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Source author record

Rahul Garg

Rahul Garg appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
math.CAComputer Visionmath.FAmath.APArtificial IntelligenceMachine LearningLogic in Computer Sciencemath.NTmath.RT

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Published work

12 published item(s)

preprint2026arXiv

MathConstraint: Automated Generation of Verified Combinatorial Reasoning Instances for LLMs

We introduce MathConstraint, a hard, adaptive benchmark for evaluating the combinatorial reasoning capabilities of LLMs. We combine constraint satisfaction problems with rigorous solver-based verification and design an adaptive generator to create instances that remain challenging as the LLMs improve in their reasoning capabilities. Unlike existing benchmarks that quickly saturate on fixed datasets or use LLM-as-a-judge for checking solutions,MathConstraint uses parameterized problem types that enable scalable generation of arbitrarily difficult and automatically verifiable instances. We release MathConstraint-Easy ($266$ instances), on which frontier models achieve between $72.6\%$ (gemini-3.1-flash-lite) and $87.6\%$ (gpt-5.5) accuracy, and MathConstraint ($329$ instances) on which the same models drop to between $18.5\%$ (claude-4.6-sonnet) and $66.9\%$ (gpt-5.5) accuracy, demonstrating the resilience of our benchmark generator against rapid progress in LLM reasoning capabilities. We evaluate 12 frontier and open-weight models with and without access to a sandboxed Python environment that includes generic SAT/SMT solvers. Tool access roughly doubles frontier accuracy on MathConstraint (mean $+28$pp; up to $+52$pp for claude-4.6-sonnet). Further, halving the tool-call budget from $8$ to $4$ rounds erases up to $37$ points -- a sensitivity that most single-budget benchmarks miss. We release the generator, dataset, and evaluation harness as a robust environment for studying combinatorial reasoning and tool-use behavior under adversarially-tunable difficulty.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A View Independent Classification Framework for Yoga Postures

Yoga is a globally acclaimed and widely recommended practice for a healthy living. Maintaining correct posture while performing a Yogasana is of utmost importance. In this work, we employ transfer learning from Human Pose Estimation models for extracting 136 key-points spread all over the body to train a Random Forest classifier which is used for estimation of the Yogasanas. The results are evaluated on an in-house collected extensive yoga video database of 51 subjects recorded from 4 different camera angles. We propose a 3 step scheme for evaluating the generalizability of a Yoga classifier by testing it on 1) unseen frames, 2) unseen subjects, and 3) unseen camera angles. We argue that for most of the applications, validation accuracies on unseen subjects and unseen camera angles would be most important. We empirically analyze over three public datasets, the advantage of transfer learning and the possibilities of target leakage. We further demonstrate that the classification accuracies critically depend on the cross validation method employed and can often be misleading. To promote further research, we have made key-points dataset and code publicly available.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Zoom-to-Inpaint: Image Inpainting with High-Frequency Details

Although deep learning has enabled a huge leap forward in image inpainting, current methods are often unable to synthesize realistic high-frequency details. In this paper, we propose applying super-resolution to coarsely reconstructed outputs, refining them at high resolution, and then downscaling the output to the original resolution. By introducing high-resolution images to the refinement network, our framework is able to reconstruct finer details that are usually smoothed out due to spectral bias - the tendency of neural networks to reconstruct low frequencies better than high frequencies. To assist training the refinement network on large upscaled holes, we propose a progressive learning technique in which the size of the missing regions increases as training progresses. Our zoom-in, refine and zoom-out strategy, combined with high-resolution supervision and progressive learning, constitutes a framework-agnostic approach for enhancing high-frequency details that can be applied to any CNN-based inpainting method. We provide qualitative and quantitative evaluations along with an ablation analysis to show the effectiveness of our approach. This seemingly simple, yet powerful approach, outperforms state-of-the-art inpainting methods. Our code is available in https://github.com/google/zoom-to-inpaint

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Du$^2$Net: Learning Depth Estimation from Dual-Cameras and Dual-Pixels

