Mathematics

The work introduces label-free bias-only test-time reinforcement learning: the pretrained backbone stays frozen while only about 100K bias parameters (down_proj.bias across 28 MLP layers) are optimized against majority-vote pseudo-label rewards, reaching 76.67% on MATH-500 with Qwen2.5-7B and 79.50% with Qwen2.5-Math-7B, improving vision-language and audio reasoning under the same procedure, and transferring frozen bias vectors to 4,500 verified-disjoint MATH problems to lift Qwen2.5-7B from 46.3% to 70.9% and Qwen2.5-Math-7B from 52.5% to 75.4%, with pseudo-label reliability and accessible gradient energy explaining why a restricted subspace still adapts.

The work proposes RIDE (RL-Induced Direction Extrapolation): on student-generated trajectories it computes the layerwise hidden-state residual between an RL-trained teacher and its pre-RL checkpoint, then regresses the student's hidden states toward targets displaced beyond the teacher along that residual; across four base/RL-teacher pairs (R1-Distill-1.5B, Qwen3-4B, Llama-3.2-3B, Phi-4-mini) RIDE's mean Avg@16 on AIME24, AIME25 and AIMO approaches or exceeds the RL-trained teacher on every pair, the only compared method whose mean does so, and it consistently outperforms output-space extrapolation.

The work introduces EvoDuet, a bi-level method that co-evolves solutions and web search queries with fixed model parameters: at each iteration a knowledge-gap-based retrieval gate decides whether to retrieve new documents, reuse stored ones, or proceed without them, an inner loop refines queries and ranks documents by the solution scores they are predicted to yield, and an outer loop generates candidates in parallel and records evaluated outcomes for later searches; across 21 optimization tasks with one candidate per iteration it raises OpenEvolve's normalized discovery gain from 74.1% to 78.0% with GPT-5.6-Luna and from 61.3% to 82.3% with Gemini-3.8-Flash, Qwen3.

The authors introduce the Endless Exam, a benchmark spanning fourteen parameterised families of mathematical construction problems with 69 evaluation instances, where each submitted object is automatically checked for validity and given an uncapped relative quality score (100 marks average reference parity); across nine models and seventeen configurations, tool-free overall scores span 7.55 to 91.90, and with code and web access GPT-6 Astra, GPT-5.6 Luna and Claude Opus 5.5 reach 143.16, 119.35 and 180.06, while none of the 30 published-frontier references is surpassed.

Using truncated-continuation probes, the work finds that in on-policy self-distillation (OPSD) the teacher's advantage over the student is concentrated on failed trajectories (77% versus 37% recovery at 1.7B) and shrinks with scale, and therefore proposes OASIS: keeping the OPSD objective unchanged, it applies supervision only along the shortest outcome-verified on-policy trajectory and replaces the written reference solution with a distinct same-problem self-generated rollout, typically the student's own unverified attempt, improving mean Avg@12 over OPSD by 0.59, 1.86 and 3.05 points on Qwen3-1.7B, 4B and 8B across AIME 2024, AIME 2025 and HMMT 2025 while requiring no written solutions.

LANTERN trains a linear classifier on Qwen3-32B activations to rank 50 million candidate relations among the 10,000 most-referenced OEIS sequences, then applies staged filtering, hypothesis generation, executable verification and analytical checking to produce 62 verified relations without an existing OEIS cross-reference; a content screen retained 13, nine of them informative or insightful, four not found in the OEIS or a targeted literature search, with the end-to-end process taking under 8 hours.

The work defines the length-scaling tax (LST) as the excess response length that RL post-training adds on already-solved queries without a matching accuracy gain, and proposes Length Self-Distillation (LSD), which routes solved prompt groups to on-policy distillation while keeping the original RLVR objective for unsolved groups, using an exponential moving average of the same policy lineage as teacher with no external model; LSD reduces LST from 19.0% to -3.7% on single-turn reasoning and from 31.4% to 13.7% on multi-turn agentic tasks while matching or improving average Pass@1 over RL.

The work shows that Direct-OPD's token-level log-ratio reward measures only relative change and can stay fixed while the probability mass that both checkpoints assign to the student's candidate tokens vanishes, whereas the teacher–reference JSD and both KL directions vanish with that mass; it therefore proposes S²D-OPD, which ranks student-sampled states by teacher–reference JSD and masks Direct-OPD supervision at low-divergence states, retaining only the top 10% per response, improving held-out accuracy over dense Direct-OPD on AIME and HMMT benchmarks in seven of eight settings across two teacher pairs and four student models from 1.7B to 8B parameters and matching it in the eighth, without extra forward passes.

In this guest post, Rachel Webb draws on her own mathematical research experience to argue that LLMs let her execute research faster and turn some of her lands of mathematical fantasy into worlds she can realistically start exploring, while her metric for mathematical interest stays unchanged and humans keep doing math for two humanistic reasons: math is interesting to us individually, and math creates communities.