Deep neural networks trained with gradient descent exhibit varying rates of learning for different patterns. However, the complexity of fitting models to data makes direct elucidation of the dynamics of learned patterns challenging. To circumvent this, many works have opted to characterize phases of learning through summary statistics known as order parameters. In this work, we propose a unifying framework for constructing order parameters based on the Neural Tangent Kernel (NTK), in which the relationship with the data set is more transparent. In particular, we derive a local approximation of the NTK for a class of deep regression models (SIRENs) trained to reconstruct natural images. In so doing, we analytically connect three seemingly distinct phase transitions: the emergence of wave patterns in residuals (a novel observation), loss rate collapse, and NTK alignment. Our results provide a dynamical perspective on the observed biases of SIRENs, and deep image regression models more generally.

In this work, we demonstrate that these two seemingly orthogonal concepts are remarkably well-suited for each other.

Detecting out-of-distribution (OOD) objects is indispensable for safely deploying object detectors in the wild. Although distance-based OOD detection methods have demonstrated promise in image classification, they remain largely unexplored in object-level OOD detection. This paper bridges the gap by proposing a distance-based framework for detecting OOD objects, which relies on the model-agnostic representation space and provides strong generality across different neural architectures. Our proposed framework SIREN contributes two novel components: (1) a representation learning component that uses a trainable loss function to shape the representations into a mixture of von Mises-Fisher (vMF) distributions on the unit hypersphere, and (2) a test-time OOD detection score leveraging the learned vMF distributions in a parametric or non-parametric way. SIREN achieves competitive performance on both the recent detection transformers and CNN-based models, improving the AUROC by a large margin compared to the previous best method.

Implicitly defined, continuous, differentiable signal representations parameterized by neural networks have emerged as a powerful paradigm, offering many possible benefits over conventional representations. However, current network architectures for such implicit neural representations are incapable of modeling signals with fine detail, and fail to represent a signal's spatial and temporal derivatives, despite the fact that these are essential to many physical signals defined implicitly as the solution to partial differential equations. We propose to leverage periodic activation functions for implicit neural representations and demonstrate that these networks, dubbed sinusoidal representation networks or SIRENs, are ideally suited for representing complex natural signals and their derivatives. We analyze SIREN activation statistics to propose a principled initialization scheme and demonstrate the representation of images, wavefields, video, sound, and their derivatives. Further, we show how SIRENs can be leveraged to solve challenging boundary value problems, such as particular Eikonal equations (yielding signed distance functions), the Poisson equation, and the Helmholtz and wave equations. Lastly, we combine SIRENs with hypernetworks to learn priors over the space of SIREN functions.