arXiv subjects

Utkarsh Gupta

Publications and source records attributed to Utkarsh Gupta.

15 recordsLinked to original sources

arXiv2026

Spinverse: Differentiable Physics for Permeability-Aware Microstructure Reconstruction from Diffusion MRI

Diffusion MRI (dMRI) is sensitive to microstructural barriers, yet most existing methods either assume impermeable boundaries or estimate voxel-level parameters without recovering explicit interfaces. We present Spinverse, a permeability-aware reconstruction method that inverts dMRI measurements through a fully differentiable Bloch-Torrey simulator. Spinverse represents tissue on a fixed tetrahedral grid and treats each interior face permeability as a learnable parameter; low-permeability faces act as diffusion barriers, so microstructural boundaries whose topology is not fixed a priori (up to the resolution of the ambient mesh) emerge without changing mesh connectivity or vertex positions. Given a target signal, we optimize face permeabilities by backpropagating a signal-matching loss through the PDE forward model, and recover an interface by thresholding the learned permeability field. To mitigate the ill-posedness of permeability inversion, we use mesh-based geometric priors; to avoid local minima, we use a staged multi-sequence optimization curriculum. Across a collection of synthetic voxel meshes, Spinverse reconstructs diverse geometries and demonstrates that sequence scheduling and regularization are critical to avoid outline-only solutions while improving both boundary accuracy and structural validity.

cs.CV↗

arXiv2025

Improved Bounds on Diffsequences with Gaps in Powers of 2

Let $D$ be a set of positive integers. A $D$-diffsequence of length $k$ is a sequence of positive integers $a_1 < \cdots < a_k$ such that $a_{i+1}-a_i\in D$ for $i=1,\ldots,k-1$. For $D=\{2^i\mid i\in \mathbb{Z}_{\ge 0}\}$, it is known that there exists a minimum integer $n$, denoted by $\Delta(D,k)$, such that every $2$-coloring of $\{1,\ldots n \}$ admits a monochromatic $D$-diffsequence of length $k$. In this work, we prove a new lower bound for $\Delta(D,k)$ to $\Delta(D,k)\ge \left(\sqrt{\frac{8k-5}{12}}-\frac12\right)2^{\left(\sqrt{\frac{8k-5}{3}}-3\right)}$, asymptotically improving the exponential constant in the bound proved by Clifton.

math.CO↗

arXiv2025

A Malliavin calculus approach to score functions in diffusion generative models

Score-based diffusion generative models have recently emerged as a powerful tool for modelling complex data distributions. These models aim at learning the score function, which defines a map from a known probability distribution to the target data distribution via deterministic or stochastic differential equations (SDEs). The score function is typically estimated from data using a variety of approximation techniques, such as denoising or sliced score matching, Hyv\"arien's method, or Schr\"odinger bridges. In this paper, we derive an exact, closed-form, expression for the score function for a broad class of nonlinear diffusion generative models. Our approach combines modern stochastic analysis tools such as Malliavin derivatives and their adjoint operators (Skorokhod integrals or Malliavin Divergence) with a new Bismut-type formula. The resulting expression for the score function can be written entirely in terms of the first and second variation processes, with all Malliavin derivatives systematically eliminated, thereby enhancing its practical applicability. The theoretical framework presented in this work offers a principled foundation for advancing score estimation methods in generative modelling, enabling the design of new sampling algorithms for complex probability distributions. Our results can be extended to broader classes of stochastic differential equations, opening new directions for the development of score-based diffusion generative models.

stat.ML↗

arXiv2025

Malliavin Calculus for Score-based Diffusion Models

We introduce a new framework based on Malliavin calculus to derive exact analytical expressions for the score function $\nabla \log p_t(x)$, i.e., the gradient of the log-density associated with the solution to stochastic differential equations (SDEs). Our approach combines classical integration-by-parts techniques with modern stochastic analysis tools, such as Bismut's formula and Malliavin calculus, and it works for both linear and nonlinear SDEs. In doing so, we establish a rigorous connection between the Malliavin derivative, its adjoint, the Malliavin divergence (Skorokhod integral), and diffusion generative models, thereby providing a systematic method for computing $\nabla \log p_t(x)$. In the linear case, we present a detailed analysis showing that our formula coincides with the analytical score function derived from the solution of the Fokker--Planck equation. For nonlinear SDEs with state-independent diffusion coefficients, we derive a closed-form expression for $\nabla \log p_t(x)$. We evaluate the proposed framework across multiple generative tasks and find that its performance is comparable to state-of-the-art methods. These results can be generalised to broader classes of SDEs, paving the way for new score-based diffusion generative models.

