Related papers: Smooth Integer Encoding via Integral Balance
Quantum embedding is an appealing route to fragment a large interacting quantum system into several smaller auxiliary `cluster' problems to exploit the locality of the correlated physics. In this work we critically review approaches to…
We encode/decode Prolog terms as unique natural numbers. Our encodings have the following properties: a) are bijective b) natural numbers always decode to syntactically valid terms c) they work in low polynomial time in the bitsize of the…
We present a new procedure to infer size bounds for integer programs automatically. Size bounds are important for the deduction of bounds on the runtime complexity or in general, for the resource analysis of programs. We show that our…
Several methods for solving efficiently the one-dimensional deconvolution problem are proposed. The problem is to solve the Volterra equation ${\mathbf k} u:=\int_0^t k(t-s)u(s)ds=g(t),\quad 0\leq t\leq T$. The data, $g(t)$, are noisy. Of…
We present a novel approach for super-resolution that utilizes implicit neural representation (INR) to effectively reconstruct and enhance low-resolution videos and images. By leveraging the capacity of neural networks to implicitly encode…
We propose symmetric power transformation to enhance the capacity of Implicit Neural Representation~(INR) from the perspective of data transformation. Unlike prior work utilizing random permutation or index rearrangement, our method…
We mainly study numerical integration of real valued functions defined on the $d$-dimensional unit cube with all partial derivatives up to some finite order $r\ge1$ bounded by one. It is well known that optimal algorithms that use $n$…
$O(N)$ invariants are the observables of real tensor models. We use regular colored graphs to represent these invariants, the valence of the vertices of the graphs relates to the tensor rank. We enumerate $O(N)$ invariants as $d$-regular…
Implicit Neural Representations (INRs) have revolutionized signal representation by leveraging neural networks to provide continuous and smooth representations of complex data. However, existing INRs face limitations in capturing…
We introduce algorithms for robustly computing intrinsic coordinates on point clouds. Our approach relies on generating many candidate coordinates by subsampling the data and varying hyperparameters of the embedding algorithm (e.g.,…
Quantized Indexing is a fast and space-efficient form of enumerative (combinatorial) coding, the strongest among asymptotically optimal universal entropy coding algorithms. The present advance in enumerative coding is similar to that made…
In this paper, we present an approach to integer factorization using distributed representations formed with Vector Symbolic Architectures. The approach formulates integer factorization in a manner such that it can be solved using neural…
We discuss a path toward the generalisation of the nested soft-collinear subtraction scheme to arbitrary $2\rightarrow n$ processes. The scheme is designed to provide an efficient and process-independent procedure to extract and regulate…
We give exact formulae for a wide family of complexity measures that capture the organization of hidden nonlinear processes. The spectral decomposition of operator-valued functions leads to closed-form expressions involving the full…
Discrete gradient methods are a class of numerical integrators producing solutions with exact preservation of first integrals of ordinary differential equations. In this paper, we apply order theory combined with the symmetrized Itoh--Abe…
An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…
Implicit Neural Representations (INRs) are increasingly recognized as a versatile data modality for representing discretized signals, offering benefits such as infinite query resolution and reduced storage requirements. Existing signal…
We introduce a new approach for designing numerical schemes for stochastic differential equations (SDEs). The approach, which we have called direction and norm decomposition method, proposes to approximate the required solution $X_t$ by…
Central to rough path theory is the signature transform of a path, an infinite series of tensors given by the iterated integrals of the underlying path. The signature poses an effective way to capture sequentially ordered information,…
The integral image, an intermediate image representation, has found extensive use in multi-scale local feature detection algorithms, such as Speeded-Up Robust Features (SURF), allowing fast computation of rectangular features at constant…