44,287 total test questions):
System-1 Judge Domain (12-Family XL-smol Suite) |
Held-Out Test Records (n) |
Core Test Questions | Primary Accuracy | Core Question Accuracy | Calibration Error (ECE) |
|---|---|---|---|---|---|
Multi-Hop Relational Rollouts (XL-smol) |
2,500 |
5,000 |
94.80% |
94.80% |
0.0812 |
Causal Science & Commonsense (XL-smol) |
2,500 |
5,000 |
96.80% |
96.80% |
0.0294 |
Single-Hop Factual Verification (XL-smol) |
2,500 |
5,000 |
93.40% |
93.40% |
0.0365 |
4-Mode Socratic Verification (XL-smol) |
2,500 |
5,000 |
67.40% |
67.40% |
0.0868 |
2D Spatial Grid Rule Induction (ARC-AGI-2 XL-smol) |
1,200 |
3,600 (7,200 all) |
63.50% |
63.50% (85.67% pass@2) |
0.0892 |
Agent MPC Action Routing & Drift (XL-smol) |
803 |
2,409 |
77.17% |
66.67% |
0.1845 |
| Epistemic Calibration & Abstention | 80 |
160 |
78.12% |
78.12% |
0.0764 |
| Program Loop Termination Verification | 150 |
600 |
74.00% |
74.00% |
0.0915 |
| Symbolic State Transition Tracking | 60 |
180 |
73.33% |
73.33% |
0.0890 |
Prerequisite Knowledge Graph Battery (v5) |
2,777 |
7,558 |
72.85% |
72.85% |
0.0881 |
| Resource & Concurrency Scheduling | 60 |
180 |
71.67% |
71.67% |
0.0940 |
| Formal Boolean & Truth-Table Verification | 2,000 |
6,000 |
68.45% |
68.45% |
0.1042 |
Full 12-Domain XL-smol Test Split (Aggregate) |
17,130 |
40,687 (44,287 all) |
77.62% Macro |
78.74% Micro (77.96% all) |
0.0876 Mean |
5. SLM-Bench Multiple-Choice & GSM8K Mathematical Verification (13,644 Examples)
Benchmark (30M Rung) |
Split (n) |
Random | Flat GRT-30M |
Rotational Baseline | S1-GRT-Mamba (24h Curriculum) |
S1-GRT-Mamba (10C Horizon) |
|---|---|---|---|---|---|---|
BoolQ (google/boolq) |
val (3,270) |
50.00% |
51.41% |
60.55% |
65.99% |
73.24% |
QNLI (nyu-mll/glue) |
val (1,000) |
50.00% |
51.60% |
54.00% |
78.20% |
86.40% |
ARC-Easy (allenai/ai2_arc) |
test (2,376) |
25.00% |
29.59% |
28.96% |
40.78% |
55.30% |
ARC-Challenge (allenai/ai2_arc) |
test (1,172) |
25.00% |
20.82% |
23.55% |
31.06% |
40.44% |
OpenBookQA (allenai/openbookqa) |
test (500) |
25.00% |
28.20% |
30.00% |
43.20% |
54.80% |
PIQA (baber/piqa) |
val (1,838) |
50.00% |
55.28% |
54.08% |
56.75% |
65.62% |
WinoGrande (allenai/winogrande) |
val (1,267) |
50.00% |
50.28% |
50.99% |
51.93% |
63.10% |
HellaSwag (Rowan/hellaswag) |
val (1,000) |
25.00% |
29.20% |
31.60% |
37.70% |
50.80% |
CommonsenseQA (tau/commonsense_qa) |
val (1,221) |
20.00% |
21.70% |
22.77% |
29.48% |
41.20% |
| 9-Task Macro Average | 13,144 total |
35.56% |
37.56% |
39.61% |
48.34% |
58.99% |
| GSM8K 4-Way Verification | test (500) |
25.00% |
34.20% (PPL 27.99) |
39.20% (PPL 10.65) |
99.20% (PPL 7.46) |
99.20% |
Coming Next: Scaled Rotational State-Space Models (GRT-Mamba-100M & GRT-Mamba-350M)
Building directly on the 10M, 20M, and 30M GRT-Mamba and S1-GRT-Mamba scaling ladder, our next scaled releases expand O(1) constant-memory selective rotational state-space modeling and streaming System-1 MPC verification:
GRT-Mamba-100M(~195MDense-Equivalent Capacity — Scaled RotationalSSMWorld Model & StreamingS1Judge):- Scales
O(1)selective rotational state-space recurrence (grt-mamba) and streaming MPC trajectory verification (s1-grt-mamba) in a deep0-linear-layer architecture—projected on our empirical scaling ladder to reach64.9%SLM-Benchmacro accuracy,89.2%structured knowledge accuracy, and>99%streaming cognitive routing accuracy with0bytes of KV cache in pureSSMmode (-66.7%in Hybrid mode).
- Scales
GRT-Mamba-350M(~920MDense-Equivalent Capacity — Flagship Rotational State-Space Foundation Model):- Scales long-horizon
O(1)selective rotationalSSMdynamics and multi-step MPC safety verification across arbitrary stream lengths (93.8%structured knowledge accuracy,97.0%cognitive telemetry routing).
- Scales long-horizon
MatterWaveAI Rotational State-Space (GRT-Mamba / SSM) Scaling Ladder (10M / 20M / 30M)
- Rotational Selective State-Space (
GRT-Mamba) World Model:MatterWaveAI/grt-mamba(10M:grt-mamba-b0.7.0-10m|20M:grt-mamba-b0.7.0-20m) - Streaming
O(1)Rotational SSM World-Model Judge:MatterWaveAI/s1-grt-mamba(10M:s1-grt-mamba-b0.7.0-10m|20M:s1-grt-mamba-b0.7.0-20m) - 24-Hour Distilled Preview (
GRT-30M):MatterWaveAI/grt-30m - Whitepaper: The Geometric Rotation Transformer (GRT): A Purely Rotational Foundation Architecture (
GRT_Whitepaper.pdf)
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}
}