arXiv subjects

Chandrajit Bajaj

Publications and source records attributed to Chandrajit Bajaj.

At least 19 recordsLinked to original sources

arXiv2026

QC-PHAST Search: Classical--Quantum Query Benchmarks for Finite-Pool Rare-Regime Discovery

Rare-regime discovery in parameterized dynamical systems is an active-search problem: find one verified parameter at which a scientifically defined qualitative threshold is crossed, even when acceptable candidates are rare, nonconvex, or fragmented. We introduce Quantum-Classical Phase-space and Stability-Threshold Search (QC-PHAST), an evidence-gated decision protocol and query-accounting framework for finite candidate libraries. A candidate induces a dynamical object, simulator-derived criticality score, and verified first-hit predicate. Scientific metadata and charged pilot evidence are used to assess whether equation-aware search, scalar-score active search, predicate-only search, or only a query-model comparison is admissible. The quantum row is the inherited Grover/Boyer--Brassard--Hoyer--Tapp (BBHT) unknown-$M$ marked-set query reference; it is not a new quantum-search theorem, materialized circuit, or hardware-speedup claim. The result is a regime map. Direct boundary constructions, geometry controls, online simulator loops, and learned-label accounting further identify when classical structure, false positives, calibration cost, or state preparation erases the query-model margin. QC-PHAST is therefore an auditable protocol for deciding when a finite-pool marked-set reference is informative and when classical or resource-aware search should dominate.

quant-ph↗

arXiv2026

Queryable LoRA: Instruction-Regularized Routing Over Shared Low-Rank Update Atoms

We present a data-adaptive method for parameter-efficient fine-tuning of large neural networks. Standard low-rank adaptation methods improve efficiency by restricting each layer update to a fixed low-rank form, but this static parameterization can be too rigid when the appropriate correction depends on the input and on the evolving depth-wise computation of the network. Our approach replaces a purely layer-local adapter with a shared queryable memory of low-rank update atoms. For each block of layers, the model forms a query from the current low-rank state and a running summary of previous blocks, uses this query to retrieve a content-dependent combination of shared update components via attention, and applies the resulting routed operator within the low-rank bottleneck. In this way, the method retains the efficiency and scalability of low-rank adaptation while allowing the effective update to vary across inputs and to share reusable structure across layers. The resulting architecture provides a principled middle ground between static LoRA-style updates and fully generated parameter updates: it remains compact and parameter-efficient while supporting dynamic, context-sensitive adaptation. Further, we incorporate instruction-regularization by augmenting routing logits with a language-induced prior over update atoms, thereby biasing the selection of low-rank transformations toward semantically relevant directions without generating unconstrained parameter updates. Experiments on noisy non-linear regression tasks and LLM fine-tuning suggest that this queryable update-memory formulation can improve final test performance and training stability compared to standard low-rank adaptation, while using a comparable number of trainable parameters.

cs.LG↗

arXiv2026

When Descent Is Too Stable: Event-Triggered Hamiltonian Learning to Optimize

Fixed-budget nonconvex optimization can fail not because local descent is unstable, but because it is too stable: after reaching a nearby stationary point, an optimizer may spend the remaining evaluations refining an uninformative local minimum. We formulate this failure mode as a control problem over optimizer dynamics, where the learner must decide when to descend, when to exploit a promising basin, and when stagnation should trigger movement elsewhere. We introduce SHAPE, a structured adaptive port-Hamiltonian task-family optimizer for event-triggered minima hunting under local information. Starting from gradient-descent dynamics, SHAPE lifts optimization to an augmented phase space $(q, p)$, where the primal state $q$ represents the candidate solution, the cotangent variable $p$ carries directional sensitivity, and a controller $u$ provides processed information from current gradient oracle. Within each stage, a learned Hamiltonian vector field induces structured local descent; across stages, a fixed event clock in the implementation updates ports and memory when local equilibria are detected, with stage-dependent horizons treated in the analysis as a direct generalization. This design preserves a passivity-compatible structure while allowing the same trained policy to use clean, stochastic, or estimated gradient inputs. Experiments on fixed-budget nonconvex optimization tasks show that SHAPE improves best-so-far performance compared with fixed-policy optimizers. These results suggest that adaptive Hamiltonian energy shaping provides a principled mechanism for balancing descent, exploration, and budget allocation in difficult optimization landscapes.

