arXiv subjects

Kashif Khan

Publications and source records attributed to Kashif Khan.

4 recordsLinked to original sources

arXiv2026

Congruence modules and Wiles defects of determinantal rings of maximal minors

Let $O$ be a discrete valuation ring and $A := O[X_{m \times n}]/I_{m}(X)$ the determinantal ring of maximal minors. We consider algebra maps $\lambda \colon A \to O$, which is tantamount to choosing rank-deficient matrices $a \in O^{m \times n}$. Following Iyengar--Khare--Manning, we compute the congruence module and the Wiles defect of $A$ at $\lambda$, expressing them in terms of the $(m - 1)$-sized minors of $a$.

math.AC↗

arXiv2020

Adversarial Learning on the Latent Space for Diverse Dialog Generation

Generating relevant responses in a dialog is challenging, and requires not only proper modeling of context in the conversation but also being able to generate fluent sentences during inference. In this paper, we propose a two-step framework based on generative adversarial nets for generating conditioned responses. Our model first learns a meaningful representation of sentences by autoencoding and then learns to map an input query to the response representation, which is in turn decoded as a response sentence. Both quantitative and qualitative evaluations show that our model generates more fluent, relevant, and diverse responses than existing state-of-the-art methods.

cs.CL↗

arXiv2019

Constructing Hard Examples for Graph Isomorphism

We describe a method for generating graphs that provide difficult examples for practical Graph Isomorphism testers. We first give the theoretical construction, showing that we can have a family of graphs without any non-trivial automorphisms which also have high Weisfeiler-Leman dimension. The construction is based on properties of random 3XOR-formulas. We describe how to convert such a formula into a graph which has the desired properties with high probability. We validate the method by an experimental implementation. We construct random formulas and validate them with a SAT solver to filter through suitable ones, and then convert them into graphs. Experimental results demonstrate that the resulting graphs do provide hard examples that match the hardest known benchmarks for graph isomorphism.

cs.CC↗

arXiv2014

Techniques and tools for measuring energy efficiency of scientific software applications

The scale of scientific High Performance Computing (HPC) and High Throughput Computing (HTC) has increased significantly in recent years, and is becoming sensitive to total energy use and cost. Energy-efficiency has thus become an important concern in scientific fields such as High Energy Physics (HEP). There has been a growing interest in utilizing alternate architectures, such as low power ARM processors, to replace traditional Intel x86 architectures. Nevertheless, even though such solutions have been successfully used in mobile applications with low I/O and memory demands, it is unclear if they are suitable and more energy-efficient in the scientific computing environment. Furthermore, there is a lack of tools and experience to derive and compare power consumption between the architectures for various workloads, and eventually to support software optimizations for energy efficiency. To that end, we have performed several physical and software-based measurements of workloads from HEP applications running on ARM and Intel architectures, and compare their power consumption and performance. We leverage several profiling tools (both in hardware and software) to extract different characteristics of the power use. We report the results of these measurements and the experience gained in developing a set of measurement techniques and profiling tools to accurately assess the power consumption for scientific workloads.

cs.DC↗