We introduce Neural Conjugate Flows (NCF), a class of neural-network architectures equipped with exact flow structure. By leveraging topological conjugation, we prove that these networks are not only naturally isomorphic to a continuous group, but are also universal approximators for flows of ordinary differential equation (ODEs). Furthermore, topological properties of these flows can be enforced by the architecture in an interpretable manner. We demonstrate in numerical experiments how this topological group structure leads to concrete computational gains over other physics informed neural networks in estimating and extrapolating latent dynamics of ODEs, while training up to five times faster than other flow-based architectures.

Physics-Informed Neural Networks (PINNs) have emerged as a powerful frame- work for solving partial differential equations (PDEs). However, standard MLP- based PINNs often fail to converge when dealing with complex initial value problems, leading to solutions that violate causality and suffer from a spectral bias towards low-frequency components. To address these issues, we introduce NeuSA (Neuro-Spectral Architectures), a novel class of PINNs inspired by classi- cal spectral methods, designed to solve linear and nonlinear PDEs with variable coefficients. NeuSA learns a projection of the underlying PDE onto a spectral basis, leading to a finite-dimensional representation of the dynamics which is then integrated with an adapted Neural ODE (NODE). This allows us to overcome spectral bias, by leveraging the high-frequency components enabled by the spectral representation; to enforce causality, by inheriting the causal structure of NODEs, and to start training near the target solution, by means of an initialization scheme based on classical methods. We validate NeuSA on canonical benchmarks for lin- ear and nonlinear wave equations, demonstrating strong performance as compared to other architectures, with faster convergence, improved temporal consistency and superior predictive accuracy. Code and pretrained models are available in https://github.com/arthur-bizzi/neusa.

As datasets grow larger, matching and merging entries from different databases has become a costly task in modern data pipelines. To avoid expensive comparisons between entries, blocking similar items is a popular preprocessing step. In this paper, we introduce BlockBoost, a novel boosting-based method that generates compact binary hash codes for database entries, through which blocking can be performed efficiently. The algorithm is fast and scalable, resulting in computational costs that are orders of magnitude lower than current benchmarks. Unlike existing alternatives, BlockBoost comes with associated feature importance measures for interpretability, and possesses strong theoretical guarantees, including lower bounds on critical performance metrics like recall and reduction ratio. Finally, we show that BlockBoost delivers great empirical results, outperforming state-of-the-art blocking benchmarks in terms of both performance metrics and computational cost.

Recent developments in intra-prediction show the advantage of increasing the number of prediction directions. This trend can be observed in most previous standards, and should remain in the future. However, increasing the number of intra-prediction directions incurs a non-negligible side-information bit-rate. To reduce this side-information bit-rate, we propose a method to adaptively decide whether to use a larger or smaller set of candidate intra-prediction directions by simply evaluating the maximum gradient magnitude, theoretically motivated by the prediction inaccuracy model. In this scenario, we can achieve most of the gain from using the larger intra-prediction direction set while only requiring a small amount of side-information. This method yields a significant BD-rate reduction on multiple resolutions of images using fixed block-size when implemented in a simplified HEVC-based encoder.

Recent studies have shown that there may be a significant improvement in the compression of a signal when multiple-transforms are used to exploit local characteristics [1]. By choosing an appropriate transform from a set of transforms, we can have a significant encoding improvement. In this paper, our objective is to find which transform is optimal for each block of a given signal, and to determine how many coefficients we should allocate in each block, from an energy compaction perspective, as defined in [2]. Two algorithms were proposed in [2] to solve this problem. The first algorithm, called Algorithm A, is an iterative method, that converges to a locally optimal solution. The second algorithm, called Algorithm B, first considers an alternate metric based on rate distortion and uses convex optimization techniques.We propose two new methods to solve this problem [3]. The first method, called Algorithm C, uses thresholding to solve the rate-distortion optimization problem. We threshold the magnitude-squared of the transform coecients by the rate-distortion parameter for all transforms, and choose the best transform. The second method, called Algorithm D, uses dynamic programming to find the best transform and coefficient allocation for the current block based on that of all the previous blocks. This method solves the problem of finding the best transform and coecient allocation in terms of energy compaction. In comparing these methods, Algorithm A is the fastest, although only locally optimal. Algorithm C is faster than Algorithm B. Both Algorithm B and Algorithm C solve only the rate-distortion problem. Algorithm D solves the original energy compaction problem, but is the slowest among the four methods.