cs.LG↗

arXiv2026

Learning Material-Aware Hamiltonian Risk Fields for Safe Navigation

Risk-aware navigation should be selective: a policy should expose evasive degrees of freedom only when the local scene admits a lower-risk feasible maneuver, and suppress them when no safer alternative exists. We show that adding one context-energy term to a port-Hamiltonian navigation policy produces a learned force channel with exactly this falsifiable signature. When the local risk field contains a feasible lower-risk direction, the induced context force activates toward it; when the apparent escape is blocked or not yet available, a route-aware gate suppresses lateral force rather than hallucinating an unsafe maneuver. A CVaR tail-risk objective focuses gradient updates on rare but consequential risk transitions. We validate the selectivity signature across four settings. In the primary delayed-required-escape benchmark, route-aware CVaR reduces premature force activation from 0.950 to 0.180 versus DWA while raising success from 0.480 to 0.810 with zero replans. On real off-road terrain (RELLIS-3D), route-aware enrichment achieves correct activation rate 0.837 and false activation rate 0.114, compared to 0.378/0.752 for scalar risk gradients. On static semantic maps (DFC2018), enrichment reduces catastrophic failure from 0.60 to 0.10 and oscillation by 90.7% while preserving path efficiency. In highway traffic, collisions drop from 100% to 0% when a lane escape is feasible; when no escape exists, the policy suppresses the lateral maneuver. The selectivity property follows from the gradient structure of the context energy rather than from training-time tuning.

cs.LG↗

arXiv2026

PHAST: Port-Hamiltonian Architecture for Structured Temporal Dynamics Forecasting

Real physical systems are dissipative -- a pendulum slows, a circuit loses charge to heat -- and forecasting their dynamics from partial observations is a central challenge in scientific machine learning. We address the \emph{position-only} (q-only) problem: given only generalized positions~$q_t$ at discrete times (momenta~$p_t$ latent), learn a structured model that (a)~produces stable long-horizon forecasts and (b)~recovers physically meaningful parameters when sufficient structure is provided. The port-Hamiltonian framework makes the conservative-dissipative split explicit via $\dot{x}=(J-R)\nabla H(x)$, guaranteeing $dH/dt\le 0$ when $R\succeq 0$. We introduce \textbf{PHAST} (Port-Hamiltonian Architecture for Structured Temporal dynamics), which decomposes the Hamiltonian into potential~$V(q)$, mass~$M(q)$, and damping~$D(q)$ across three knowledge regimes (KNOWN, PARTIAL, UNKNOWN), uses efficient low-rank PSD/SPD parameterizations, and advances dynamics with Strang splitting. Across thirteen q-only benchmarks spanning mechanical, electrical, molecular, thermal, gravitational, and ecological systems, PHAST achieves the best long-horizon forecasting among competitive baselines and enables physically meaningful parameter recovery when the regime provides sufficient anchors. We show that identification is fundamentally ill-posed without such anchors (gauge freedom), motivating a two-axis evaluation that separates forecasting stability from identifiability.

cs.LG↗

arXiv2025

GRL-SNAM: Geometric Reinforcement Learning with Path Differential Hamiltonians for Simultaneous Navigation and Mapping in Unknown Environments

We present GRL-SNAM, a geometric reinforcement learning framework for Simultaneous Navigation and Mapping(SNAM) in unknown environments. A SNAM problem is challenging as it needs to design hierarchical or joint policies of multiple agents that control the movement of a real-life robot towards the goal in mapless environment, i.e. an environment where the map of the environment is not available apriori, and needs to be acquired through sensors. The sensors are invoked from the path learner, i.e. navigator, through active query responses to sensory agents, and along the motion path. GRL-SNAM differs from preemptive navigation algorithms and other reinforcement learning methods by relying exclusively on local sensory observations without constructing a global map. Our approach formulates path navigation and mapping as a dynamic shortest path search and discovery process using controlled Hamiltonian optimization: sensory inputs are translated into local energy landscapes that encode reachability, obstacle barriers, and deformation constraints, while policies for sensing, planning, and reconfiguration evolve stagewise via updating Hamiltonians. A reduced Hamiltonian serves as an adaptive score function, updating kinetic/potential terms, embedding barrier constraints, and continuously refining trajectories as new local information arrives. We evaluate GRL-SNAM on two different 2D navigation tasks. Comparing against local reactive baselines and global policy learning references under identical stagewise sensing constraints, it preserves clearance, generalizes to unseen layouts, and demonstrates that Geometric RL learning via updating Hamiltonians enables high-quality navigation through minimal exploration via local energy refinement rather than extensive global mapping. The code is publicly available on \href{https://github.com/CVC-Lab/GRL-SNAM}{Github}.

