arXiv subjects

Akshat Kaushal

Publications and source records attributed to Akshat Kaushal.

3 recordsLinked to original sources

arXiv2026

A Mutual Information Lower Bound for Multimodal Regression Active Learning

Active learning for continuous regression has lacked an acquisition function that targets epistemic uncertainty when the predictive distribution is multimodal: variance misses modal disagreement, and information-theoretic targets like BALD are designed for discrete outputs. We introduce a Two-Index framework that makes this separation explicit: one stochastic index selects among competing model hypotheses (epistemic source), while a second governs within-hypothesis randomness (aleatoric source). An entropy decomposition within the framework identifies the mutual information between the output and the epistemic index as a principled acquisition objective, and we prove this quantity vanishes as the model is trained on growing datasets, confirming that it captures exactly the uncertainty data can resolve. Because this mutual information is intractable for continuous outputs, we derive the Mutual Information Lower Bound (MI-LB) acquisition function, a closed-form approximation for Mixture Density Network ensembles. On benchmarks featuring multimodal systems, MI-LB matches or beats every baseline evaluated and is the only method to do so consistently -- geometric and Fisher-based baselines compete only when the input space already encodes the multimodality, and collapse otherwise.

cs.LG↗

arXiv2026

Multimodal Scientific Learning Beyond Diffusions and Flows

Scientific machine learning (SciML) increasingly requires models that capture multimodal conditional uncertainty arising from ill-posed inverse problems, multistability, and chaotic dynamics. While recent work has favored highly expressive implicit generative models such as diffusion and flow-based methods, these approaches are often data-hungry, computationally costly, and misaligned with the structured solution spaces frequently found in scientific problems. We demonstrate that Mixture Density Networks (MDNs) provide a principled yet largely overlooked alternative for multimodal uncertainty quantification in SciML. As explicit parametric density estimators, MDNs impose an inductive bias tailored to low-dimensional, multimodal physics, enabling direct global allocation of probability mass across distinct solution branches. This structure delivers strong data efficiency, allowing reliable recovery of separated modes in regimes where scientific data is scarce. We formalize these insights through a unified probabilistic framework contrasting explicit and implicit distribution networks, and demonstrate empirically that MDNs achieve superior generalization, interpretability, and sample efficiency across a range of inverse, multistable, and chaotic scientific regression tasks.

cs.LG↗

arXiv2025

DAMM-LOAM: Degeneracy Aware Multi-Metric LiDAR Odometry and Mapping

LiDAR Simultaneous Localization and Mapping (SLAM) systems are essential for enabling precise navigation and environmental reconstruction across various applications. Although current point-to-plane ICP algorithms perform effec- tively in structured, feature-rich environments, they struggle in scenarios with sparse features, repetitive geometric structures, and high-frequency motion. This leads to degeneracy in 6- DOF pose estimation. Most state-of-the-art algorithms address these challenges by incorporating additional sensing modalities, but LiDAR-only solutions continue to face limitations under such conditions. To address these issues, we propose a novel Degeneracy-Aware Multi-Metric LiDAR Odometry and Map- ping (DAMM-LOAM) module. Our system improves mapping accuracy through point cloud classification based on surface normals and neighborhood analysis. Points are classified into ground, walls, roof, edges, and non-planar points, enabling accurate correspondences. A Degeneracy-based weighted least squares-based ICP algorithm is then applied for accurate odom- etry estimation. Additionally, a Scan Context based back-end is implemented to support robust loop closures. DAMM-LOAM demonstrates significant improvements in odometry accuracy, especially in indoor environments such as long corridors

cs.RO↗