Hanlin Zhang

Mechanisms for continued self-improvement of language models without external supervision remain an open challenge. We propose Peer-Predictive Self-Training (PST), a label-free fine-tuning framework in which multiple language models improve collaboratively by leveraging a cross-model aggregated response as an internal training signal. Given a prompt question, the models generate responses sequentially; the final aggregated answer—often more reliable than individual responses in practice—serves as an internal reference for learning. We measure how informative each intermediate response is about the aggregate using pointwise mutual information (PMI), and use this signal to scale self-training updates. Responses already aligned with the aggregate are updated less, while less informative or misaligned responses are updated more. On mathematical reasoning benchmarks (SimulEq, MATH-500-Numeric, and MultiArith), PST improves exact-match accuracy by 2.2–4.3 percentage points across Gemma-2-2B, LLaMA-3.2-1B, and Qwen2.5-1.5B, and reduces the average generator–verifier gap (GV-Gap) by 26–40%, while requiring no external supervision or teacher–student hierarchy and relying solely on cross-model interactions. These results suggest that cross-model generations and peer-predictive feedback can serve as an effective approach for self-supervised training.

Public LLM leaderboards contain rich observational evidence about post-training, but this evidence is strongly confounded by base-model family. We study capability transfer: whether improving one capability tends to improve another, and whether that carryover differs across related families. Our goal is to study this question mainly from cheap observational evaluation data rather than from large collections of expensive training runs. We propose Hierarchical Component Analysis (HCA), a family-aware latent-factor method for studying capability transfer from observational data alone. Applied to Llama and Qwen families containing 1500+ models from the Open LLM Leaderboard, HCA identifies a three-factor structure whose most stable pattern is a positive link from an instruction-aligned factor to a math-aligned factor. We then verify this finding via real fine-tuning with external dataset, showing that it is not merely a benchmark artifact. Overall, this work shows that observational data can already suggest concrete post-training predictions.