cs.LG↗

arXiv2025

Learning Generalized Hamiltonian Dynamics with Stability from Noisy Trajectory Data

We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and port-Hamiltonian systems might share the same initial total energy of a closed system, it is challenging for a single Hamiltonian network model to capture the distinctive and varying motion dynamics and physics of a phase space, from sampled observational phase space trajectories. To address this complicated Hamiltonian manifold learning challenge, we extend sparse symplectic, random Fourier Gaussian processes learning with predictive successive numerical estimations of the Hamiltonian landscape, using a generalized form of state and conjugate momentum Hamiltonian dynamics, appropriate to different classes of conservative, dissipative and port-Hamiltonian physical systems. In addition to the kernelized evidence lower bound (ELBO) loss for data fidelity, we incorporate stability and conservation constraints as additional hyper-parameter balanced loss terms to regularize the model's multi-gradients, enforcing physics correctness for improved prediction accuracy with bounded uncertainty.

cs.LG↗

arXiv2025

Self-Balancing, Memory Efficient, Dynamic Metric Space Data Maintenance, for Rapid Multi-Kernel Estimation

We present a dynamic self-balancing octree data structure that enables efficient neighborhood maintenance in evolving metric spaces, a key challenge in modern machine learning systems. Many learning and generative models operate as dynamical systems whose representations evolve during training, requiring fast, adaptive spatial organization. Our two-parameter octree supports logarithmic-time updates and queries, eliminating the need for costly full rebuilds as data distributions shift. We demonstrate its effectiveness in four areas: (1) accelerating Stein variational gradient descent by supporting more particles with lower overhead; (2) enabling real-time, incremental KNN classification with logarithmic complexity; (3) facilitating efficient, dynamic indexing and retrieval for retrieval-augmented generation; and (4) improving sample efficiency by jointly optimizing input and latent spaces. Across all applications, our approach yields exponential speedups while preserving accuracy, particularly in high-dimensional spaces where maintaining adaptive spatial structure is critical.

cs.LG↗

arXiv2025

Scalable Robust Bayesian Co-Clustering with Compositional ELBOs

Co-clustering exploits the duality of instances and features to simultaneously uncover meaningful groups in both dimensions, often outperforming traditional clustering in high-dimensional or sparse data settings. Although recent deep learning approaches successfully integrate feature learning and cluster assignment, they remain susceptible to noise and can suffer from posterior collapse within standard autoencoders. In this paper, we present the first fully variational Co-clustering framework that directly learns row and column clusters in the latent space, leveraging a doubly reparameterized ELBO to improve gradient signal-to-noise separation. Our unsupervised model integrates a Variational Deep Embedding with a Gaussian Mixture Model (GMM) prior for both instances and features, providing a built-in clustering mechanism that naturally aligns latent modes with row and column clusters. Furthermore, our regularized end-to-end noise learning Compositional ELBO architecture jointly reconstructs the data while regularizing against noise through the KL divergence, thus gracefully handling corrupted or missing inputs in a single training pipeline. To counteract posterior collapse, we introduce a scale modification that increases the encoder's latent means only in the reconstruction pathway, preserving richer latent representations without inflating the KL term. Finally, a mutual information-based cross-loss ensures coherent co-clustering of rows and columns. Empirical results on diverse real-world datasets from multiple modalities, numerical, textual, and image-based, demonstrate that our method not only preserves the advantages of prior Co-clustering approaches but also exceeds them in accuracy and robustness, particularly in high-dimensional or noisy settings.

cs.LG↗

arXiv2024

Low-cost Robust Night-time Aerial Material Segmentation through Hyperspectral Data and Sparse Spatio-Temporal Learning

Material segmentation is a complex task, particularly when dealing with aerial data in poor lighting and atmospheric conditions. To address this, hyperspectral data from specialized cameras can be very useful in addition to RGB images. However, due to hardware constraints, high spectral data often come with lower spatial resolution. Additionally, incorporating such data into a learning-based segmentation framework is challenging due to the numerous data channels involved. To overcome these difficulties, we propose an innovative Siamese framework that uses time series-based compression to effectively and scalably integrate the additional spectral data into the segmentation task. We demonstrate our model's effectiveness through competitive benchmarks on aerial datasets in various environmental conditions.

