Correcting Stochastic Update Bias in Preconditioned Language Model Optimizers

Preconditioned optimizers are central to language model training, but their stochastic update rules are usually treated as direct approximations to population preconditioned descent. We show that this view misses two finite-sample biases. First, the gradient and preconditioner are typically estimated from the same minibatch, introducing gradient--preconditioner coupling bias. Second, even when the preconditioner estimate is unbiased, its inverse or inverse-root is generally biased because inversion is nonlinear. We propose a single-batch bias-correction framework that addresses both effects: cross-fitted preconditioning estimates the numerator and preconditioner from independent microbatch groups, while variance-corrected inversion uses microbatch variability to subtract the leading delta-method bias term. The framework applies to diagonal moment, diagonal curvature, and matrix preconditioning methods, instantiated in AdamW, Sophia, and Shampoo. Bias correction reduces held-out pretraining loss on Qwen2.5-0.5B by $0.15$, $0.07$, and $0.11$ nats, respectively; the effects on mixed-quality pretraining and downstream instruction tuning are consistently neutral-to-positive. Together, these results establish bias correction as a practical mechanism for reducing finite-sample update bias and improving the performance of preconditioned optimizers.

Pioneer Agent: Continual Improvement of Small Language Models in Production

Small language models are attractive for production deployment due to their low cost, fast inference, and ease of specialization. However, adapting them to a specific task remains a challenging engineering loop, driven not by training itself but by surrounding decisions: data curation, failure diagnosis, regression avoidance, and iteration control. We present Pioneer Agent, a closed-loop system that automates this lifecycle. In cold-start mode, given only a natural-language task description, the agent acquires data, constructs evaluation sets, and iteratively trains models by jointly optimizing data, hyperparameters, and learning strategy. In production mode, given a deployed model with labeled failures, it diagnoses error patterns, constructs targeted training data, and retrains under explicit regression constraints. To evaluate this setting, we introduce AdaptFT-Bench, a benchmark of synthetic inference logs with progressively increasing noise, designed to test the full adaptation loop: diagnosis, curriculum synthesis, retraining, and verification. Across eight cold-start benchmarks spanning reasoning, math, code generation, summarization, and classification, Pioneer Agent improves over base models by 1.6-83.8 points. On AdaptFT-Bench, it improves or preserves performance in all seven scenarios, while naive retraining degrades by up to 43 points. On two production-style deployments built from public benchmark tasks, it raises intent classification from 84.9% to 99.3% and Entity F1 from 0.345 to 0.810. Beyond performance gains, the agent often discovers effective training strategies, including chain-of-thought supervision, task-specific optimization, and quality-focused data curation, purely from downstream feedback.