Training overparameterized neural networks often yields solutions with varying generalization capabilities, even when achieving similar training losses. Recent evidence indicates a strong correlation between the sharpness of a minimum and its generalization error, leading to increased interest in optimization methods that explicitly seek flatter minima for improved generalization. Despite its contemporary relevance to overparameterization, however, this sharpness-aware minimization (SAM) strategy has not been studied much yet as to exactly how it is affected by overparameterization. In this work, we analyze SAM under varying degrees of overparameterization, presenting both empirical and theoretical findings that reveal its critical influence on SAM’s effectiveness. First, we conduct extensive numerical experiments across diverse domains and show that SAM consistently improves with overparameterization. Next, we attribute this phenomenon to the interplay between the enlarged solution space and increased implicit bias resulting from overparameterization. Furthermore, we show that this effect is particularly pronounced in practical settings involving label noise and sparsity, and yet, sufficient regularization is necessary. Last but not least, we provide other theoretical insights into how overparameterization helps SAM achieve minima with more uniform Hessian moments compared to SGD, and much faster convergence at a linear rate.

This work suggests fundamentally rethinking the current practice of pruning large language models (LLMs).The way it is done is by divide and conquer: split the model into submodels, sequentially prune them, and reconstruct predictions of the dense counterparts on small calibration data one at a time; the final model is obtained simply by putting the resulting sparse submodels together.While this approach enables pruning under memory constraints, it generates high reconstruction errors.In this work, we first present an array of reconstruction techniques that can significantly reduce this error by more than 90%.Unwittingly, however, we discover that minimizing reconstruction error is not always ideal and can overfit the given calibration data, resulting in rather increased language perplexity and poor performance at downstream tasks.We find out that a strategy of self-generating calibration data can mitigate this trade-off between reconstruction and generalization, suggesting new directions in the presence of both benefits and pitfalls of reconstruction for pruning LLMs. 1

Concept bottleneck models (CBMs) are a class of interpretable neural network models that predict the target response of a given input based on its high-level concepts. Unlike the standard end-to-end models, CBMs enable domain experts to intervene on the predicted concepts and rectify any mistakes at test time, so that more accurate task predictions can be made at the end. While such intervenability provides a powerful avenue of control, many aspects of the intervention procedure remain rather unexplored. In this work, we develop various ways of selecting intervening concepts to improve the intervention effectiveness and conduct an array of in-depth analyses as to how they evolve under different circumstances. Specifically, we find that an informed intervention strategy can reduce the task error more than ten times compared to the current baseline under the same amount of intervention counts in realistic settings, and yet, this can vary quite significantly when taking into account different intervention granularity. We verify our findings through comprehensive evaluations, not only on the standard real datasets, but also on synthetic datasets that we generate based on a set of different causal graphs. We further discover some major pitfalls of the current practices which, without a proper addressing, raise concerns on reliability and fairness of the intervention procedure.