cs.CV↗

arXiv2024

4DRecons: 4D Neural Implicit Deformable Objects Reconstruction from a single RGB-D Camera with Geometrical and Topological Regularizations

This paper presents a novel approach 4DRecons that takes a single camera RGB-D sequence of a dynamic subject as input and outputs a complete textured deforming 3D model over time. 4DRecons encodes the output as a 4D neural implicit surface and presents an optimization procedure that combines a data term and two regularization terms. The data term fits the 4D implicit surface to the input partial observations. We address fundamental challenges in fitting a complete implicit surface to partial observations. The first regularization term enforces that the deformation among adjacent frames is as rigid as possible (ARAP). To this end, we introduce a novel approach to compute correspondences between adjacent textured implicit surfaces, which are used to define the ARAP regularization term. The second regularization term enforces that the topology of the underlying object remains fixed over time. This regularization is critical for avoiding self-intersections that are typical in implicit-based reconstructions. We have evaluated the performance of 4DRecons on a variety of datasets. Experimental results show that 4DRecons can handle large deformations and complex inter-part interactions and outperform state-of-the-art approaches considerably.

cs.CV↗

arXiv2024

Physics-informed neural networks via stochastic Hamiltonian dynamics learning

In this paper, we propose novel learning frameworks to tackle optimal control problems by applying the Pontryagin maximum principle and then solving for a Hamiltonian dynamical system. Applying the Pontryagin maximum principle to the original optimal control problem shifts the learning focus to reduced Hamiltonian dynamics and corresponding adjoint variables. Then, the reduced Hamiltonian networks can be learned by going backwards in time and then minimizing loss function deduced from the Pontryagin maximum principle's conditions. The learning process is further improved by progressively learning a posterior distribution of the reduced Hamiltonians. This is achieved through utilizing a variational autoencoder which leads to more effective path exploration process. We apply our learning frameworks called NeuralPMP to various control tasks and obtain competitive results.

math.OC↗

arXiv2024

A Differential and Pointwise Control Approach to Reinforcement Learning

Reinforcement learning (RL) in continuous state-action spaces remains challenging in scientific computing due to poor sample efficiency and lack of pathwise physical consistency. We introduce Differential Reinforcement Learning (Differential RL), a novel framework that reformulates RL from a continuous-time control perspective via a differential dual formulation. This induces a Hamiltonian structure that embeds physics priors and ensures consistent trajectories without requiring explicit constraints. To implement Differential RL, we develop Differential Policy Optimization (dfPO), a pointwise, stage-wise algorithm that refines local movement operators along the trajectory for improved sample efficiency and dynamic alignment. We establish pointwise convergence guarantees, a property not available in standard RL, and derive a competitive theoretical regret bound of $\mathcal{O}(K^{5/6})$. Empirically, dfPO outperforms standard RL baselines on representative scientific computing tasks, including surface modeling, grid control, and molecular dynamics, under low-data and physics-constrained conditions.

cs.LG↗

arXiv2024

GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models

This paper introduces GenCorres, a novel unsupervised joint shape matching (JSM) approach. Our key idea is to learn a mesh generator to fit an unorganized deformable shape collection while constraining deformations between adjacent synthetic shapes to preserve geometric structures such as local rigidity and local conformality. GenCorres presents three appealing advantages over existing JSM techniques. First, GenCorres performs JSM among a synthetic shape collection whose size is much bigger than the input shapes and fully leverages the datadriven power of JSM. Second, GenCorres unifies consistent shape matching and pairwise matching (i.e., by enforcing deformation priors between adjacent synthetic shapes). Third, the generator provides a concise encoding of consistent shape correspondences. However, learning a mesh generator from an unorganized shape collection is challenging, requiring a good initialization. GenCorres addresses this issue by learning an implicit generator from the input shapes, which provides intermediate shapes between two arbitrary shapes. We introduce a novel approach for computing correspondences between adjacent implicit surfaces, which we use to regularize the implicit generator. Synthetic shapes of the implicit generator then guide initial fittings (i.e., via template-based deformation) for learning the mesh generator. Experimental results show that GenCorres considerably outperforms state-of-the-art JSM techniques. The synthetic shapes of GenCorres also achieve salient performance gains against state-of-the-art deformable shape generators.

