Hanyu Yang — mathematics and AI research

In a 100-step Qwen2.5-Coder-3B trial with fixed coding tasks, a tag-format placebo reward gives no detectable math gain, while execution-checked rewards gain 5.7 and 5.1 percentage points across two seeds on six math benchmarks. The result is limited to this short code-to-math setting; the second seed was scored only with Absolute Zero's prompt.

Using 200 FLORES-200 devtest sentences per language across 21 languages, Qwen3.5-9B with its MTP head and Gemma 4 E4B with its assistant show no rise in acceptance with tokenizer fertility; every non-English language has lower acceptance length than English. A six-language vLLM follow-up finds smaller speedups than English in the other five languages for both built-in drafters. These serving measurements use a single run on one A100 at batch size 1; speculative greedy outputs often differ from plain greedy.

On 14 released base/derived pairs (OLMo-2, Qwen2.5, SmolLM2; 1B–7B), a context-free token bias recovers at most 9.8% of the web-text loss increase out of sample, and bias plus temperature up to 36%, mostly in overconfident OLMo-2 preference-tuned models. Math continued pretraining loses up to 0.8 nats per token and recovers at most 3.1%.

In three matched 665M models (full attention, SWA-128, SWA-128 with NoPE global layers), a look-alike fake fact shows no jump in pull as it crosses the 128-token window edge; the preregistered window-capture test fails (ΔS = −0.054 [−0.069, −0.039]). The standard hybrid picks the fake fact more often at every distance (71% against 35% at 96 tokens).

On 125 public C4 checkpoints (7M–2.8B parameters, 1–64 epochs), cross-fitted scalar temperature scaling removes about a third of the fitted data-repetition penalty: ρ = 0.682 (95% bootstrap interval 0.580–0.858). The results are exploratory: the preregistered evaluator check failed, and the hypothesis that at least half of the fitted penalty would disappear was not supported.

Chunks of one code repository or paper give correlated gradients out to 16K tokens. At equal tokens, a whole-document 16K block has 3.5–4.9× fewer effective independent samples than packed web text on code and about 2.3× fewer on arXiv, measured with 512-token chunks on Pythia and OLMo-2 checkpoints; books stay close to the control.

Kalai, Nachum, Vempala and Zhang argue that pretraining keeps the slack term δ of their hallucination bound small, but do not measure it. On their birthday example, with OLMo-2's public corpus for the weights, the 7B base model gives δ = +0.028 (95% CI [0.017, 0.042]); the result is fragile to the weighting, and the floor is vacuous on this frame.

Liu asked whether AdaGrad's threshold p = 4/3 under heavy-tailed noise is real. It is, and it is caused by asymmetry: with symmetric noise the rate is T^{−(p−1)/(2p)} for every p, while with general noise and small damping (3p−4)/(4p) is sharp for every step size. Damping closes the gap, linearly in α wherever the exponent is positive.

Re-expressing the 60 released runs of Tao et al. (2024) in bits per character moves their 70B vocabulary prescription from 212K to 106K–119K or 550K–764K, depending on the fitting approach. With a whole model size held out, every procedure misses the best vocabulary at 1.13B by 8–40% compute-equivalent, and the corrected metric does not reduce the miss.

Kozma and Voderholzer showed that byte-pair encoding recovers between 1/3 and 5/8 of the optimal pair-encoding utility in the worst case. An explicit family of strings lowers the upper bound to (1−e⁻²)/2 ≈ 0.4323, and against encodings whose tokens have length at most three that constant is exact.

A forward error bound for FlashAttention-2: it shares its worst-case term with two-pass attention and is more accurate on peaked attention. The split-KV merge does not renormalize, and an output that should be exactly 1 comes back up to 2.2% off on an NVIDIA L4. Also counterexamples to a published O(u log n) bound.

Conjectures 10.1 and 10.2 of Althöfer et al. (2015) are settled. Conjecture 10.3 has verified witnesses at 54 orders; its infinite tail is not proved. The fourth problem remains open.

All 56,070 non-abelian groups of order 256 and all 20,154 of order 384 given an explicit terrace — the two orders left open by Theorem 32(vi) of Ollis's dynamic survey, so that with it every non-abelian group of order at most 511 is terraced. 76,325 witness records, checked by a standard-library Python verifier, nine negative controls, a coverage count, and a GAP check tying every record to its SmallGroup id.

R(4,4,4;3) ≥ 84, R(4,6;3) ≥ 64 and R(5,5;4) ≥ 36 — three entries of §7.1(a) of Small Ramsey Numbers improved, each by a group-invariant colouring printed as a table over group orbits, regenerated without a solver and checked by complete enumeration.

61 ≤ K(8,1,2) ≤ 64 — the lower bound formalised in Lean 4 with zero sorrys, plus an elementary even-n theorem improving five published lower bounds.

β = 0.2801694990 — ten correctly-rounded decimal places, proved in Arb interval arithmetic, where the 1985 Varga–Carpenter rigorous enclosure determines five.

α_disk(14) ≥ 0.0767158857710289397517847755066… — an explicit 14-point configuration in exact integer coordinates, about +1.075% above the best earlier documented value; a certified lower bound, not a proved record.