相关论文: Dream resolution and principalization I: enough de…
Often in the analysis of first-order methods, assuming the existence of a quadratic growth bound (a generalization of strong convexity) facilitates much stronger convergence analysis. Hence the analysis is done twice, once for the general…
We give an alternative construction of the Betti realization functor on the derived category of motives of complex algebraic varieties via the category of CW complexes instead of the category of complex analytic spaces. In particular we…
We introduce a multiplicative neural network architecture in which multiplicative interactions constitute the fundamental representation, rather than appearing as auxiliary components within an additive model. We establish a universal…
Consider a sequence of meromorphic functions $(f_n)_n$. This paper presents a technique that enables the transfer of convergence properties from $(f_n^{(m+1)}/f_n^{(m)})_n$ to subsequences of $(f_n^{(m)}/f_n^{(m-1)})_n$. As an application,…
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
By introducing the generalized master function of order up to four together with corresponding weight function, we have obtained all quasi-exactly solvable second order differential equations. It is shown that these differntial equations…
Reductions---rules that reduce input size while maintaining the ability to compute an optimal solution---are critical for developing efficient maximum independent set algorithms in both theory and practice. While several simple reductions…
The feasibility-seeking approach provides a systematic scheme to manage and solve complex constraints for continuous problems, and we explore it for the floorplanning problems with increasingly heterogeneous constraints. The classic…
We propose the complex-plane generalization of a powerful algebraic sequence acceleration algorithm, the Method of Weighted Averages (MWA), to guarantee exponential-cum-algebraic convergence of Fourier and Fourier-Hankel (F-H) integral…
Total Variation (TV) is a popular regularization strategy that promotes piece-wise constant signals by constraining the $\ell_1$-norm of the first order derivative of the estimated signal. The resulting optimization problem is usually…
The ability to decompose a signal in an orthonormal basis (a set of orthogonal components, each normalized to have unit length) using a fast numerical procedure rests at the heart of many signal processing methods and applications. The…
At present, the quantification methods of neural network models are mainly divided into post-training quantization (PTQ) and quantization aware training (QAT). Post-training quantization only need a small part of the data to complete the…
Normalization methods such as batch [Ioffe and Szegedy, 2015], weight [Salimansand Kingma, 2016], instance [Ulyanov et al., 2016], and layer normalization [Baet al., 2016] have been widely used in modern machine learning. Here, we study the…
Data augmentation is one of the most popular techniques for improving the robustness of neural networks. In addition to directly training the model with original samples and augmented samples, a torrent of methods regularizing the distance…
Affine quantization is a relatively new procedure, and it can solve many new problems. This essay reviews this new, and novel, procedure for particle problems, as well as those of fields and gravity. New quantization tools, which are…
The RNN transducer is a promising end-to-end model candidate. We compare the original training criterion with the full marginalization over all alignments, to the commonly used maximum approximation, which simplifies, improves and speeds up…
In this article we introduce generalized projective spaces (Definitions $[2.1, 2.5]$) and prove three main theorems in two different contexts. In the first context we prove, in main Theorem $A$, the surjectivity of the Chinese remainder…
We introduce a new definition of a generalized logarithmic module of multiarrangements by uniting those of the logarithmic derivation and the differential modules. This module is realized as a logarithmic derivation module of an arrangement…
This work introduces a Hamiltonian approach to regularization and linearization of central-force particle dynamics through a new canonical extension of the so-called "projective decomposition". The regularization scheme is formulated within…
Math Word Problems (MWP) is an important task that requires the ability of understanding and reasoning over mathematical text. Existing approaches mostly formalize it as a generation task by adopting Seq2Seq or Seq2Tree models to encode an…