Computational stereo has reached a high level of accuracy, but degrades in the presence of occlusions, repeated textures, and correspondence errors along edges. We present a novel approach based on neural networks for depth estimation that combines stereo from dual cameras with stereo from a dual-pixel sensor, which is increasingly common on consumer cameras. Our network uses a novel architecture to fuse these two sources of information and can overcome the above-mentioned limitations of pure binocular stereo matching. Our method provides a dense depth map with sharp edges, which is crucial for computational photography applications like synthetic shallow-depth-of-field or 3D Photos. Additionally, we avoid the inherent ambiguity due to the aperture problem in stereo cameras by designing the stereo baseline to be orthogonal to the dual-pixel baseline. We present experiments and comparisons with state-of-the-art approaches to show that our method offers a substantial improvement over previous works.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Learning to Autofocus

Autofocus is an important task for digital cameras, yet current approaches often exhibit poor performance. We propose a learning-based approach to this problem, and provide a realistic dataset of sufficient size for effective learning. Our dataset is labeled with per-pixel depths obtained from multi-view stereo, following "Learning single camera depth estimation using dual-pixels". Using this dataset, we apply modern deep classification models and an ordinal regression loss to obtain an efficient learning-based autofocus technique. We demonstrate that our approach provides a significant improvement compared with previous learned and non-learned methods: our model reduces the mean absolute error by a factor of 3.6 over the best comparable baseline algorithm. Our dataset and code are publicly available.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Localisation of Spectral Sums corresponding to the sub-Laplacian on the Heisenberg Group

In this article we study localisation of spectral sums $\{S_R\}_{R > 0}$ associated to the sub-Laplacian $\mathcal{L}$ on the Heisenberg Group $\mathbb{H}^d$ where $S_R f := \int_0^R dE_{λ}f$, with $\mathcal{L} = \int_0^{\infty} λ\, dE_λ$ being the spectral resolution of $\mathcal{L}.$ We prove that for any compactly supported function $f \in L^2(\mathbb{H}^d)$, and for any $γ< \frac{1}{2}$, $R^γ S_R f \to 0$ as $ R \to \infty$, almost everywhere off $supp (f)$.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

On the role of Riesz potentials in Poisson's equation and Sobolev embeddings

In this paper, we study the mapping properties of the classical Riesz potentials acting on $L^p$-spaces. In the supercritical exponent, we obtain new "almost" Lipschitz continuity estimates for these and related potentials (including, for instance, the logarithmic potential). Applications of these continuity estimates include the deduction of new regularity estimates for distributional solutions to Poisson's equation, as well as a proof of the supercritical Sobolev embedding theorem first shown by Brezis and Wainger in 1980.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

The lattice point counting problem on the Heisenberg groups

We consider the radial and Heisenberg-homogeneous norms on the Heisenberg groups given by $N_{α,A}((z,t)) = \left(|z|^α+ A |t|^{α/2}\right)^{1/α}$, for $α\ge 2$ and $A>0$. This natural family includes the canonical Cygan-Korányi norm, corresponding to $α=4$. We study the lattice points counting problem on the Heisenberg groups, namely establish an error estimate for the number of points that the lattice of integral points has in a ball of large radius $R$. The exponent we establish for the error in the case $α=2$ is the best possible, in all dimensions.

0 citations0 reviewsNo code linkedOpen access
preprint2012arXiv

Variations on a theorem of Beurling

We consider functions satisfying the subcritical Beurling's condition, viz., $$\int_{\R^n}\int_{\R^n} |f(x)| |\hat{f}(y)| e^{a |x \cdot y|} \, dx \, dy < \infty$$ for some $ 0 < a < 1.$ We show that such functions are entire vectors for the Schrödinger representations of the Heisenberg group. If an eigenfunction $f$ of the Fourier transform satisfies the above condition we show that the Hermite coefficients of $f$ have certain exponential decay which depends on $a$.

0 citations0 reviewsNo code linkedOpen access