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The bulk of computational approaches for modeling physical systems in materials science derive from either analytical (i.e. physics based) or data-driven (i.e. machine-learning based) origins. In order to combine the strengths of these two…
We define several differential graded operads, some of them being related to families of polytopes : simplices and permutohedra. We also obtain a presentation by generators and relations of the operad K on associahedra introduced in a…
In [arXiv:2109.13991], the author explained a relation between enhanced ind-sheaves and enhanced subanalytic sheaves. In this paper, we shall define C-constructability for enhanced subanalytic sheaves which was announced in…
Convolutional neural networks learns spatial features and are heavily interlinked within kernels. The SE module have broken the traditional route of neural networks passing the entire result to next layer. Instead SE only passes important…
While vector-based language representations from pretrained language models have set a new standard for many NLP tasks, there is not yet a complete accounting of their inner workings. In particular, it is not entirely clear what aspects of…
Energy-based learning algorithms are alternatives to backpropagation and are well-suited to distributed implementations in analog electronic devices. However, a rigorous theory of convergence is lacking. We make a first step in this…
In this study, we investigate learning rate adaption at different levels based on the hyper-gradient descent framework and propose a method that adaptively learns the optimizer parameters by combining multiple levels of learning rates with…
We exhibit a connection between two constructions of twisted modules for a general vertex operator algebra with respect to inner automorphisms. We also study pseudo-derivations, pseudo-endomorphisms, and twist deformations of ordinary…
We study the asymptotic behavior of the maximum degree in the preferential attachment model with a choice-based edge-step. We add vertex type to the model and prove, among others types of behavior, the effect of condensation on multiple…
The angular response of thin diffractive optical elements is highly correlated. For example, the angles of incidence and diffraction of a grating are locked through the grating momentum determined by the grating period. Other diffractive…
Anisotropic Porous Medium Equation (APME) is developed as an extension of the Porous Medium Equation (PME) for anisotropic porous media. A special analytical solution is derived for APME for time-independent diffusion. Anisotropic mesh…
Modeling long-range dependencies in sequential data is a crucial step in sequence learning. A recently developed model, the Structured State Space (S4), demonstrated significant effectiveness in modeling long-range sequences. However, It is…
We construct nontrivial L-equivalence between curves of genus one and degree five, and between elliptic surfaces of multisection index five. These results give the first examples of L-equivalence for curves (necessarily over…
We combine multi-task learning and semi-supervised learning by inducing a joint embedding space between disparate label spaces and learning transfer functions between label embeddings, enabling us to jointly leverage unlabelled data and…
The Fourier-Mukai transform is lifted to the derived category of sheaves with connection on abelian varieties. The case of flat connections (D-modules) is discussed in detail.
Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a tensor representation whose entries are predicted by models…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one. An interesting class of such multiplications is related to the affine Dynkin diagrams of A, D, E-type. In this paper we…
We revisit the results on admissible transformations between normal linear systems of second-order ordinary differential equations with an arbitrary number of dependent variables under several appropriate gauges of the arbitrary elements…
We develop some aspects of the homological algebra of persistence modules, in both the one-parameter and multi-parameter settings, considered as either sheaves or graded modules. The two theories are different. We consider the graded module…
We introduce layers to modal type theories, which subsequently enables type theories for pattern matching on code in meta-programming and clean and straightforward semantics.