SFGA: A Statistics-First Gating Architecture with Adjudicative Escalation for Trustworthy SFT Data Procurement

Data selection during supervised fine-tuning (SFT) can critically change the behavior of large language models (LLMs). Although existing work has studied the effect of selecting data based on heuristics such as perplexity, difficulty, or length, the reported findings are often inconsistent or context-dependent. In this work, we systematically study the role of data difficulty in fine-tuning from both empirical and theoretical perspectives, and find that there is no universally optimal difficulty level; rather, its effectiveness depends on the dataset size. We show that for a fixed data budget, there exists an optimal data difficulty for SFT, and that this optimal difficulty shifts toward harder data as the data budget increases. To explain this phenomenon, we conduct controlled synthetic experiments that reveal a simple underlying mechanism: the interplay between the (in-distribution) generalization gap and the extrapolation gap. We further support this mechanism through a theoretical analysis using PAC-Bayesian generalization bounds. Overall, our results clarify how data size and difficulty jointly affect the trade-off between generalization and extrapolation in SFT, providing guidance for difficulty-based data selection under certain model and data conditions.

Supervised fine-tuning (SFT) data selection is commonly formulated as instance ranking: score each example and retain a top-$k$ subset. However, effective SFT training subsets are often produced through ordered curation recipes, where filtering, mixing, and deduplication operators jointly shape the final data distribution. We formulate this problem as fixed-pool data recipe search: given a raw instruction pool and a library of grounded operators, the goal is to discover an executable recipe that constructs a high-quality selected subset under a limited budget of full SFT evaluations, without generating, rewriting, or augmenting training samples. We introduce AutoSelection, a two-layer solver that decouples fixed-pool materialization based on cached task-, data-, and model-side signals from expensive full evaluation, using warmup probes, realized subset states, local recipe edits, Gaussian-process-assisted ranking, and stagnation-triggered reseeding. Experiments on a 90K instruction pool show that AutoSelection achieves the strongest in-distribution reasoning average across three base models, outperforming full-data training, random recipe search, random top-$k$, and single-operator selectors. Additional Out-of-distribution graph-reasoning results, search-stability analyses, structural ablations, and 1.5B-to-7B transfer checks further show that recipe structure matters beyond individual selection operators. Code is available at https://github.com/w253/AutoSelection.

Supervised fine-tuning (SFT) is often treated as a capability-adaptation step, while alignment is attributed to later preference optimization or reinforcement learning. This separation is incomplete: when examples are scored and kept online during fine-tuning, the choice of which data to train on already changes the model's behavioral preferences. We study online data selection as an implicit alignment mechanism. Given the same base model, optimizer, and selected-token budget, we compare random, loss-based, quality-based, and diversity-based online selectors and measure the behavioral drift they induce without any preference optimization. The proposed evaluation tracks helpfulness, refusal rate, verbosity, truthfulness, sycophancy, calibration, and jailbreak robustness, together with diagnostics for which behavioral modes are over-represented in the selected data. We formalize online selection as a reweighted SFT objective whose weights define an implicit preference over response styles and safety postures, so that an online scorer plays the role usually assigned to a reward model. This view predicts that high-scoring data can systematically favor longer, more assertive, more compliant, or more refusal-prone behaviors depending on how the online score is defined. Empirically, selectors that are statistically indistinguishable in task accuracy diverge sharply in refusal rate, verbosity, and sycophancy, and we show that the direction of the shift is predictable from the attribute mixture of the selected data. We introduce Alignment Drift Auditing (ADA), a controlled protocol for quantifying selection-induced behavioral movement, and Alignment-Aware Selection (AAS), a diagnostic online selector that retains data efficiency while constraining drift along safety and style axes.