Reasoning & Test-Time Compute

When you can't make the model bigger, make it think longer — or in parallel.

Long chain-of-thought trained with RL on verifiable rewards is now the default for every frontier model, and reasoning effort is a product dial: Claude low/med/high/max, OpenAI none through xhigh plus Pro, and Gemini Deep Think. The 2026 change is parallel compute. Kimi's Agent Swarm fans out to up to 100 sub-agents, OpenAI's contested Navier–Stokes attempt reportedly ran ~10,000 agents for ~88 hours, and its 377 claimed math results averaged ~3 GPU-hours each. Competition math is effectively solved: several AI systems reportedly scored 42/42 at IMO 2026, after 35/42 gold in 2025. The open questions have moved to verification of research-level claims and to whether reasoning stays legible. Reports that GPT-6 Astra reasons partly in recurrent depth turned CoT monitorability from a theory into a design constraint.

Why it matters

Reasoning benchmarks saturate in months. Claude Fable 5.1 (Sep 2026, Anthropic model card) scores 60.9% on Humanity's Last Exam without tools and 65.0% with tools. FrontierMath Tier 4 went from 31% (GPT-5.2 Pro, Jan) to 38% (GPT-5.4, Mar) per Epoch.
Test-time compute now scales out as well as up. Parallel agents, search and verification let labs spend hours of GPU time on a single problem, and the bottleneck shifts to checking answers.
RLVR mostly sharpens what the base model can already sample (Yue et al., NeurIPS 2025 runner-up). Base-model quality and parallel search are what push past the base model's pass@k ceiling.
Reasoning traces are a safety asset. OpenAI's monitorability evaluations (13 evals, 24 environments) found that monitoring the CoT is far more effective than monitoring outputs alone, and that longer reasoning is more monitorable. Architectures or training that hide reasoning give that up.

State of the art

2025-2026

Effort control is standard in shipped models. Claude Opus 5 (Jul 2026) shipped with thinking on by default plus low/med/high effort, and OpenAI ranges from none to xhigh. GPT-6 Sol's factual error rate reportedly fell from 10.8% to 4.5% at xhigh.
Parallel agent compute: Kimi K2.5's Agent Swarm (Parallel-Agent RL, up to 100 sub-agents), OpenAI's multi-agent math campaigns, and PRM-guided inference for Gemini Deep Think (PRISM, Mar 2026).
Olympiad-level reasoning is commoditised. DeepSeek-V3.2-Speciale (Dec 2025, open) reached IMO and IOI 2025 gold. At IMO 2026, RedNote's dots-note-3.0 and Huawei's Celia received officially graded perfect scores, and an open 'simple and unified scaling' recipe for gold-medal olympiad reasoning appeared in 2026.
Research-level math is contested, not settled. OpenAI's model disproved the Erdős unit-distance conjecture (May 2026, OpenAI). Its Sep 2026 Navier–Stokes claim is disputed, and the Clay Institute still lists the problem as open. Its 377 'results' (Oct 2026) were later revised to 372 and verification is disputed. Verifier-based evaluation of mathematical discovery is now its own research area.
Latent and looped reasoning: Ouro's looped LMs gain mostly in knowledge manipulation. GPT-6 Astra is reported (unconfirmed by OpenAI) to use recurrent depth, which reignited the 'neuralese' debate about reasoning that never appears in the CoT.
Test-time learning: test-time curricula and Titans-style memorisation let a model adapt during a long task. This is the closest thing to continual learning in deployed reasoning systems.

The recipe

A frontier-grade implementation, in order.

Cold-start reasoning

SFT on a few thousand high-quality reasoning traces (distilled from your strongest reasoner or written by humans). LIMO/S1 showed ~1k can be enough to unlock long CoT.

RLVR at scale

Math with answer checking, code with unit tests, formal proofs (Lean), and agentic tasks with outcome checks. Use GRPO-family algorithms (DAPO/GSPO for stability on MoE). Forecast the run with a ScaleRL-style sigmoid fit before committing compute.

Train the effort dial

Train on truncated and extended traces with budget tokens so one model serves everything from no-thinking to max effort. Calibrate each level against latency and cost targets. Users now expect explicit effort settings.

Add parallel compute

Self-consistency → best-of-N with a verifier or PRM → multi-agent decomposition (orchestrator plus sub-agents, trained with parallel-agent RL). Budget verification compute alongside generation compute.

Keep reasoning legible

Measure CoT monitorability (intervention, process and outcome-property evals, as in OpenAI's suite) before and after RL and architecture changes. Avoid optimisation pressure directly on the CoT.

Verify claims, not just answers

For research-grade output, require machine-checkable artifacts (Lean proofs, reproducible code) and independent expert review before you announce. The 2026 math controversies show the cost of skipping this step.

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Common pitfalls

Reasoning models overthink simple queries. Route by difficulty or default to a lower effort level.

PRMs and LLM judges get reward-hacked: the model learns to write convincing but wrong steps. Validate against held-out outcome accuracy.

Putting optimisation pressure on the CoT itself (e.g. penalising 'bad thoughts') teaches the model to hide them. That destroys the monitoring signal you were relying on.

Saturated benchmarks mislead, and aggregator leaderboards for HLE, FrontierMath and ARC-AGI sometimes disagree by more than 5 points. Cite lab model cards with dates.

Massively parallel agent runs amplify mistakes as well as insight. A 10,000-agent proof attempt that nobody can read is not yet a result.