cs.LG↗

arXiv2025

ReMiDi: Reconstruction of Microstructure Using a Differentiable Diffusion MRI Simulator

We propose ReMiDi, a novel method for inferring neuronal microstructure as arbitrary 3D meshes using a differentiable diffusion Magnetic Resonance Imaging (dMRI) simulator. We first implemented in PyTorch a differentiable dMRI simulator that simulates the forward diffusion process using a finite-element method on an input 3D microstructure mesh. To achieve significantly faster simulations, we solve the differential equation semi-analytically using a matrix formalism approach. Given a reference dMRI signal $S_{ref}$, we use the differentiable simulator to iteratively update the input mesh such that it matches $S_{ref}$ using gradient-based learning. Since directly optimizing the 3D coordinates of the vertices is challenging, particularly due to ill-posedness of the inverse problem, we instead optimize a lower-dimensional latent space representation of the mesh. The mesh is first encoded into spectral coefficients, which are further encoded into a latent $\textbf{z}$ using an auto-encoder, and are then decoded back into the true mesh. We present an end-to-end differentiable pipeline that simulates signals that can be tuned to match a reference signal by iteratively updating the latent representation $\textbf{z}$. We demonstrate the ability to reconstruct microstructures of arbitrary shapes represented by finite-element meshes, with a focus on axonal geometries found in the brain white matter, including bending, fanning and beading fibers. Our source code is available online.

eess.IV↗

arXiv2024

Bounds on the Statistical Leakage-Resilience of Shamir's Secret Sharing

Secret sharing is an instrumental tool for sharing secret keys in distributed systems. In a classical threshold setting, this involves a dealer who has a secret/key, a set of parties/users to which shares of the secret are sent, and a threshold on the number of users whose presence is needed in order to recover the secret. In secret sharing, secure links with no leakage are often assumed between the involved parties. However, when the users are nodes in a communication network and all the links are physical links, e.g., wireless, such assumptions are not valid anymore. In order to study this critical problem, we propose a statistical leakage model of secret sharing, where some noisy versions of all the secret shares might be independently leaked to an adversary. We then study the resilience of the seminal Shamir's secret sharing scheme with statistical leakage, and bound certain measures of security (i.e., semantic security, mutual information security), given other parameters of the system including the amount of leakage from each secret share. We show that for an extreme scenario of Shamir's scheme, in particular when the underlying field characteristic is $2$, the security of each bit of the secret against leakage improves exponentially with the number of users. To the best of our knowledge, this is the first attempt towards understanding secret sharing under general statistical noisy leakage.

cs.IT↗

arXiv2024

BMapEst: Estimation of Brain Tissue Probability Maps using a Differentiable MRI Simulator

Reconstructing digital brain phantoms in the form of voxel-based, multi-channeled tissue probability maps for individual subjects is essential for capturing brain anatomical variability, understanding neurological diseases, as well as for testing image processing methods. We demonstrate the first framework that estimates brain tissue probability maps (Grey Matter - GM, White Matter - WM, and Cerebrospinal fluid - CSF) with the help of a Physics-based differentiable MRI simulator that models the magnetization signal at each voxel in the volume. Given an observed $T_1$/$T_2$-weighted MRI scan, the corresponding clinical MRI sequence, and the MRI differentiable simulator, we estimate the simulator's input probability maps by back-propagating the L2 loss between the simulator's output and the $T_1$/$T_2$-weighted scan. This approach has the significant advantage of not relying on any training data and instead uses the strong inductive bias of the MRI simulator. We tested the model on 20 scans from the BrainWeb database and demonstrated a highly accurate reconstruction of GM, WM, and CSF. Our source code is available online: https://github.com/BioMedAI-UCSC/BMapEst.

