Decoupled Topological Coprocessing for Mitigating Reasoning Deadlocks and Non-Invasive Trajectory Steering in Large Language Models (DTC v2.0)
Abstract
Overview We are proud to announce the formal release of Decoupled Topological Coprocessing (DTC v2.0). DTC v2.0 introduces an asynchronous, non-invasive coprocessor architecture that detects and resolves reasoning deadlocks—specifically circular reasoning loops and unanchored extrinsic hallucinations—in Large Reasoning Models (LRMs) during test-time scaling. By coupling real-time Persistent Homology ($H_1$ cycles) over outbound Server-Sent Events (SSE) token streams with host Prefix Caching, DTC achieves real-time trajectory steering with zero modification to model weights or computation kernels, operating with an average background latency of 38.61 ms (completely hidden behind token generation intervals). 🌟 Key Highlights & Major Breakthroughs Dual-Regime Empirical Validation: Soundness on Mathematical Deduction (AIME 2026): Evaluated against 15 challenging problems from the official February 2026 American Invitational Mathematics Examination (MAA AIME 2026 I & II, $N=3$). DTC achieved a 0.0% false-positive intervention rate (100% pass rate), proving that it imposes Zero Alignment Tax on sound deductive exploration. Active Safeguard on Adversarial Trident Benchmark: Across 30 empirical trials spanning circular logic traps and ungrounded knowledge traps, DTC demonstrated a 93.3% anomaly abort rate and a 100% deadlock breakout rate, eliminating 20,705 unproductive tokens (45.3% reduction) with a net compute energy ROI of 99.2%. Quantization Noise Compensation Hypothesis: Direct cross-scale comparison between full-precision (Gemma 4 E2B, FP16) and low-bit quantized (Gemma 4 26B, 4-bit Q4_0 + 4-bit KV cache) architectures revealed that 4-bit quantization rounding noise creates artificial potential wells (pseudo-attractors) that trap reasoning irreversibly (0.0% natural termination), whereas smooth FP16 attention gradients permit spontaneous recovery (23.3%). DTC acts as an external equalizer, enabling commodity low-bit deployments to achieve full-precision reasoning stability. Prefix-Cache-Aligned Rollback & Low-Latency Abort: Abruptly terminates transport-layer connections upon cycle detection ($0\ \mathrm{ms}$ thread halt) and rolls back context to $t_{\mathrm{rollback}} = t_{\mathrm{interrupt}} - k$ ($k=2$). Reuses pre-loop KV blocks via Prefix Caching ($0\ \mathrm{ms}$ recomputation) and injects an immutable Epistemic Introspection Anchor to induce an attention phase transition. Guaranteed Combinatorial Upper Bound & Fail-Open Architecture: Computational complexity is strictly bounded by $\binom{8}{3} = 56$ 2-simplices, completely preventing latency spikes. Implements a fail-open design where overloaded supervisory steps defer to the next window without blocking host generation. 📦 What's Included in this Release 📄 Official Academic Papers: English PDF: paper/dtc_v2_paper_en.pdf (10 pages) Japanese PDF: paper/dtc_v2_paper_ja.pdf (9 pages) Complete LaTeX build sources with professional TikZ vector architecture diagrams (paper/compile_pdf.py). 🗂️ Benchmark Suite & Reproducibility Package (benchmarks/): datasets/trident_benchmark_suite.json: 10 targeted challenges (5 loop traps + 5 hallucination traps). datasets/aime_2026_15problems.json: Official MAA AIME 2026 15-problem evaluation subset. results/: Complete raw JSON execution traces for AIME 2026, Trident, and ablation studies. runner_sample.py: Standalone evaluation runner for OpenAI-compatible endpoints. 🇯🇵 日本語サマリー (Japanese Summary) 本リリースは、並行位相幾何コプロセッシングの第2世代アーキテクチャ DTC v2.0 の正式版です。 AIME 2026 公式問題(15問, $N=3$): 誤介入率 0.0%(健全な演繹の100%パス) を実証(アライメント・タックス・ゼロ)。 敵対的 Trident スイート(30試行): 93.3% の早期遮断 と 100% の膠着解消・正常収束 を達成(総計20,705トークン削減、純エネルギーROI 99.2%)。 量子化ノイズ補償仮説の確立: 4bit量子化丸めノイズが自己注意機構に擬似アトラクターを形成して思考を不可逆捕捉する物理機序(自力脱出0.0%)を特定し、DTCがエッジ低ビット運用の脆弱性を克服する不可欠な軌道調律機構であることを証明しました。 Citation @article{matsumoto2026dtc_v2, author = {Matsumoto, Kouta}, title = {Decoupled Topological Coprocessing for Mitigating Reasoning Deadlocks and Non-Invasive Trajectory Steering in Large Language Models (DTC v2.0)}, year = {2026}, month = {September}, doi = {10.5281/zenodo.22726133}, url = {https://github.com/Oshiruko3/decoupled-topological-coprocessing} }