arXiv subjects

Ishan Joshi

Publications and source records attributed to Ishan Joshi.

6 recordsLinked to original sources

arXiv2026

A Recurrence Based Summation Method for Ultra-Rapid Divergent Series and Renormalon Type Expansions

Classical summation methods are often organized around particular growth regimes. Standard Borel summation is suited to Gevrey-1 series, while higher-order Gevrey behavior is commonly handled by changing the kernel, for instance through Mittag-Leffler summation. In this paper, we introduce a recurrence-based summation method, called C-summation, whose primary input is a first-order inhomogeneous recurrence. The recurrence does not determine a unique solution, since different solutions may differ by a homogeneous term. We remove this ambiguity by passing to a normalized tail, where the homogeneous ambiguity becomes an additive constant, and then extracting the finite part of that tail. The resulting finite-part selector is defined through a Bromwich transform on the normalized tail differences. We prove that, under a precise $M$-admissibility hypothesis, the resulting value is independent of the chosen solution of the recurrence and of the chosen admissible recurrence presentation of the same formal series. We also show that C-summation is regular and homogeneous, and that it is stable under an explicit shift-compatibility condition on the normalized tail. In a certain Borel-summable class, we prove agreement with Borel-Laplace summation.

math.CA↗

arXiv2026

PolyKV: A Shared Asymmetrically-Compressed KV Cache Pool for Multi-Agent LLM Inference

We present PolyKV, a system in which multiple concurrent inference agents share a single, asymmetrically compressed KV cache pool. Rather than allocating a separate KV cache per agent -- the standard paradigm -- PolyKV writes a compressed cache once and injects it into N independent agent contexts via HuggingFace DynamicCache objects. Compression is asymmetric: Keys are quantized at int8 (q8_0) to preserve softmax stability, while Values are compressed using TurboQuant MSE -- a Fast Walsh-Hadamard Transform (FWHT) rotation followed by 3-bit Lloyd-Max quantization with centroids tuned to N(0,1). We evaluate across two model scales (SmolLM2-1.7B-Instruct and Llama-3-8B-Instruct), three context lengths (600-7,194 tokens), and up to 15 concurrent agents. PolyKV achieves a stable 2.91x compression ratio across all configurations. On Llama-3-8B with 15 agents sharing a 4K-token context, PolyKV reduces KV cache memory from 19.8 GB to 0.45 GB -- a 97.7% reduction -- while maintaining only +0.57% perplexity degradation and a mean BERTScore F1 of 0.928. PPL delta does not grow with agent count and improves as context length increases, inverting to -0.26% at 1,851 coherent tokens. To our knowledge, no prior work combines a single shared, lossy-compressed KV pool with multi-reader concurrent agent access.

cs.LG↗

arXiv2025

On Some Continued Fractions and Divergent Series Arising From Integral Families

In this paper we present a method to derive Eulerian continued fractions arising from a sequence of integrals. As examples, through a new derivation, we reproduce classical continued fraction expansions for the natural logarithm, the Riemann zeta function $\zeta(s)$, and polylogarithms, while also obtaining several new identities. Finally, we apply the method to construct a divergent continued fraction, which provides a natural assignment of the Euler Mascheroni constant $\gamma$ as the sum of a particular divergent series through a new summation method which we propose.

math.NT↗

arXiv2025

Think Inside the JSON: Reinforcement Strategy for Strict LLM Schema Adherence

In this paper, we address the challenge of enforcing strict schema adherence in large language model (LLM) generation by leveraging LLM reasoning capabilities. Building on the DeepSeek R1 reinforcement learning framework, our approach trains structured reasoning skills of a 1.5B parameter model through a novel pipeline that combines synthetic reasoning dataset construction with custom reward functions under Group Relative Policy Optimization (GRPO). Specifically, we first perform R1 reinforcement learning on a 20K sample unstructured-to-structured dataset, mirroring the original DeepSeek R1 methods, to establish core reasoning abilities. Subsequently, we performed supervised fine-tuning on a separate 10K reasoning sample dataset, focusing on refining schema adherence for downstream tasks. Despite the relatively modest training scope, requiring approximately 20 hours on an 8xH100 GPU cluster for GRPO training and 3 hours on 1xA100 for SFT, our model demonstrates robust performance in enforcing schema consistency. We compare our ThinkJSON approach against the original DeepSeek R1 (671B), distilled versions of DeepSeek R1 (Qwen-1.5B and Qwen-7B), and Gemini 2.0 Flash (70B), showcasing its effectiveness in real-world applications. Our results underscore the practical utility of a resource-efficient framework for schema-constrained text generation.

cs.CL↗

arXiv2024

PromptSet: A Programmer's Prompting Dataset

The rise of capabilities expressed by large language models has been quickly followed by the integration of the same complex systems into application level logic. Algorithms, programs, systems, and companies are built around structured prompting to black box models where the majority of the design and implementation lies in capturing and quantifying the `agent mode'. The standard way to shape a closed language model is to prime it for a specific task with a tailored prompt, often initially handwritten by a human. The textual prompts co-evolve with the codebase, taking shape over the course of project life as artifacts which must be reviewed and maintained, just as the traditional code files might be. Unlike traditional code, we find that prompts do not receive effective static testing and linting to prevent runtime issues. In this work, we present a novel dataset called PromptSet, with more than 61,000 unique developer prompts used in open source Python programs. We perform analysis on this dataset and introduce the notion of a static linter for prompts. Released with this publication is a HuggingFace dataset and a Github repository to recreate collection and processing efforts, both under the name \texttt{pisterlabs/promptset}.

cs.SE↗

arXiv2019

Systematic Analysis of Image Generation using GANs

Generative Adversarial Networks have been crucial in the developments made in unsupervised learning in recent times. Exemplars of image synthesis from text or other images, these networks have shown remarkable improvements over conventional methods in terms of performance. Trained on the adversarial training philosophy, these networks aim to estimate the potential distribution from the real data and then use this as input to generate the synthetic data. Based on this fundamental principle, several frameworks can be generated that are paragon implementations in several real-life applications such as art synthesis, generation of high resolution outputs and synthesis of images from human drawn sketches, to name a few. While theoretically GANs present better results and prove to be an improvement over conventional methods in many factors, the implementation of these frameworks for dedicated applications remains a challenge. This study explores and presents a taxonomy of these frameworks and their use in various image to image synthesis and text to image synthesis applications. The basic GANs, as well as a variety of different niche frameworks, are critically analyzed. The advantages of GANs for image generation over conventional methods as well their disadvantages amongst other frameworks are presented. The future applications of GANs in industries such as healthcare, art and entertainment are also discussed.

cs.LG↗