cs.CV↗

arXiv2024

Sample Efficient Learning of Factored Embeddings of Tensor Fields

Data tensors of orders 2 and greater are now routinely being generated. These data collections are increasingly huge and growing. Many scientific and medical data tensors are tensor fields (e.g., images, videos, geographic data) in which the spatial neighborhood contains important information. Directly accessing such large data tensor collections for information has become increasingly prohibitive. We learn approximate full-rank and compact tensor sketches with decompositive representations providing compact space, time and spectral embeddings of tensor fields. All information querying and post-processing on the original tensor field can now be achieved more efficiently and with customizable accuracy as they are performed on these compact factored sketches in latent generative space. We produce optimal rank-r sketchy Tucker decomposition of arbitrary order data tensors by building compact factor matrices from a sample-efficient sub-sampling of tensor slices. Our sample efficient policy is learned via an adaptable stochastic Thompson sampling using Dirichlet distributions with conjugate priors.

cs.LG↗

arXiv2024

Motion Code: Robust Time Series Classification and Forecasting via Sparse Variational Multi-Stochastic Processes Learning

Despite extensive research, time series classification and forecasting on noisy data remain highly challenging. The main difficulties lie in finding suitable mathematical concepts to describe time series and effectively separate noise from the true signals. Unlike traditional methods treating time series as static vectors or fixed sequences, we propose a novel framework that views each time series, regardless of length, as a realization of a continuous-time stochastic process. This mathematical approach captures dependencies across timestamps and detects hidden, time-varying signals within the noise. However, real-world data often involves multiple distinct dynamics, making it insufficient to model the entire process with a single stochastic model. To address this, we assign each dynamic a unique signature vector and introduce the concept of "most informative timestamps" to infer a sparse approximation of the individual dynamics from these vectors. The resulting model, called Motion Code, includes parameters that fully capture diverse underlying dynamics in an integrated manner, enabling simultaneous classification and forecasting of time series. Extensive experiments on noisy datasets, including real-world Parkinson's disease sensor tracking, demonstrate Motion Code's strong performance against established benchmarks for time series classification and forecasting.

cs.LG↗

arXiv2023

DeblurSR: Event-Based Motion Deblurring Under the Spiking Representation

We present DeblurSR, a novel motion deblurring approach that converts a blurry image into a sharp video. DeblurSR utilizes event data to compensate for motion ambiguities and exploits the spiking representation to parameterize the sharp output video as a mapping from time to intensity. Our key contribution, the Spiking Representation (SR), is inspired by the neuromorphic principles determining how biological neurons communicate with each other in living organisms. We discuss why the spikes can represent sharp edges and how the spiking parameters are interpreted from the neuromorphic perspective. DeblurSR has higher output quality and requires fewer computing resources than state-of-the-art event-based motion deblurring methods. We additionally show that our approach easily extends to video super-resolution when combined with recent advances in implicit neural representation. The implementation and animated visualization of DeblurSR are available at https://github.com/chensong1995/DeblurSR.

cs.CV↗

arXiv2023

Deep Contrastive Patch-Based Subspace Learning for Camera Image Signal Processing

Camera Image Signal Processing (ISP) pipelines can get appealing results in different image signal processing tasks. Nonetheless, the majority of these methods, including those employing an encoder-decoder deep architecture for the task, typically utilize a uniform filter applied consistently across the entire image. However, it is natural to view a camera image as heterogeneous, as the color intensity and the artificial noise are distributed vastly differently, even across the two-dimensional domain of a single image. Varied Moire ringing, motion blur, color-bleaching, or lens-based projection distortions can all potentially lead to a heterogeneous image artifact filtering problem. In this paper, we present a specific patch-based, local subspace deep neural network that improves Camera ISP to be robust to heterogeneous artifacts (especially image denoising). We call our three-fold deep-trained model the Patch Subspace Learning Autoencoder (PSL-AE). The PSL-AE model does not make assumptions regarding uniform levels of image distortion. Instead, it first encodes patches extracted from noisy a nd clean image pairs, with different artifact types or distortion levels, by contrastive learning. Then, the patches of each image are encoded into corresponding soft clusters within their suitable latent sub-space, utilizing a prior mixture model. Furthermore, the decoders undergo training in an unsupervised manner, specifically trained for the image patches present in each cluster. The experiments highlight the adaptability and efficacy through enhanced heterogeneous filtering, both from synthesized artifacts but also realistic SIDD image pairs.

eess.IV↗