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.

Proper initialisation strategy is of primary importance to mitigate gradient explosion or vanishing when training neural networks. Yet, the impact of initialisation parameters still lacks a precise theoretical understanding for several well-established architectures. Here, we propose a new initialisation for networks with sinusoidal activation functions such as \texttt{SIREN}, focusing on gradients control, their scaling with network depth, their impact on training and on generalization. To achieve this, we identify a closed-form expression for the initialisation of the parameters, differing from the original \texttt{SIREN} scheme. This expression is derived from fixed points obtained through the convergence of pre-activation distribution and the variance of Jacobian sequences. Controlling both gradients and targeting vanishing pre-activation helps preventing the emergence of inappropriate frequencies during estimation, thereby improving generalization. We further show that this initialisation strongly influences training dynamics through the Neural Tangent Kernel framework (NTK). Finally, we benchmark \texttt{SIREN} with the proposed initialisation against the original scheme and other baselines on function fitting and image reconstruction. The new initialisation consistently outperforms state-of-the-art methods across a wide range of reconstruction tasks, including those involving physics-informed neural networks.