Related papers: Drifting Fields are not Conservative
Many existing transductive bounds rely on classical complexity measures that are computationally intractable and often misaligned with empirical behavior. In this work, we establish new representation-based generalization bounds in a…
When using stochastic gradient descent to solve large-scale machine learning problems, a common practice of data processing is to shuffle the training data, partition the data across multiple machines if needed, and then perform several…
We compute the non-Gaussianity of the curvature perturbation generated by ekpyrotic collapse with multiple fields. The transition from the multi-field scaling solution to a single-field dominated regime converts initial isocurvature field…
Discriminative approaches to classification often learn shortcuts that hold in-distribution but fail even under minor distribution shift. This failure mode stems from an overreliance on features that are spuriously correlated with the…
Recent progress in compressing explicit radiance field representations, particularly 3D Gaussian Splatting, has substantially reduced memory consumption while improving real-time rendering performance. However, existing approaches remain…
Scalar QED is studied with higher order derivatives for the scalar field kinetic energy. A local potential is generated for the gauge field due to the covariant derivatives and the vacuum with non-vanishing expectation value for the scalar…
In this work, we investigate the margin-maximization bias exhibited by gradient-based algorithms in classifying linearly separable data. We present an in-depth analysis of the specific properties of the velocity field associated with…
The field of computer graphics was revolutionized by models such as Neural Radiance Fields and 3D Gaussian Splatting, displacing triangles as the dominant representation for photogrammetry. In this paper, we argue for a triangle comeback.…
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…
The key to generalization is controlling the complexity of the network. However, there is no obvious control of complexity -- such as an explicit regularization term -- in the training of deep networks for classification. We will show that…
Sampling from unnormalized densities is analogous to the generative modeling problem, but the target distribution is defined by a known energy function instead of data samples. Because evaluating the energy function is often costly, a…
A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…
We propose DrivingForward, a feed-forward Gaussian Splatting model that reconstructs driving scenes from flexible surround-view input. Driving scene images from vehicle-mounted cameras are typically sparse, with limited overlap, and the…
A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…
Neural Radiance Fields (NeRF) have achieved remarkable progress in neural rendering. Extracting geometry from NeRF typically relies on the Marching Cubes algorithm, which uses a hand-crafted threshold to define the level set. However, this…
We study a free scalar field $\phi$ in a fixed curved background spacetime subject to a higher derivative field equation of the form $F(\Box)\phi =0$, where $F$ is a polynomial of the form $F(\Box)= \prod_i (\Box-m_i^2)$ and all masses…
Data stream processing has become a landmark in modern machine learning applications, with concept drifts and novel class appearances posing the primary challenges faced by sophisticated recognition methods. This work proposes an…
Classical Gaussian processes and Kriging models are commonly based on stationary kernels, whereby correlations between observations depend exclusively on the relative distance between scattered data. While this assumption ensures analytical…
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…
We present a framework enabling variational data assimilation for gradient flows in general metric spaces, based on the minimizing movement (or Jordan-Kinderlehrer-Otto) approximation scheme. After discussing stability properties in the…