Kumar Muthuraman | Searcharxiv

arXiv2026

QRAFTI: An Agentic Framework for Empirical Research in Quantitative Finance

We introduce a multi-agent framework intended to emulate parts of a quantitative research team and support equity factor research on large financial panel datasets. QRAFTI integrates a research toolkit for panel data with MCP servers that expose data access, factor construction, and custom coding operations as callable tools. It can help replicate established factors, formulate and test new signals, and generate standardized research reports accompanied by narrative analysis and computational traces. On multi-step empirical tasks, using chained tool calls and reflection-based planning may offer better performance and explainability than dynamic code generation alone.

cs.MA↗

arXiv2026

Mini-Batch Covariance, Diffusion Limits, and Oracle Complexity in Stochastic Gradient Descent: A Sampling-Design Perspective

Stochastic gradient descent (SGD) is central to simulation optimization, stochastic programming, and online M-estimation, where sampling effort is a decision variable. We study the mini-batch gradient noise as a sampling-design object. Under exchangeable fresh-sampling mini-batches, the conditional covariance given the de Finetti directing measure mu is b^{-1} G_mu(theta), and under identifiability the projected population object is b^{-1} G*(theta) -- projected Fisher information for correctly specified likelihoods, the sandwich partner of the Hessian otherwise. This identification fixes the noise matrix entering the diffusion analysis of constant-step SGD: the raw iterate path has a deterministic fluid limit, and the sqrt(b/eta)-scaled fluctuations satisfy a functional CLT with noise covariance G*; near a nondegenerate optimum the limit is Ornstein-Uhlenbeck, and its Lyapunov covariance scaled by eta/b matches the linearized discrete recursion at leading order. Under a curvature-noise compatibility condition mu_F > 0, we prove 1/N mean-square upper bounds and an i.i.d. parametric Fisher van Trees lower bound of the same rate order, with oracle-complexity guarantees depending on an effective dimension d_eff and condition number kappa_F. Numerical experiments verify the identification and confirm the Lyapunov predictions in direct SGD.

stat.ML↗