12 accepted papers
Loss spikes commonly emerge during neural network training with the Adam optimizer across diverse architectures and scales, yet their underlying mechanism remains elusive. While previous explanations attribute these phenomena to sharper loss landscapes at lower loss, we show that landscape geometry …
Current state-of-the-art methods for out-of-distribution (OOD) generalization lack the ability to effectively address datasets with heterogeneous causal subgraphs at the instance level. Existing approaches that attempt to handle such heterogeneity either rely on data augmentation, which risks alteri…
We study the gradient flow dynamics of diagonal linear networks for regression tasks under infinitesimal initialization. Extending the saddle-to-saddle dynamics described in Theorem 1 from Pesme & Flammarion (2023), we generalize the analysis to both deep diagonal linear networks and a broader class…
Adam is a widely used optimization algorithm in deep learning, yet the specific class of objective functions where it exhibits inherent advantages remains underexplored. Unlike prior studies requiring external schedulers and $\beta_2$ near 1 for convergence, this work investigates the ``natural'' au…
In this paper, we study the Karush-Kuhn-Tucker (KKT) points of the associated maximum-margin problem in homogeneous neural networks, including fully-connected and convolutional neural networks. In particular, We investigates the relationship between such KKT points across networks of different width…
Large language models have consistently struggled with complex reasoning tasks, such as mathematical problem-solving. Investigating the internal reasoning mechanisms of these models can help us design better model architectures and training strategies, ultimately enhancing their reasoning capability
Visual streaming perception (VSP) involves online intelligent processing of sequential frames captured by vision sensors, enabling real-time decision-making in applications such as autonomous driving, UAVs, and AR/VR. However, the computational efficiency of VSP on edge devices remains a challenge d…
Matrix factorization models have been extensively studied as a valuable test-bed for understanding the implicit biases of overparameterized models. Although both low nuclear norm and low rank regularization have been studied for these models, a unified understanding of when, how, and why they achiev…
Transformers have shown impressive capabilities across various tasks, but their performance on compositional problems remains a topic of debate. In this work, we investigate the mechanisms of how transformers behave on unseen compositional tasks. We discover that the parameter initialization scale…
Substantial work indicates that the dynamics of neural networks (NNs) is closely related to their initialization of parameters. Inspired by the phase diagram for two-layer ReLU NNs with infinite width (Luo et al., 2021), we make a step towards drawing a phase diagram for three-layer ReLU NNs with in…
Empirical works show that for ReLU neural networks (NNs) with small initialization, input weights of hidden neurons (the input weight of a hidden neuron consists of the weight from its input layer to the hidden neuron and its bias term) condense onto isolated orientations. The condensation dynamics…
Understanding the structure of loss landscape of deep neural networks (DNNs) is obviously important. In this work, we prove an embedding principle that the loss landscape of a DNN "contains" all the critical points of all the narrower DNNs. More precisely, we propose a critical embedding such that a…