cs.CV↗

arXiv2024

GaSpCT: Gaussian Splatting for Novel CT Projection View Synthesis

We present GaSpCT, a novel view synthesis and 3D scene representation method used to generate novel projection views for Computer Tomography (CT) scans. We adapt the Gaussian Splatting framework to enable novel view synthesis in CT based on limited sets of 2D image projections and without the need for Structure from Motion (SfM) methodologies. Therefore, we reduce the total scanning duration and the amount of radiation dose the patient receives during the scan. We adapted the loss function to our use-case by encouraging a stronger background and foreground distinction using two sparsity promoting regularizers: a beta loss and a total variation (TV) loss. Finally, we initialize the Gaussian locations across the 3D space using a uniform prior distribution of where the brain's positioning would be expected to be within the field of view. We evaluate the performance of our model using brain CT scans from the Parkinson's Progression Markers Initiative (PPMI) dataset and demonstrate that the rendered novel views closely match the original projection views of the simulated scan, and have better performance than other implicit 3D scene representations methodologies. Furthermore, we empirically observe reduced training time compared to neural network based image synthesis for sparse-view CT image reconstruction. Finally, the memory requirements of the Gaussian Splatting representations are reduced by 17% compared to the equivalent voxel grid image representations.

eess.IV↗

arXiv2024

ScripTONES: Sentiment-Conditioned Music Generation for Movie Scripts

Film scores are considered an essential part of the film cinematic experience, but the process of film score generation is often expensive and infeasible for small-scale creators. Automating the process of film score composition would provide useful starting points for music in small projects. In this paper, we propose a two-stage pipeline for generating music from a movie script. The first phase is the Sentiment Analysis phase where the sentiment of a scene from the film script is encoded into the valence-arousal continuous space. The second phase is the Conditional Music Generation phase which takes as input the valence-arousal vector and conditionally generates piano MIDI music to match the sentiment. We study the efficacy of various music generation architectures by performing a qualitative user survey and propose methods to improve sentiment-conditioning in VAE architectures.

cs.MM↗

arXiv2023

Modified LAB Algorithm with Clustering-based Search Space Reduction Method for solving Engineering Design Problems

A modified LAB algorithm is introduced in this paper. It builds upon the original LAB algorithm (Reddy et al. 2023), which is a socio-inspired algorithm that models competitive and learning behaviours within a group, establishing hierarchical roles. The proposed algorithm incorporates the roulette wheel approach and a reduction factor introducing inter-group competition and iteratively narrowing down the sample space. The algorithm is validated by solving the benchmark test problems from CEC 2005 and CEC 2017. The solutions are validated using standard statistical tests such as two-sided and pairwise signed rank Wilcoxon test and Friedman rank test. The algorithm exhibited improved and superior robustness as well as search space exploration capabilities. Furthermore, a Clustering-Based Search Space Reduction (C-SSR) method is proposed, making the algorithm capable to solve constrained problems. The C-SSR method enables the algorithm to identify clusters of feasible regions, satisfying the constraints and contributing to achieve the optimal solution. This method demonstrates its effectiveness as a potential alternative to traditional constraint handling techniques. The results obtained using the Modified LAB algorithm are then compared with those achieved by other recent metaheuristic algorithms.

cs.LG↗

arXiv2022

A New Algebraic Approach for String Reconstruction from Substring Compositions

We consider the problem of binary string reconstruction from the multiset of its substring compositions, i.e., referred to as the substring composition multiset, first introduced and studied by Acharya et al. We introduce a new algorithm for the problem of string reconstruction from its substring composition multiset which relies on the algebraic properties of the equivalent bivariate polynomial formulation of the problem. We then characterize specific algebraic conditions for the binary string to be reconstructed that guarantee the algorithm does not require any backtracking through the reconstruction, and, consequently, the time complexity is bounded polynomially. More specifically, in the case of no backtracking, our algorithm has a time complexity of $O(n^2)$ compared to the algorithm by Acharya et al., which has a time complexity of $O(n^2\log(n))$, where $n$ is the length of the binary string. Furthermore, it is shown that larger sets of binary strings are uniquely reconstructable by the new algorithm and without the need for backtracking leading to codebooks of reconstruction codes that are larger, by a linear factor in size, compared to the previously known construction by Pattabiraman et al., while having $O(n^2)$ reconstruction complexity.

