GRT-30M-Reranker (MatterWaveAI/grt-30m-reranker)

GRT-30M-Reranker (GRTForSequenceClassification) is a 100% Native Rotational Cross-Encoder Reranker (29,305,759 parameters, zero nn.Linear layers) compatible with both Hugging Face AutoModelForSequenceClassification and sentence-transformers CrossEncoder.

Unlike conventional cross-encoders that apply dense linear classification projections (nn.Linear), GRTForSequenceClassification pairs a 12-block Givens/Clifford rotational backbone (GRTModel) with a zero-nn.Linear GRTCosineClassificationHead (reranker.score):

1. Hermitian Planar-Pair Phase Agreement (u* v): Circular-pooled query and document representations (u, v) over D / 2 = 128 planar (x, y) pairs are combined via the Hermitian complex conjugate product (ux*vx + uy*vy, ux*vy - uy*vx) and scored against learned planar phase_angles and pair_scales.
2. Multi-Vector Rotational Late Interaction (MaxSim / MinSim): Token-level rotational cosine similarity matrices between query and document token trajectories extract bidirectional MaxSim (q→d and d→q), worst-case token alignment MinSim (q→d), and lexical polar circular agreement (lex_cos), weighted by late_weights and calibrated by output_scale + bias.

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Reranking Benchmark Results (AllNLI & STS-B)

Model / Pipeline	Architecture	AllNLI 200×10 MRR@10	AllNLI 200×10 NDCG@10	Recall@1	Recall@3	STS-B Test Spearman (ρ)	Throughput (pairs/s)
MatterWaveAI/grt-30m (Base Unaligned)	GRTModel (circular pool)	37.99	52.12	20.5%	41.0%	32.51	120
MatterWaveAI/grt-30m-embedding (Bi-Encoder)	SentenceTransformer (circular)	52.56	63.74	32.5%	68.0%	62.42	152
MatterWaveAI/grt-30m-reranker (Head-Only Calibrated Checkpoint)	GRTForSequenceClassification (CrossEncoder)	56.93	67.13	38.5%	70.0%	61.75	123
Two-Stage Hybrid (grt-30m-embedding + Head-Only grt-30m-reranker)	Bi-Encoder + Cross-Encoder Fusion	57.05	67.21	38.5%	70.0%	62.94	123
MatterWaveAI/grt-30m-reranker (Top-Block Joint HessianPairAdam / CyclideAdam)	GRTForSequenceClassification (blocks[-1] + score)	63.50	72.26	46.0%	76.5%	63.12	123
Two-Stage Hybrid (grt-30m-embedding + Top-Block Joint grt-30m-reranker)	Bi-Encoder + Cross-Encoder Fusion	62.14	71.18	44.0%	76.0%	64.09	123

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8-Way Classical Geometric Optimizer Ablation (AllNLI Reranking + STS-B Cross-Encoder)

To evaluate how classical geometric, Riemannian, conic, gyroscopic, Kuramoto–Huygens synchronization, and Gromov–Liouville symplectic optimizers (transformers.models.grt.optimization_grt) shape cross-encoder token-level MaxSim/MinSim and Hermitian phase alignment, we ran a controlled 8-way optimizer ablation on AMD Radeon 8060S Graphics (ROCm / gfx1151) with fused HIP Givens/Clifford kernels:

• Trainable Parameters (812,169 / 0 nn.Linear layers): Top rotational transformer block reranker.model.blocks[-1] (811,651 parameters: [11, 128] Q/K/V/O Givens cascades, [1, 128] Clifford mixer cascade, [21, 512] FFN expand/contract butterfly cascades, paired radial softplus scales, and Cl(2,0) bivector coupling tensors) + final_norm (128 parameters) + GRTCosineClassificationHead (262 parameters: phase_angles, pair_scales, late_weights, output_scale, bias), with Theorem 2.1 Cauchy–Riemann scale-partner pairing active on both blocks[-1] and score.phase_angles.
• Controlled Schedule: 200 steps (batch_size = 128 AllNLI hard-negative triplets + 128 STS-B graded pairs per step, backbone_lr = 1.5e-4, seed = 42), evaluated on AllNLI 200×10 Hard-Negative Reranking, AllNLI 100×20 Extended Candidate Reranking, STS-B Validation (1,500 pairs), STS-B Test (1,379 pairs), and Two-Stage Hybrid (Bi-Encoder + Cross-Encoder) Fusion:

Rank (200×10 MRR)	Optimizer (optimization_grt.py)	AllNLI 200×10 MRR@10	AllNLI 200×10 NDCG@10	200×10 Recall@1 / @3	AllNLI 100×20 MRR@10	AllNLI 100×20 NDCG@10	STS-B Val Spearman (×100)	STS-B Test Spearman / Pearson (×100)	Hybrid 100×20 MRR@10	Hybrid STS-B Test Spearman (×100)	ROCm Time (200 Steps)
1	HessianPairAdam (Sophia-Torus Curvature)	63.50 (BEST)	72.26 (BEST)	46.0% (BEST) / 76.0%	57.03	67.45	71.16	62.61 / 63.47	54.97	64.02	93.8s
2	HuygensSymplecticAdam (Two-Stage Curriculum)	63.27 (#2)	72.09 (#2)	45.5% (#2) / 76.0%	57.38 (#3)	67.70 (#3)	71.18	62.49 / 63.40	56.95 (BEST)	63.95	94.0s
3	SymplecticAdam (Non-Squeezing Floor + Cavity)	63.13 (#3)	72.00 (#3)	45.0% (#3) / 76.0%	56.79	67.25	71.23	62.43 / 63.37	54.80	63.93	93.8s
4	CyclideAdam (Dupin Cyclide Conic + Twist)	63.06 (#4)	71.91 (#4)	45.0% (#3) / 76.5% (BEST)	57.44 (BEST)	67.75 (BEST)	71.85 (#2)	63.12 (BEST) / 64.07	56.30 (#2)	64.09 (BEST)	93.8s
5	GyricAdam (Poinsot–Landé + Thomas Precession)	62.75	71.68	44.5% / 76.5% (BEST)	57.14	67.50	71.87 (BEST)	63.08 / 64.09 (#2)	55.76	64.01	93.9s
6	HuygensAdam (Circular Order Parameter R_p)	62.50	71.50	44.0% / 76.0%	56.07	66.71	71.78	63.11 (#2) / 64.09 (#2)	56.27 (#3)	64.08 (#2)	93.7s
7	PolarNaturalAdam (Riemannian Polar Metric)	62.41	71.42	44.0% / 76.5% (BEST)	57.24	67.58	71.83 (#3)	63.11 (#2) / 64.12 (BEST)	55.82	64.06	93.7s
8	PairAdam (Factored Toroidal Baseline)	62.25	71.31	43.5% / 76.5% (BEST)	57.41 (#2)	67.71 (#2)	71.73	63.11 (#2) / 64.07	55.77	64.06	93.3s
—	Head-Only PairAdam (Published Checkpoint)	56.93	67.13	38.5% / 70.0%	—	—	—	61.75 / 62.99	—	62.94	—
—	Bi-Encoder grt-30m-embedding (circular pool)	52.56	63.74	32.5% / 68.0%	45.63	57.33	71.79	62.42 / 63.30	—	—	—

