Recently, there has been growing evidence that if the width and depth of a neural network are scaled toward the so-called rich feature learning limit ( µ P and its depth extension), then some hyperparameters -- such as the learning rate -- exhibit transfer from small to very large models. From an optimization perspective, this phenomenon is puzzling, as it implies that the loss landscape is consistently similar across very different model sizes. In this work, we study the landscape through the lens of the loss Hessian, with a focus on its largest eigenvalue (i.e. the sharpness), and find that certain spectral properties under µ P are largely independent of the size of the network, and remain consistent as training progresses. We name this property Super Consistency of the landscape. On the other hand, we show that in the Neural Tangent Kernel (NTK) and other scaling regimes, the sharpness exhibits very different dynamics at different scales.

Unlike distance metric learning where the subsequent tasks utilizing the estimated distance metric is the usual focus, the proposal focuses on the estimated metric characterizing the geometry structure. Despite the illustrated taxi and MNIST examples, it is still open to finding more compelling applications that target the data space geometry. Interpreting mathematical concepts such as Riemannian metric and geodesic in the context of potential application (e.g., cognition and perception research where similarity measures are common) could be inspiring. Our proposal requires sufficiently dense data, which could be demanding, especially for high-dimensional data due to the curse of dimensionality. Dimensional reduction (e.g., manifold embedding as in the MNIST example) can substantially alleviate the curse of dimensionality, and the dense data requirement will more likely hold true.

The key quantity of interest here is the Riemannian metric, which characterizes the Riemannian geometry and defines straight lines and derivatives on the manifold.

The conditional quantile treatment effect (CQTE) can provide insight into the effect of a treatment beyond the conditional average treatment effect (CA TE). This ability to provide information over multiple quantiles of the response makes the CQTE especially valuable in cases where the effect of a treatment is not well-modelled by a location shift, even conditionally on the covariates. Nevertheless, the estimation of the CQTE is challenging and often depends upon the smoothness of the individual quantiles as a function of the covariates rather than smoothness of the CQTE itself. This is in stark contrast to the CA TE where it is possible to obtain high-quality estimates which have less dependency upon the smoothness of the nuisance parameters when the CA TE itself is smooth. Moreover, relative smoothness of the CQTE lacks the interpretability of smoothness of the CA TE making it less clear whether it is a reasonable assumption to make.

We present a novel alignment-before-generation approach to tackle the challenging task of generating general 3D shapes based on 2D images or texts.

Probabilistic modelling lies at the heart of machine learning.

Data-driven models learned often struggle to generalize due to widespread subpopulation shifts, especially the presence of both spurious correlations and group imbalance (SC-GI).

Recent studies show that even advanced attacks cannot break such defenses effectively, since the purification process induces an extremely deep computational graph which poses the potential problem of vanishing/exploding gradient, high memory cost, and unbounded randomness.