Dan Qiao

Dan Qiao, Yu-Xiang Wang

We consider the problem of generalization of arbitrarily overparameterized two-layer ReLU Neural Networks with univariate input. Recent work showed that under square loss, flat solutions (motivated by flat / stable minima and Edge of Stability phenomenon) provably cannot overfit, but it remains unclear whether the same phenomenon holds for logistic loss. This is a puzzling open problem because existing work on logistic loss shows that gradient descent with increasing step size converges to interpolating solutions (at infinity, for the margin-separable cases). In this paper, we prove that the \emph{flatness implied generalization} is more delicate under logistic loss. On the positive side, we show that flat solutions enjoy near-optimal generalization bounds within a region between the left-most and right-most \emph{uncertain} sets determined by each candidate solution. On the negative side, we show that there exist arbitrarily flat yet overfitting solutions at infinity that are (falsely) certain everywhere, thus certifying that flatness alone is insufficient for generalization in general. We demonstrate the effects predicted by our theory in a well-controlled simulation study.

Tongtong Liang, Dan Qiao, Yu-Xiang Wang et al.

We study the implicit bias of flatness / low (loss) curvature and its effects on generalization in two-layer overparameterized ReLU networks with multivariate inputs -- a problem well motivated by the minima stability and edge-of-stability phenomena in gradient-descent training. Existing work either requires interpolation or focuses only on univariate inputs. This paper presents new and somewhat surprising theoretical results for multivariate inputs. On two natural settings (1) generalization gap for flat solutions, and (2) mean-squared error (MSE) in nonparametric function estimation by stable minima, we prove upper and lower bounds, which establish that while flatness does imply generalization, the resulting rates of convergence necessarily deteriorate exponentially as the input dimension grows. This gives an exponential separation between the flat solutions vis-à-vis low-norm solutions (i.e., weight decay), which knowingly do not suffer from the curse of dimensionality. In particular, our minimax lower bound construction, based on a novel packing argument with boundary-localized ReLU neurons, reveals how flat solutions can exploit a kind of ''neural shattering'' where neurons rarely activate, but with high weight magnitudes. This leads to poor performance in high dimensions. We corroborate these theoretical findings with extensive numerical simulations. To the best of our knowledge, our analysis provides the first systematic explanation for why flat minima may fail to generalize in high dimensions.

Yuyang Ding, Dan Qiao, Juntao Li et al.

Distantly supervised named entity recognition (DS-NER) has emerged as a cheap and convenient alternative to traditional human annotation methods, enabling the automatic generation of training data by aligning text with external resources. Despite the many efforts in noise measurement methods, few works focus on the latent noise distribution between different distant annotation methods. In this work, we explore the effectiveness and robustness of DS-NER by two aspects: (1) distant annotation techniques, which encompasses both traditional rule-based methods and the innovative large language model supervision approach, and (2) noise assessment, for which we introduce a novel framework. This framework addresses the challenges by distinctly categorizing them into the unlabeled-entity problem (UEP) and the noisy-entity problem (NEP), subsequently providing specialized solutions for each. Our proposed method achieves significant improvements on eight real-world distant supervision datasets originating from three different data sources and involving four distinct annotation techniques, confirming its superiority over current state-of-the-art methods.

Keyan Zhou, Zecheng Tang, Lingfeng Ming et al.

The rapid advancement of large vision language models (LVLMs) has led to a significant expansion of their context windows. However, an extended context window does not guarantee the effective utilization of the context, posing a critical challenge for real-world applications. Current evaluations of such long-context faithfulness are predominantly focused on the text-only domain, while multimodal assessments remain limited to short contexts. To bridge this gap, we introduce MMLongCite, a comprehensive benchmark designed to evaluate the fidelity of LVLMs in long-context scenarios. MMLongCite comprises 8 distinct tasks spanning 6 context length intervals and incorporates diverse modalities, including text, images, and videos. Our evaluation of state-of-the-art LVLMs reveals their limited faithfulness in handling long multimodal contexts. Furthermore, we provide an in-depth analysis of how context length and the position of crucial content affect the faithfulness of these models.

Dan Qiao, Kaiqi Zhang, Esha Singh et al.

We study the generalization of two-layer ReLU neural networks in a univariate nonparametric regression problem with noisy labels. This is a problem where kernels (\emph{e.g.} NTK) are provably sub-optimal and benign overfitting does not happen, thus disqualifying existing theory for interpolating (0-loss, global optimal) solutions. We present a new theory of generalization for local minima that gradient descent with a constant learning rate can \emph{stably} converge to. We show that gradient descent with a fixed learning rate $η$ can only find local minima that represent smooth functions with a certain weighted \emph{first order total variation} bounded by $1/η- 1/2 + \widetilde{O}(σ+ \sqrt{\mathrm{MSE}})$ where $σ$ is the label noise level, $\mathrm{MSE}$ is short for mean squared error against the ground truth, and $\widetilde{O}(\cdot)$ hides a logarithmic factor. Under mild assumptions, we also prove a nearly-optimal MSE bound of $\widetilde{O}(n^{-4/5})$ within the strict interior of the support of the $n$ data points. Our theoretical results are validated by extensive simulation that demonstrates large learning rate training induces sparse linear spline fits. To the best of our knowledge, we are the first to obtain generalization bound via minima stability in the non-interpolation case and the first to show ReLU NNs without regularization can achieve near-optimal rates in nonparametric regression.