Kumar Muthuraman

Terence Lim, Kumar Muthuraman, Michael Sury

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.

Daniel Zantedeschi, Kumar Muthuraman

We develop a Fisher-geometric theory of stochastic gradient descent (SGD) in which mini-batch noise is an intrinsic, loss-induced matrix -- not an exogenous scalar variance. Under exchangeable sampling, the mini-batch gradient covariance is pinned down (to leading order) by the projected covariance of per-sample gradients: it equals projected Fisher information for well-specified likelihood losses and the projected Godambe (sandwich) matrix for general M-estimation losses. This identification forces a diffusion approximation with Fisher/Godambe-structured volatility (effective temperature tau = eta/b) and yields an Ornstein-Uhlenbeck linearization whose stationary covariance is given in closed form by a Fisher-Lyapunov equation. Building on this geometry, we prove matching minimax upper and lower bounds of order Theta(1/N) for Fisher/Godambe risk under a total oracle budget N; the lower bound holds under a martingale oracle condition (bounded predictable quadratic variation), strictly subsuming i.i.d. and exchangeable sampling. These results imply oracle-complexity guarantees for epsilon-stationarity in the Fisher dual norm that depend on an intrinsic effective dimension and a Fisher/Godambe condition number rather than ambient dimension or Euclidean conditioning. Experiments confirm the Lyapunov predictions and show that scalar temperature matching cannot reproduce directional noise structure.