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Illinois Mathematics and Science Academy

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Research library9linked papers
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Selected work

Representative Papers

Tunneling-Augmented Simulated Annealing for Short-Block LDPC Code Construction

Apr 01, 2026

This work addresses the challenge of constructing low-density parity-check (LDPC) codes at short block lengths, where asymptotic design methods fail due to finite-length effects and structural constraints of the underlying Tanner graph. The problem is formulated as a constrained binary combinatorial optimization task. To tackle it, the authors propose a novel global search strategy based on tunneling-enhanced simulated annealing (TASA), combined with local refinement and penalty mechanisms targeting short cycles and harmful trapping set substructures to effectively manage multiple design constraints. Simulation results over the AWGN channel for code lengths ranging from 64 to 128 demonstrate that the constructed codes achieve an average coding gain of 0.45 dB over randomly generated LDPC codes and perform within 0.6 dB of progressive-edge-growth (PEG) codes, thereby overcoming limitations inherent in conventional greedy algorithms.

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Bayesian Monocular Depth Refinement via Neural Radiance Fields

Jan 07, 2026arXiv.org

Monocular depth estimation often suffers from over-smoothing, leading to a loss of geometric detail that limits scene understanding accuracy. This work proposes MDENeRF, a novel framework that, for the first time, incorporates uncertainty modeling from NeRF volume rendering into monocular depth refinement. By employing a Bayesian fusion strategy, the method iteratively integrates monocular priors with depth information derived from NeRF trained under multi-view perturbations, thereby preserving global structural consistency while recovering high-frequency geometric details. Evaluated on the SUN RGB-D indoor dataset, MDENeRF significantly improves depth estimation accuracy, producing depth maps with more accurate structures and richer fine-grained geometry.

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Multi-Agent Pose Uncertainty: A Differentiable Rendering Cramér-Rao Bound

Oct 18, 2025

To address the lack of rigorous uncertainty quantification in visual and robotic pose estimation, this paper introduces the first differentiable-rendering-based framework for pose uncertainty quantification. Our method linearizes the rendering process via small perturbations on the pose manifold, enabling derivation of a rendering-aware Cramér–Rao lower bound (CRLB)—the first systematic integration of differentiable rendering into CRLB theory. The resulting closed-form lower bound on camera pose covariance aligns with classical bundle adjustment uncertainty estimates. The framework natively supports multi-camera systems, enabling Fisher information fusion without keypoint correspondence—facilitating cooperative perception and novel-view synthesis. Its core innovation lies in the deep coupling of geometry-aware differentiable rendering with statistical lower-bound theory, providing interpretable and verifiable uncertainty guarantees for learning-based dense pose estimation.

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Data Cartography for Detecting Memorization Hotspots and Guiding Data Interventions in Generative Models

Aug 27, 2025

Generative models are prone to overfitting and memorizing rare training samples, leading to privacy leakage and inflated benchmark performance. Method: We propose a data-centric memorization analysis framework that—novelty—integrates sample difficulty (early-training loss) and forgetting event frequency to define a memorization score, enabling a four-quadrant classification scheme to identify memorization hotspots; we theoretically prove that the memorization score’s lower bound and uniform stability jointly bound the generalization gap, and accordingly design dynamic data reweighting and pruning strategies. Contribution/Results: Removing only 10% of training data reduces synthetic watermark extraction success rate by over 40% while increasing perplexity by less than 0.5, substantially mitigating information leakage with negligible degradation in generation quality. Our core innovation lies in an interpretable, theoretically grounded, data-level intervention paradigm.

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Recent publications

Latest Papers

Tunneling-Augmented Simulated Annealing for Short-Block LDPC Code Construction

Apr 01, 2026

This work addresses the challenge of constructing low-density parity-check (LDPC) codes at short block lengths, where asymptotic design methods fail due to finite-length effects and structural constraints of the underlying Tanner graph. The problem is formulated as a constrained binary combinatorial optimization task. To tackle it, the authors propose a novel global search strategy based on tunneling-enhanced simulated annealing (TASA), combined with local refinement and penalty mechanisms targeting short cycles and harmful trapping set substructures to effectively manage multiple design constraints. Simulation results over the AWGN channel for code lengths ranging from 64 to 128 demonstrate that the constructed codes achieve an average coding gain of 0.45 dB over randomly generated LDPC codes and perform within 0.6 dB of progressive-edge-growth (PEG) codes, thereby overcoming limitations inherent in conventional greedy algorithms.

0 citationsRead paper

Bayesian Monocular Depth Refinement via Neural Radiance Fields

Jan 07, 2026arXiv.org

Monocular depth estimation often suffers from over-smoothing, leading to a loss of geometric detail that limits scene understanding accuracy. This work proposes MDENeRF, a novel framework that, for the first time, incorporates uncertainty modeling from NeRF volume rendering into monocular depth refinement. By employing a Bayesian fusion strategy, the method iteratively integrates monocular priors with depth information derived from NeRF trained under multi-view perturbations, thereby preserving global structural consistency while recovering high-frequency geometric details. Evaluated on the SUN RGB-D indoor dataset, MDENeRF significantly improves depth estimation accuracy, producing depth maps with more accurate structures and richer fine-grained geometry.

0 citationsRead paper

Multi-Agent Pose Uncertainty: A Differentiable Rendering Cramér-Rao Bound

Oct 18, 2025

To address the lack of rigorous uncertainty quantification in visual and robotic pose estimation, this paper introduces the first differentiable-rendering-based framework for pose uncertainty quantification. Our method linearizes the rendering process via small perturbations on the pose manifold, enabling derivation of a rendering-aware Cramér–Rao lower bound (CRLB)—the first systematic integration of differentiable rendering into CRLB theory. The resulting closed-form lower bound on camera pose covariance aligns with classical bundle adjustment uncertainty estimates. The framework natively supports multi-camera systems, enabling Fisher information fusion without keypoint correspondence—facilitating cooperative perception and novel-view synthesis. Its core innovation lies in the deep coupling of geometry-aware differentiable rendering with statistical lower-bound theory, providing interpretable and verifiable uncertainty guarantees for learning-based dense pose estimation.

0 citationsRead paper

Data Cartography for Detecting Memorization Hotspots and Guiding Data Interventions in Generative Models

Aug 27, 2025

Generative models are prone to overfitting and memorizing rare training samples, leading to privacy leakage and inflated benchmark performance. Method: We propose a data-centric memorization analysis framework that—novelty—integrates sample difficulty (early-training loss) and forgetting event frequency to define a memorization score, enabling a four-quadrant classification scheme to identify memorization hotspots; we theoretically prove that the memorization score’s lower bound and uniform stability jointly bound the generalization gap, and accordingly design dynamic data reweighting and pruning strategies. Contribution/Results: Removing only 10% of training data reduces synthetic watermark extraction success rate by over 40% while increasing perplexity by less than 0.5, substantially mitigating information leakage with negligible degradation in generation quality. Our core innovation lies in an interpretable, theoretically grounded, data-level intervention paradigm.

0 citationsRead paper