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Crystal Structure Prediction (CSP) aims to predict a material's 3D structure from its chemical composition, with applications from energy storage to biomedical devices. Despite its importance, existing evaluation frameworks suffer from key limitations: they rely on threshold-sensitive or incomparable metrics, focus predominantly on geometric performance while overlooking physical plausibility, and fail to account for polymorphism, where a chemical composition can crystallize into multiple stable structures. In parallel, recent Symmetry-Informed CSP (SICSP) methods often report results alongside standard CSP baselines while receiving crystallographic templates at inference, which constrain the search space and make SICSP a fundamentally different task. To address these limitations, we introduce an Orientation-invariant, Polymorph-Aware, Large Benchmark (OPAL-Bench) that evaluates CSP and SICSP as separate tasks. We evaluate 7 CSP and 2 SICSP methods under OPAL-Bench across 4 datasets using threshold-free geometric and physical distance metrics. Our results show that no method dominates across all metrics, and that geometric performance is not strongly correlated with physical plausibility. We also release OPAL-CSP, an SE(3)-equivariant flow-matching baseline for the CSP track that performs competitively on geometric metrics and ranks among the best on physical ones. By unifying geometric and physical metrics under a polymorph-aware protocol, OPAL-Bench enables a more comprehensive assessment of generative quality in CSP.
Modern dehazing networks are often computationally expensive and overfit to synthetic haze, limiting real-time deployment. This underscores an urgent demand for efficient, high-fidelity restoration methods that can operate on resource-constrained edge devices in practical, dynamic environments. We introduce PhysDNet, a lightweight multimodal architecture that fuses NIR imagery with sparse LiDAR depth and is trained with a physics-constrained dual-head objective. Differentiating through a fixed Koschmieder inversion induces density-adaptive gradient amplification, acting as an implicit resource allocation mechanism that concentrates learning on heavily degraded regions without increasing inference cost. PhysDNet delivers superior restoration with minimal capacity and enhanced training efficiency, facilitating real-time deployment on edge devices without increasing inference overhead. On the Seeing Through Fog benchmark, PhysDNet outperforms competitors by 1.67 dB at 5.2 times lower compute while recovering 54.9% of fog-induced detection loss. Ablations and cross-domain evaluations show that physics-guided training improves generalization, including under non-homogeneous haze that violates the Koschmieder assumption. PhysDNet further demonstrates compatibility with fixed-function NPUs, running at 29/45/99 FPS at <4 W across L/M/S variants. Code, deployment scripts and pre-trained checkpoints are available at https://github.com/Heatdh/PhysDnet.
Widely used dimensionality reduction methods prioritize neighborhood or distance 1 preservation, yet planar coordinates alone cannot certify the homological type or 2 sample-level support of higher-order structures. Obtaining this evidence directly 3 is costly because simplicial complexes grow rapidly with dimension. We propose 4 Certified Homology-Aware Reverse-scale Mapping (CHARM), which combines 5 two-dimensional coordinates with certified homology records and sample-level 6 localization. Diffusion coordinates guide cover proposals; safe contractions and a 7 Cover Quotient Tower reduce the domain of structural computation; exact algebra 8 certifies and tracks homology representatives; and reverse-scale layout places their 9 supports in shared coordinates. Safe contraction preserves the homotopy type of 10 the input flag complex. The quotient tower is multiplicatively 3-interleaved with 11 the coarse-graph hop-distance Rips filtration. Verifiable distance-distortion bounds 12 give an additive guarantee between the original Euclidean and coarse-graph Rips 13 filtrations, and composite multiplicative guarantees for the tower on positive scales. 14 Across 22 datasets and 41,637 samples under a fixed configuration, CHARM 15 ranks among the top two on all 15 sample-weighted metrics for nonsynthetic data, 16 including the smallest values on all four Euclidean persistence-diagram distances. 17 It also provides 957 traceable support records across the full benchmark. On a 18 spherical shell, one certified H2 record identifies 1,578 original samples in the 19 two-dimensional view. CHARM thus combines geometric exploration with explicit 20 evidence of homological type and location.
