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Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…
Traditional analyses of gradient descent show that when the largest eigenvalue of the Hessian, also known as the sharpness $S(\theta)$, is bounded by $2/\eta$, training is "stable" and the training loss decreases monotonically. Recent…
Recent results in the literature suggest that the penultimate (second-to-last) layer representations of neural networks that are trained for classification exhibit a clustering property called neural collapse (NC). We study the implicit…
Neural networks are trained by optimizing multi-dimensional sets of fitting parameters on non-convex loss landscapes. Low-loss regions of the landscapes correspond to the parameter sets that perform well on the training data. A key issue in…
The ability of deep neural networks to generalise well even when they interpolate their training data has been explained using various "simplicity biases". These theories postulate that neural networks avoid overfitting by first learning…
Machine learning models tend to learn spurious features - features that strongly correlate with target labels but are not causal. Existing approaches to mitigate models' dependence on spurious features work in some cases, but fail in…
Stochastic gradient descent (SGD) forms the core optimization method for deep neural networks. While some theoretical progress has been made, it still remains unclear why SGD leads the learning dynamics in overparameterized networks to…
Empirically, modern deep learning training often occurs at the Edge of Stability (EoS), where the sharpness of the loss exceeds the threshold below which classical convergence analysis applies. Despite recent progress, existing theoretical…
Existing analyses of optimization in deep learning are either continuous, focusing on (variants of) gradient flow, or discrete, directly treating (variants of) gradient descent. Gradient flow is amenable to theoretical analysis, but is…
Deep learning models are prone to learning shortcut solutions to problems using spuriously correlated yet irrelevant features of their training data. In high-risk applications such as medical image analysis, this phenomenon may prevent…
Many modern learning tasks involve fitting nonlinear models to data which are trained in an overparameterized regime where the parameters of the model exceed the size of the training dataset. Due to this overparameterization, the training…
Deep neural networks have achieved great success both in computer vision and natural language processing tasks. However, mostly state-of-art methods highly rely on external training or computing to improve the performance. To alleviate the…
Deep neural networks do not discriminate between spurious and causal patterns, and will only learn the most predictive ones while ignoring the others. This shortcut learning behaviour is detrimental to a network's ability to generalize to…
Graph Neural Networks (GNNs) often perform better for high-degree nodes than low-degree nodes on node classification tasks. This degree bias can reinforce social marginalization by, e.g., privileging celebrities and other high-degree actors…
Stochastic Gradient Descent (SGD) is the workhorse algorithm of deep learning technology. At each step of the training phase, a mini batch of samples is drawn from the training dataset and the weights of the neural network are adjusted…
An important characteristic of neural networks is their ability to learn representations of the input data with effective features for prediction, which is believed to be a key factor to their superior empirical performance. To better…
Stochastic gradient descent (SGD) has been found to be surprisingly effective in training a variety of deep neural networks. However, there is still a lack of understanding on how and why SGD can train these complex networks towards a…
Learning-based stereo matching and depth estimation networks currently excel on public benchmarks with impressive results. However, state-of-the-art networks often fail to generalize from synthetic imagery to more challenging real data…
Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing…
In gradient descent dynamics of neural networks, the top eigenvalue of the loss Hessian (sharpness) displays a variety of robust phenomena throughout training. This includes early time regimes where the sharpness may decrease during early…