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ZFO (McGee et al., arXiv:2610.02190): Decouples direction selection (FO/AdamW) from step size via 1D zeroth-order line searches (Taylor/Padé) using Common Random Numbers (CRN). Padé3 improves RLVR/GRPO fine-tuning over FO in 14 of 16 LLM settings (up to +8.81 on ARC-Challenge, +38% on OpenBookQA for Qwen-2.5-Math-1.5B) with minimal compute overhead.

ScholarCatalyst (Kim et al., arXiv:2610.02202): 207 AI projects/184 authors benchmarked for retrieving catalyst papers from 191k CS papers. Dense embedding (Gemini-Emb-2 R@20 0.38, Qwen3-Emb-8B R@20 0.37) matches or beats LLM agents (o3 deep research R@20 0.33, GPT-4.1 tool-calling R@20 0.37). Hard negatives have equal or higher semantic/lexical similarity to queries than actual inspiration papers.

Chiesa, Guan, and Yildiz (arXiv:2610.01995) prove that in the random oracle model, zero-knowledge proofs and debate protocols for general oracle-aided computation are impossible even with super-polynomial provers/verifiers. However, if the oracle signs each answer, every oracle-aided computation can be verified in zero knowledge with efficient provers/verifiers assuming only collision-resistant hash functions.

VISTA (Kaiming He's group, arXiv:2610.02200) disproved the requirement for program synthesis on ARC-AGI-3, achieving 100.00 RHAE using direct visual reasoning with lossless visual memory, model-directed inspection, and pixel readout. Rendered 512x512 images cost 308 tokens vs 4,000 for text grids.

VISTA (Han, Hu, Qiu, Wu, He, arXiv:2610.02200) achieves 100.00 RHAE on ARC-AGI-3 without program synthesis using Claude Opus 5.0 (7,302 actions vs 17,135 human baseline, -57.4%). Replacing text grids with 512x512 rendered images cut tokens per frame from ~4,000 to 308 and tokens per game from 71.9M to 30.7M. Harness ablations on GPT-5.6 Sol: baseline 13.33 -> PNGs 47.32 -> continuous compaction 65.82 -> markdown scratchpads (GUIDE/WORKING.md) 70.05 -> lossless visual memory/inspect 94.10 -> read_pixels 99.00.

Cambridge study (Piskorz et al., 2026) disentangling distillation dynamics shows catastrophic forgetting and update sparsity depend on learning rate, not rollout policy; forward KL is invariant to rollout policy (within 5.2% accuracy across spectrum), while reverse KL destabilizes without student rollouts; yet off-policy checkpoints ultimately yield higher sustained RLVR performance than on-policy ones.

TACO (Jiang et al., Oct 2026) derives an optimizer via steepest descent under a dimension-normalized L_inf -> L_1 operator norm, yielding an update with exactly one non-zero entry per column (ternary: +1, -1, 0 scaled by sqrt(m/n)). Despite sparsity, its continuation path matches Adam's sign(z)/||z||_1 rather than Muon's z/||z||_2^2, eliminating optimizer mismatch when fine-tuning Adam-pretrained LLMs with <0.5% optimizer memory overhead.

Han et al. (arXiv:2610.02200): VISTA visual harness solves ARC-AGI-3 (RHAE 100.00 with Claude Opus 5.0, 99.00 with GPT-5.6 Sol) without program synthesis. Visual frames require ~308 tokens vs ~4,000 for 64x64 text grids, cutting total game tokens from 71.9M to 30.7M while boosting RHAE from 13.33 (official text grid) to 99.00.

VISTA (Han, Hu, Qiu, Wu, Kaiming He, arXiv:2610.02200) achieves 100.00 RHAE on ARC-AGI-3 with Claude Opus 5.0 (and 99.00 with GPT-5.6 Sol) without program synthesis, using lossless visual memory, inspection tools, and pixel readout. Swapping text grids for rendered images alone lifted baseline RHAE from 13.33 to 47.32.

Karan, Chen & Du (arXiv:2610.02140): MCMC projection of off-policy expert traces onto base model distributions allows SFT to beat RL baselines. On Qwen2.5-3B math, Sampling SFT reaches 49.5% on hard MATH vs 45.7% for GRPO and 24.3% for vanilla SFT, while preventing MMLU forgetting (69.2% vs 58.6% for SFT).

Makras & Sabanis (arXiv:2610.02158): Muon's matrix momentum orthogonalization is mathematically equivalent to relativistic/tamed kinetic energy K(p)=Tr[(I+delta*p*p^T)^(1/2)-I]/delta. The Newton-Schulz iteration functions as smooth spectral taming, saturating singular values at delta^(-1/2) and stabilizing underdamped Langevin dynamics on non-convex landscapes.

Geng et al. (arXiv:2610.02098): Standard mech interp objectives (intervention faithfulness/KL) misrank 9.4%-41.2% of circuit candidates across EAP, ACDC, Edge-SP due to context distortion (replacing excluded signals distorts inputs to retained components). Restoring intact recipient inputs fixes 96/100 misrankings.