We propose SAMBoost (Spatially Aware Mesh Boosting), a gradient boosting method that combines tree-based covariate modelling with a stochastic partial differential equation (SPDE) latent spatial field through a single penalised objective. At each boosting iteration, the predictor is decomposed into separate covariate and spatial components. The method is motivated by applications in which the spatial effect is not a nuisance to be removed but a quantity of interest that must be recovered alongside the covariates. In insurance, for example, practitioners need both flexible nonlinear covariate effects and an interpretable geographic risk surface that can be reported on its own. Existing approaches often involve trade-offs, offering flexible covariate modelling but no explicit spatial field, rigorous spatial inference with a fixed additive covariate structure, or a combination of both at computational costs that limit practicality for large datasets. SAMBoost addresses these goals within the boosting loop, and the underlying mesh produces a sparse precision structure whose cost is largely independent of sample size. On simulations and on an open benchmark, SAMBoost matches or improves on the predictive accuracy of joint Gaussian process and tree boosting approaches. It is also faster and recovers the spatial field and covariate effects more accurately. When covariate effects include interactions, it outperforms additive Bayesian spatial models. Applied to a flood insurance portfolio with 4.9 million records, SAMBoost trains on the full training set without subsampling and runs about sixteen times faster than a Bayesian reference, with a consistent spatial risk surface. A public Python implementation is available.
Masked diffusion language models generate text by iteratively unmasking positions, with practical samplers often selecting reveal positions from the model's own logits. The reveal order is therefore an endogenous latent variable of the rollout process with an enormous discrete latent space. Policy optimization objectives relying on pre-defined schedules or sampled trajectories introduce either bias or high variance. In this paper, we propose FEROM, Frontier Endogenous Reveal-Order Marginal Policy Optimization, which approximates policy gradients for the rollout-induced marginal response policy of masked diffusion LMs. FEROM derives a Rao-Blackwellized policy-gradient identity over latent reveal orders and expresses the resulting estimator as posterior edge occupancy on a reveal-state DAG. To make marginalization practical, we introduce Frontier Reveal Marginalization, a budgeted estimator that approximates this marginal edge structure by combining CDF-based computation of local probabilities of the endogenous reveal process with frontier expansion of high-mass partial states. Integrated into a GRPO-style objective, FEROM replaces single-path log-scores with a detached token-score surrogate over posterior-relevant reveal edges. Experiments on math and coding tasks show comparable or improved results over existing methods under matched scoring-state budgets. An offline proxy study further shows improved marginal-gradient approximation with increased scoring budgets.
Directing a robot to locate a target object in unseen environments remains a central challenge in embodied AI. Vision-Language Model (VLM)-based methods provide rich semantic reasoning but often produce uncalibrated and overconfident action decisions. We introduce CPNav, a navigation framework that combines collision-aware planning with statistically calibrated VLM action scoring for map-free object-goal navigation. From RGB-D input, CPNav constructs a navigability map, generates collision-free motion primitives, and queries two VLMs for goal detection and action scoring. The resulting scores are calibrated offline via conformal prediction (CP) using oracle actions obtained through a tree-structured exploration procedure with backtracking, providing finite-sample guarantees at a user-specified risk level. The CP layer is model-agnostic and can wrap any VLM policy. Online, calibrated VLM scores guide action selection, while a tree-structured exploration history records alternative actions and allows backtracking. We evaluate CPNav in both simulation and real-world hardware settings. In AI Habitat simulation, compared with the uncalibrated baseline method, CPNav achieves relative SR and SPL improvements of 6.2% and 11.4% on HM3D v0.2, and 12.4% and 8.8% on MP3D, respectively. In real-world deployment on a modified Hiwonder MentorPi robot, the corresponding improvements in SR and SPL are 24.9% and 15.2%, respectively. Code is available at https://github.com/practice-lab-ucla/CPnav.
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When deploying diffusion models in design tools, image editors, and visual production workflows, developers must account for inference latency. Generating an...
