Rahul D Ray

Rahul D Ray, Utkarsh Srivastava

Uncertainty quantification (UQ) is essential for deploying deep learning models in safety critical applications, yet no consensus exists on which UQ method performs best across different data modalities and distribution shifts. This paper presents a comprehensive benchmark of ten widely used UQ baselines including MC Dropout, SWAG, ensemble methods, temperature scaling, energy based OOD, Mahalanobis, hyperbolic classifiers, ENN, Taylor Sensus, and split conformal prediction against a simplified yet highly effective variant of VOLTA that retains only a deep encoder, learnable prototypes, cross entropy loss, and post hoc temperature scaling. We evaluate all methods on CIFAR 10 (in distribution), CIFAR 100, SVHN, uniform noise (out of distribution), CIFAR 10 C (corruptions), and Tiny ImageNet features (tabular). VOLTA achieves competitive or superior accuracy (up to 0.864 on CIFAR 10), significantly lower expected calibration error (0.010 vs. 0.044 to 0.102 for baselines), and strong OOD detection (AUROC 0.802). Statistical testing over three random seeds shows that VOLTA matches or outperforms most baselines, with ablation studies confirming the importance of adaptive temperature and deep encoders. Our results establish VOLTA as a lightweight, deterministic, and well calibrated alternative to more complex UQ approaches.

Rahul D Ray

Epistemic intelligence requires machine learning systems to recognise the limits of their own knowledge and act safely under uncertainty, especially when faced with unknown unknowns. Existing uncertainty quantification methods rely on a single signal such as confidence or density and fail to detect diverse structural anomalies. We introduce SPECTRE-G2, a multi-signal anomaly detector that combines eight complementary signals from a dual-backbone neural network. The architecture includes a spectral normalised Gaussianization encoder, a plain MLP preserving feature geometry, and an ensemble of five models. These produce density, geometry, uncertainty, discriminative, and causal signals. Each signal is normalised using validation statistics and calibrated with synthetic out-of-distribution data. An adaptive top-k fusion selects the most informative signals and averages their scores. Experiments on synthetic, Adult, CIFAR-10, and Gridworld datasets show strong performance across diverse anomaly types, outperforming multiple baselines on AUROC, AUPR, and FPR95. The model is stable across seeds and particularly effective for detecting new variables and confounders. SPECTRE-G2 provides a practical approach for detecting unknown unknowns in open-world settings.

Rahul D Ray

Conservation laws are fundamental to understanding dynamical systems, but discovering them from data remains challenging due to parameter variation, non-polynomial invariants, local minima, and false positives on chaotic systems. We introduce NGCG, a neural-symbolic pipeline that decouples dynamics learning from invariant discovery and systematically addresses these challenges. A multi-restart variance minimiser learns a near-constant latent representation; system-specific symbolic extraction (polynomial Lasso, log-basis Lasso, explicit PDE candidates, and PySR) yields closed-form expressions; a strict constancy gate and diversity filter eliminate spurious laws. On a benchmark of nine diverse systems including Hamiltonian and dissipative ODEs, chaos, and PDEs, NGCG achieves consistent discovery (DR=1.0, FDR=0.0, F1=1.0) on all four systems with true conservation laws, with constancy two to three orders of magnitude lower than the best baseline. It is the only method that succeeds on the Lotka--Volterra system, and it correctly outputs no law on all five systems without invariants. Extensive experiments demonstrate robustness to noise ($σ= 0.1$), sample efficiency (50--100 trajectories), insensitivity to hyperparameters, and runtime under one minute per system. A Pareto analysis shows that the method provides a range of candidate expressions, allowing users to trade complexity for constancy. NGCG achieves strong performance relative to prior methods for data-driven conservation-law discovery, combining high accuracy with interpretability.

