machine learning optimization teams

Abstract: What computational role does overparameterisation play during learning? Information-plane analyses suggest that neural networks can traverse representations substantially more complex than those required by their final predictors. We explore when this transient complexity serves a computational purpose by comparing the representation complexity needed for prediction with that needed to make an unknown target statistically visible through gradient feedback. We introduce an oracle model of neural network learning and use Kolmogorov \(n\)-widths to quantify effective representation complexity. Our main technical result transfers complexity bounds from the forward representation to the corresponding gradient-query features. Combined with statistical-query lower bounds, this gives a task-agnostic lower bound on the initial effective width required for target-dependent gradient information to become detectable. For \(k\)-sparse parity in \(D\) dimensions, a known target admits an \(O(k)\)-width representation, while the general bound already implies a polynomial separation between representation and discovery. We then exploit parity's invariance under coordinatewise sign reflections to identify a sharper unsigned effective width, which removes sign distinctions invisible to the parity information channel. At a transfer-compatible measurement resolution, its critical scale is \(\widetildeΘ_k\left( D^{k-1}τ^2 \right)\), up to logarithmic factors. Thus, the representation resources required to discover a predictor can substantially exceed those required to represent it once learned. Interpreting precision through accumulation over fresh samples yields a corresponding width-time frontier. Experiments support the predicted dimension dependence and examine how optimisation and generalisation depart from this idealised frontier.

Abstract: Supervised fine tuning (SFT) is commonly monitored through training and evaluation loss, but loss does not fully characterize how model functionality evolves along the same trajectory. We study this gap through dialect adaptation of Qwen3-ASR, MiMo-Audio, and FireRed-LLM across learning rates from $10^{-5}$ to $10^{-3}$. Character error rate (CER) reveals pronounced transient collapse and recovery whose severity and temporal structure are only weakly reflected by loss. Bidirectional layer patching reveals strong cross checkpoint functional incompatibility during recoverable collapse, with model dependent depth profiles that reorganize during recovery. Pairwise gradient similarity alone does not reliably indicate optimization stability, whereas raw gradient spectral analysis provides a clearer structural distinction between stable and unstable optimization: successfully converged runs approach a broad and temporally stable spectral energy distribution, while failed runs remain spectrally concentrated or exhibit persistent fluctuations. Finally, AdamW update transfer bypasses pronounced early collapse, yet substantial Mandarin degradation still emerges later in training. These results motivate three separable SFT dynamics: collapse, repair, and drift, and show that transient collapse is not necessary for persistent source domain degradation.