Key Geometric Insights for Cross-Encoder Reranking

1. Joint Top-Block Rotational Adaptation (+6.57 MRR@10 & +7.5% Recall@1 over Head-Only): Unfreezing blocks[-1] ([11, 128] QKV/O and [21, 512] FFN butterfly cascades) alongside GRTCosineClassificationHead allows token-level MaxSim/MinSim late-interaction matrices to sharpen hard-negative separation, lifting AllNLI 200×10 MRR@10 from 56.93 to 63.50 (Recall@1 from 38.5% to 46.0%) and STS-B Test Spearman from 61.75 to 63.12 (64.09 Hybrid).
2. HessianPairAdam (Sophia-Torus) Leads Top-1 Hard-Negative Discrimination (63.50 MRR@10 / 72.26 NDCG@10 / 46.0% Recall@1): Preconditioning both blocks[-1] cascade angles and score.phase_angles with exact Theorem 2.1 Cauchy–Riemann polar curvature (c_theta) and antipodal saddle-escape kicks achieves the highest 200×10 MRR@10 (+1.25 over PairAdam) and Recall@1 (+2.5% over PairAdam).
3. HuygensSymplecticAdam & SymplecticAdam Dominate Two-Stage Curriculum & Hybrid 100×20 Reranking (56.95 Hybrid 100×20 MRR@10 [BEST], 63.27 200×10 MRR@10 [#2]): Annealing early Kuramoto–Huygens circular order-parameter splay synchronization into the Gromov–Liouville symplectic non-squeezing floor and Helmholtz–Casimir wave-cavity Laplacian yields the #2 standalone 200×10 reranker (63.27 MRR@10, 45.5% Recall@1) and the #1 Two-Stage Hybrid 100×20 reranker (56.95 MRR@10, +1.18 over PairAdam).
4. CyclideAdam, GyricAdam & PolarNaturalAdam Lead Semantic Calibration & Deep Candidate Pools (57.44 100×20 MRR@10 [BEST], 63.12 STS-B Test Spearman [BEST], 64.12 Test Pearson [BEST]): Dupin Cyclide conic metrics with trace-free deviatoric twist (CyclideAdam) achieve the best 20-candidate reranking (57.44 MRR@10, 70.0% Recall@3) and best STS-B Test Spearman (63.12 standalone / 64.09 hybrid), while GyricAdam wins STS-B Validation (71.87 Spearman) and PolarNaturalAdam wins STS-B Test Pearson (64.12).

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Quickstart (sentence-transformers CrossEncoder)

from sentence_transformers import CrossEncoder

reranker = CrossEncoder("MatterWaveAI/grt-30m-reranker")
query = "How do Givens rotations replace dense linear projections in a Transformer?"
documents = [
    "Cascaded 2D Givens rotations and butterfly permutations mix planar coordinate pairs with O(D log D) steps and zero nn.Linear layers.",
    "The stock market closed slightly higher on Tuesday after retail earnings reports.",
    "Standard Transformers rely on dense matrix multiplications (nn.Linear) in QKV and FFN projections.",
]
results = reranker.rank(query, documents, return_documents=True)
for r in results:
    print(f"{r['score']:.4f} | {r['text']}")

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Complete MatterWaveAI/grt-30m* Research Suite on Hugging Face

1. Base Causal LM: MatterWaveAI/grt-30m
2. Chat Fine-Tune: MatterWaveAI/grt-30m-chat
3. 4-Expert Mixture-of-Rotations (MoR): MatterWaveAI/grt-30m-mor
4. Circular-Pooled Sentence Embedding: MatterWaveAI/grt-30m-embedding
5. Cross-Encoder Reranker: MatterWaveAI/grt-30m-reranker
6. Vision-Language (GRTVL): MatterWaveAI/grt-30m-vl
7. Canonical Tokenizer & Polar Embedding Bank: MatterWaveAI/grt-30m-tokenizer
8. Rotational Text-to-Speech (GRTTTS): MatterWaveAI/grt-30m-tts
9. Multimodal Vision-Audio-Language-Speech (GRTOmni): MatterWaveAI/grt-30m-omni

• Whitepaper: The Geometric Rotation Transformer (GRT): A Purely Rotational Foundation Architecture (GRT_Whitepaper.pdf)

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License

Apache 2.0

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Citation

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