Rahul D Ray

Deep learning models in quantitative finance often operate as black boxes, lacking interpretability and failing to incorporate fundamental economic principles such as no-arbitrage constraints. This paper introduces ARTEMIS (Arbitrage-free Representation Through Economic Models and Interpretable Symbolics), a novel neuro-symbolic framework combining a continuous-time Laplace Neural Operator encoder, a neural stochastic differential equation regularised by physics-informed losses, and a differentiable symbolic bottleneck that distils interpretable trading rules. The model enforces economic plausibility via two novel regularisation terms: a Feynman-Kac PDE residual penalising local no-arbitrage violations, and a market price of risk penalty bounding the instantaneous Sharpe ratio. We evaluate ARTEMIS against six strong baselines on four datasets: Jane Street, Optiver, Time-IMM, and DSLOB (a synthetic crash regime). Results demonstrate ARTEMIS achieves state-of-the-art directional accuracy, outperforming all baselines on DSLOB (64.96%) and Time-IMM (96.0%). A comprehensive ablation study confirms each component's contribution: removing the PDE loss reduces directional accuracy from 64.89% to 50.32%. Underperformance on Optiver is attributed to its long sequence length and volatility-focused target. By providing interpretable, economically grounded predictions, ARTEMIS bridges the gap between deep learning's power and the transparency demanded in quantitative finance.

Rahul D Ray

Physics-constrained data generation is essential for machine learning in scientific domains where real data are scarce; however, existing approaches often over-constrain models without identifying which physical components are necessary. We present a systematic ablation study of a physics-informed grating coupler spectrum generator that maps five geometric parameters to 100-point spectral responses. By selectively removing explicit energy conservation enforcement, Fabry-Perot oscillations, bandwidth variation, and noise, we uncover a physics constraint paradox: explicit energy conservation enforcement is mathematically redundant when the underlying equations are physically consistent, with constrained and unconstrained variants achieving identical conservation accuracy (mean error approximately 7 x 10^-9). In contrast, Fabry-Perot oscillations dominate threshold-based bandwidth variability, accounting for a 72 percent reduction in half-maximum bandwidth spread when removed (with bandwidth spread reduced from 132.3 nm to 37.4 nm). We further identify a subtle pitfall: standard noise-addition-plus-renormalization pipelines introduce 0.5 percent unphysical negative absorption values. The generator operates at 200 samples per second, enabling high-throughput data generation and remaining orders of magnitude faster than typical full-wave solvers reported in the literature. Finally, downstream machine learning evaluation reveals a clear physics-learnability trade-off: while central wavelength prediction remains unaffected, removing Fabry-Perot oscillations improves bandwidth prediction accuracy by 31.3 percent in R-squared and reduces RMSE by 73.8 percent. These findings provide actionable guidance for physics-informed dataset design and highlight machine learning performance as a diagnostic tool for assessing constraint relevance.

Rahul D Ray

The ability to detect out-of-distribution (OOD) inputs is fundamental to safe deployment of machine learning systems. Yet, current methods often rely on feature representations that are optimised solely for classification accuracy, neglecting the distinct requirements of epistemic uncertainty. We introduce GOEN (Geometry-Optimised Epistemic Network), a simple pipeline that combines multi-scale features, L2 normalisation, Mahalanobis distance, and a calibration head trained with real hard OOD examples. Through systematic ablation we uncover a counter-intuitive finding: CenterLoss, a popular regulariser for feature compactness, significantly degrades OOD detection performance, reducing average OOD AUROC from 0.9483 to 0.9366 despite improving classification accuracy. The best variant, GOEN-NoCenterLoss, achieves an average OOD AUROC of 0.9483, surpassing all baselines including deep ensembles (0.8827), KNN (0.8967), and ODIN (0.8870) on CIFAR-10 benchmarks, while maintaining competitive in-distribution accuracy. Our results challenge the prevailing assumption that better classification geometry automatically leads to better epistemic uncertainty. Instead, we show that overly tight feature clusters compress inter-class margins and distort the covariance structure needed for effective OOD detection. GOEN is efficient, training in under 20 minutes on a single GPU, and provides a practical blueprint for building AI systems that reliably recognise their own limitations.