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Large language models (LLMs) show impressive performance in solving complex language tasks. However, its large number of parameters presents significant challenges for the deployment. So, compressing LLMs to low bits can enable to deploy on…
A class of highest weight irreducible representations of the quantum algebra U_h(gl_\infty) is constructed. Within each module a basis is introduced and the transformation relations of the basis under the action of the Chevalley generators…
Finitely generated Z-modules have canonical decompositions. When such modules are given in a finitely presented form there is a classical algorithm for computing a canonical decomposition. This is the algorithm for computing the Smith…
Let $U_q(\hat{\cal G})$ denote the quantized affine Lie algebra and $U_q({\cal G}^{(1)})$ the quantized {\em nontwisted} affine Lie algebra. Let ${\cal O}_{\rm fin}$ be the category defined in section 3. We show that when the deformation…
A majority of numerical scientific computation relies heavily on handling and manipulating matrices, such as solving linear equations, finding eigenvalues and eigenvectors, and so on. Many quantum algorithms have been developed to advance…
We develop a crystal base theory for the general linear Lie superalgebra $gl(m,n)$. We prove that any irreducible $U_q(gl(m,n))$-module in some category has a crystal base, and prove that its associated crystal base is parameterized by…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
Research in uncertainty quantification (UQ) for large language models (LLMs) is increasingly important towards guaranteeing the reliability of this groundbreaking technology. We explore the integration of LLM UQ methods in argumentative…
We shall derive Kazhdan-Lusztig type character formula for the irreducible modules with arbitrary non-critical highest weights over affine Lie algebras from the rational case by using the translation functor, the Enright functor and…
Logistic regression (LR) is an important machine learning model for classification, with wide applications in text classification, image analysis and medicine diagnosis, etc. However, training LR generally entails an iterative gradient…
Computing a basis for the exponent lattice of algebraic numbers is a basic problem in the field of computational number theory with applications to many other areas. The main cost of a well-known algorithm…
The rapid scaling of Large Language Models (LLMs) elevates inference costs and compounds substantial deployment barriers. While quantization to 8 or 4 bits mitigates this, sub-3-bit methods face severe accuracy, scalability, and efficiency…
We present a necessary and sufficient condition for a finite-dimensional highest weight representation of the $sl_2$ loop algebra to be irreducible. In particular, for a highest weight representation with degenerate parameters of the…
We present ongoing work on a new automatic code generation approach for supporting quantized generative inference on LLMs such as LLaMA or OPT on off-the-shelf CPUs. Our approach is informed by the target architecture and a performance…
For any root system corresponding to a semisimple simply-laced Lie algebra a logarithmic CFT is constructed. Characters of irreducible representations were calculated in terms of theta functions.
The method of differential equations has been proven to be a powerful tool for the computation of multi-loop Feynman integrals appearing in quantum field theory. It has been observed that in many instances a canonical basis can be chosen,…
A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as…
We give an efficient algorithm for Lang's Theorem in split connected reductive groups defined over finite fields of characteristic greater than 3. This algorithm can be used to construct many important structures in finite groups of Lie…
We give a new interpretation of representation theory of the finite-dimensional half-integer weight modules over the queer Lie superalgebra $\mathfrak{q}(n)$. It is given in terms of Brundan's work of finite-dimensional integer weight…
Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…