cs.IT↗

arXiv2020

Worst-Case Optimal Covering of Rectangles by Disks

We provide the solution for a fundamental problem of geometric optimization by giving a complete characterization of worst-case optimal disk coverings of rectangles: For any $\lambda\geq 1$, the critical covering area $A^*(\lambda)$ is the minimum value for which any set of disks with total area at least $A^*(\lambda)$ can cover a rectangle of dimensions $\lambda\times 1$. We show that there is a threshold value $\lambda_2 = \sqrt{\sqrt{7}/2 - 1/4} \approx 1.035797\ldots$, such that for $\lambda<\lambda_2$ the critical covering area $A^*(\lambda)$ is $A^*(\lambda)=3\pi\left(\frac{\lambda^2}{16} +\frac{5}{32} + \frac{9}{256\lambda^2}\right)$, and for $\lambda\geq \lambda_2$, the critical area is $A^*(\lambda)=\pi(\lambda^2+2)/4$; these values are tight. For the special case $\lambda=1$, i.e., for covering a unit square, the critical covering area is $\frac{195\pi}{256}\approx 2.39301\ldots$. The proof uses a careful combination of manual and automatic analysis, demonstrating the power of the employed interval arithmetic technique.

cs.CG↗

arXiv2019

LEAF-QA: Locate, Encode & Attend for Figure Question Answering

We introduce LEAF-QA, a comprehensive dataset of $250,000$ densely annotated figures/charts, constructed from real-world open data sources, along with ~2 million question-answer (QA) pairs querying the structure and semantics of these charts. LEAF-QA highlights the problem of multimodal QA, which is notably different from conventional visual QA (VQA), and has recently gained interest in the community. Furthermore, LEAF-QA is significantly more complex than previous attempts at chart QA, viz. FigureQA and DVQA, which present only limited variations in chart data. LEAF-QA being constructed from real-world sources, requires a novel architecture to enable question answering. To this end, LEAF-Net, a deep architecture involving chart element localization, question and answer encoding in terms of chart elements, and an attention network is proposed. Different experiments are conducted to demonstrate the challenges of QA on LEAF-QA. The proposed architecture, LEAF-Net also considerably advances the current state-of-the-art on FigureQA and DVQA.

cs.CV↗

arXiv2019

Continuous Reachability for Unordered Data Petri nets is in PTime

Unordered data Petri nets (UDPN) are an extension of classical Petri nets with tokens that carry data from an infinite domain and where transitions may check equality and disequality of tokens. UDPN are well-structured, so the coverability and termination problems are decidable, but with higher complexity than for Petri nets. On the other hand, the problem of reachability for UDPN is surprisingly complex, and its decidability status remains open. In this paper, we consider the continuous reachability problem for UDPN, which can be seen as an over-approximation of the reachability problem. Our main result is a characterization of continuous reachability for UDPN and polynomial time algorithm for solving it. This is a consequence of a combinatorial argument, which shows that if continuous reachability holds then there exists a run using only polynomially many data values.

cs.FL↗

arXiv2018

Document Chunking and Learning Objective Generation for Instruction Design

Instructional Systems Design is the practice of creating of instructional experiences that make the acquisition of knowledge and skill more efficient, effective, and appealing. Specifically in designing courses, an hour of training material can require between 30 to 500 hours of effort in sourcing and organizing reference data for use in just the preparation of course material. In this paper, we present the first system of its kind that helps reduce the effort associated with sourcing reference material and course creation. We present algorithms for document chunking and automatic generation of learning objectives from content, creating descriptive content metadata to improve content-discoverability. Unlike existing methods, the learning objectives generated by our system incorporate pedagogically motivated Bloom's verbs. We demonstrate the usefulness of our methods using real world data from the banking industry and through a live deployment at a large pharmaceutical company.

cs.CL↗