CoTS: Probability Competition and Soft-to-Discrete Phase Lock¶
Paper information¶
| Field | Value |
|---|---|
| Paper | arXiv 2610.20642; v1 full text |
| Original title | CoTS: Competitive Token Selection for Latent Reasoning in Large Language Models |
| Affiliations | Jie Yu: Xiaomi AI Lab and Nanyang Technological University (PDF affiliations 1 and 2); grouped under Xiaomi AI Lab, the first affiliation. Work performed during a Xiaomi internship. |
| First public release | 2026-10-08 (arXiv v1), 2026-10-08T02:47:16Z |
| Authors' code | OkinoYu/CoTSReasoning; no clear license identified, so implemented from equations without vendoring. |
| Adapter | Catalog key cots, adapter: null |
| Local code | src/auto_research/foundation_models/cots.py; scripts/run_oct16_foundation_components.py |
| Status | component_only, L1 mechanism diagnostic; evolve_integrated: false |
| Full study | Too costly; not reproduced (review DONE), not_reproduced_high_cost |
Original paper¶
Background and contribution¶
Continuous soft tokens may drift from a discrete reasoning trajectory. CoTS uses top-two probability competition to control soft mixing, retains at least half the sampled token's weight, and irreversibly switches to discrete output after reasoning. See Sections 3.1–3.3, Equations 1–6 and Section 4 for experiments and ablations.
flowchart LR
A[Next-token probabilities] --> B[Top-two competition sets alpha]
A --> C[Top-k normalized soft embedding]
A --> D[Externally sampled token]
D --> E[Reasoning end and formatting guards]
B --> F[Convex mixture]
C --> F
D --> F
E --> F
F --> G[Next-step input embedding]Key figure from the paper¶
Original Figure 1: Competition and convex mixing in the paper, not local generation. Copyright belongs to the authors.
Core equations¶
\(q(v)=p(v)/\sum_{u\in S}p(u)\) and \(s=\sum_{v\in S}q(v)E(v)\). For top-two \(p_1\ge p_2\), \(\alpha=p_2/(p_1+p_2)\in[0,0.5]\), \(\widetilde\alpha=r(1-d)\alpha\), and \(x=(1-\widetilde\alpha)E(y)+\widetilde\alpha s\). Even for \(y\notin S\), \(1-\widetilde\alpha\ge0.5\) and \(\|x-E(y)\|\le0.5\|s-E(y)\|\). Emitting </think> sets \(r=0\) immediately and permanently. Protected math/format tokens set \(d=1\) for that step only.
Paper results¶
| Table 1: mean Pass@1 over six tasks | CoT sampling | CoTS |
|---|---|---|
| Qwen3.5-9B | 76.27% | 81.48% |
| Gemma-4-12B-IT | 81.85% | 86.76% |
Not every task improves: Qwen3.5-9B GPQA trails sampling. Fixed mixture and removed-anchor ablations are separate. No online A/B was reported.
Local reproduction¶
Implement competition, top-k soft embedding, discrete anchor, per-item irreversible phase lock, and EOS state. Sampling outside top-k is supported. Probabilities and embeddings remain differentiable, without NumPy or straight-through substitutes. Callers explicitly supply protection and end-think IDs.
Data and execution¶
Seeds 42/43/44 use synthetic synthetic-formula-tensors@oct16-component-v1: 8×31 probabilities, 31×12 embeddings, top-k=9. No checkpoint, actual tasks, gold, or paid API.
PYTHONPATH=src python scripts/run_oct16_foundation_components.py \
--papers cots --device cpu --seeds 42,43,44 \
--output runs/oct16-foundation/cots-cpu.json
CUDA runs the same operator and requires an available device; CPU results do not substitute for a separate receipt.
Results¶
CPU metrics report minimum discrete weights 0.5612643 / 0.5542747 / 0.5258285, all ≥0.5. Half-drift, immediate and irreversible end-think, one-step format protection, and sticky EOS passed. Logit and embedding gradients were finite and nonzero. These are formula contracts, not reasoning accuracy.
Code map and limits¶
| Interface | Implementation |
|---|---|
| Distribution and sampling | Caller supplies competitive_token_selection(probabilities,embeddings,sampled_tokens,state,...) inputs |
| Equations 1–5 | CotsStep returns soft/discrete embeddings, alpha, sampled coefficient, and support weights |
| Equation 6 and stopping | CotsState.reasoning/finished; caller stops decoding when finished |
| Consumer | Pass CotsStep.next_embedding to the model; no fabricated full loop |
| Tests | tests/foundation_models/test_cots.py: closed form, outside-top-k anchor, support/competition independence, double-precision gradcheck, control tokens |
Cost and unreproduced scope¶
Section 4 uses 4B/9B/12B models, 2,107 questions across six benchmarks, output up to 38,912 tokens, multiple baselines/ablations, and eight A100s. Training-free does not make the full inference study cheap. Not reproduced for cost (review DONE) on the one-A100/A30 or Mac budget; no checkpoint/task download or full probe. No actual reasoning outputs. diagnostic_only: true, promotion_eligible: false, adapter: null; no Evolve entry.