Papers

This paper studies the computational difficulty of clustering problems that are defined directly on a continuous probability density. Rather than working with finite samples, we assume the density is given as a polynomial and ask whether it contains certain cluster structures. Four natural questions are examined. First, do there exist several points with high density that are far apart from each other. Second, do two high density points have a midpoint with low density, creating a valley between them. Third, does the region where the density is above a threshold have at least a given number of separate connected pieces. Fourth, does that same region contain a hole, meaning a loop that cannot be shrunk to a point. We prove that the first two problems, separated points and valley detection, are exactly as hard as the existential theory of the reals, a complexity class that contains NP and is believed to be strictly larger. In contrast, the topological problems of counting connected pieces and detecting holes are at least as hard as the existential theory of the reals, but their exact complexity remains open. Placing them inside that class would need a major advance in real algebraic geometry. These results give the first rigorous classification of exact continuous clustering inside the real polynomial hierarchy. They also show that even basic clustering criteria are not NP complete unless unexpected collapses occur.

Natural gas is undoubtedly an essential component of the global energy system. Accurate short-term forecasting of natural gas price is challenging due to pronounced volatility driven by seasonal demand patterns, geopolitical developments, and shifting macroeconomic conditions. The nonlinear dynamics and frequent regime changes can limit the effectiveness of traditional time-series models. In this study, we explore the use of Liquid Neural Networks (LNNs) for short-horizon forecasting of the Henry Hub spot price, a primary benchmark for pricing. LNNs are designed to adapt continuously to evolving temporal patterns through dynamic internal state updates, making them well suited for nonstationary price behavior. By improving forecast accuracy in volatile market conditions, this work aims to reduce uncertainty and enhance decision support across energy trading and power market applications.

Vision-language-action (VLA) models can learn to perform diverse manipulation skills "out of the box," but achieving the precision and speed that real-world tasks demand requires further fine-tuning – for example, via reinforcement learning (RL). We introduce a lightweight method that enables sample-efficient online RL fine-tuning of pretrained VLAs using just a few hours of real-world practice. We (1) adapt the VLA to expose an "RL token," a compact readout representation that preserves task-relevant pretrained knowledge while serving as an efficient interface for online RL, and (2) train a small actor-critic head on this RL token to refine the actions, while anchoring the learned policy to the VLA. Online RL with the RL token (RLT) makes it possible to fine-tune even large VLAs with RL quickly and efficiently. Across four real-robot tasks (screw installation, zip tie fastening, charger insertion, and Ethernet insertion), RLT improves the speed on the hardest part of the task by up to 3x and raises success rates significantly within minutes to a few hours of practice. It can even surpass the speed of human teleoperation on some of the tasks.

Large language models (LLMs) show promise for molecular optimization, but aligning them with selective and competing drug-design constraints remains challenging. We propose C-Moral, a reinforcement learning post-training framework for controllable multi-objective molecular optimization. C-Moral combines group-based relative optimization, property score alignment for heterogeneous objectives, and bottleneck-sensitive non-linear reward aggregation to improve stability across competing molecular properties. Experiments on C-MuMOInstruct and S$^2$-Bench MolOpt show that C-Moral achieves the best performance among compared methods on both benchmarks. On C-MuMOInstruct, C-Moral achieves the best Success Optimized Rate (SOR) of 48.9% on in-domain tasks and 39.5% on out-of-domain tasks while preserving scaffold similarity. On S$^2$-Bench MolOpt, it also achieves the strongest results across LogP, MR, and QED optimization tasks. These results suggest that C-Moral is an effective way to align molecular LLMs with continuous and constrained molecular design objectives. Our code and models are publicly available at https://github.com/Rwigie/C-MORAL.

We propose a simple yet effective alternative to reward normalization in policy gradient reinforcement learning by integrating a 1D Kalman filter for online reward estimation. Instead of relying on fixed heuristics, our method recursively estimates the latent reward mean, smoothing high-variance returns and adapting to non-stationary environments. This approach incurs minimal overhead and requires no modification to existing policy architectures. Experiments on LunarLander and CartPole demonstrate that Kalman-filtered rewards significantly accelerate convergence and reduce training variance compared to standard normalization techniques. Code is available at https://github.com/Sumxiaa/Kalman_Normalization.

Predicting the outcomes of prospective clinical trials remains a major challenge. Clinical trial outcomes result from complex interactions among experimental factors such as drug interventions, participant demographics, and protocols. Here, we introduce DeepImagine, a framework that predicts target trial outcomes through stepwise counterfactual imagination anchored on historical trials with observed results. Starting from a relevant historical trial, DeepImagine sequentially modifies one differing experimental factor at a time. With each step a large language model (LLM) is posed a local counterfactual: how would the current imagined outcome change with this single perturbation? The updated result is carried forward as the input to the next step, until the historical configuration exactly matches the target, yielding the final prediction. Empirically, DeepImagine consistently outperforms direct one-step prediction across several off-the-shelf LLMs, with further gains when multiple imagination pathways, initiated from different historical anchors, are aggregated. We also construct natural counterfactuals augmented with synthetic reasoning traces and train a family of specialized language models, each dedicated to learning one factor's local counterfactual transition. Integrating these learned local operators into DeepImagine yields substantial improvements over general-purpose LLM baselines. Our findings position stepwise counterfactual imagination, distinct from both correlational prediction and explicit structural causal modeling, as a promising direction for clinical trial outcome prediction. All code, training scripts, and evaluation scripts are available at \href{https://github.com/deepimagine-counterfactual/DeepImagine}{https://github.com/deepimagine-counterfactual/DeepImagine}.

Mixed Binary Quadratic Programs (MBQPs) are an important and complex set of problems in combinatorial optimization. As solving large-scale combinatorial optimization problems is challenging, primal heuristics have been developed to quickly identify high-quality solutions within a short amount of time. Recently, a growing body of research has also used machine learning to accelerate solution methods for challenging combinatorial optimization problems. Despite the increasing popularity of these ML-guided methods, a large body of work has focused on Mixed-Integer Linear Programs (MILPs). MBQPs are challenging to solve due to the combinatorial complexity coupled with nonlinearities. This work proposes ML-guided primal heuristics for Mixed Binary Quadratic Programs (MBQPs) by adapting and extending existing work on ML-guided MILP solution prediction to MBQPs. We introduce a new neural network architecture for MBQP solution prediction and a new training data collection procedure. Moreover, we extend existing loss functions in solution prediction and propose to combine contrastive and weighted cross-entropy losses. We evaluate the methods on standard and real-world MBQP benchmarks and show that the developed ML-guided methods significantly outperform existing primal heuristics and state-of-the-art solvers. Furthermore, models trained with our proposed extension with combined losses outperform other ML-based methods adapted from MILPs and improve generalization in cross-regional inference on a real-world wind farm layout optimization problem.

We argue that current definitions of machine unlearning are underspecified for second-order optimizers. We compare first-order and second-order learners for their ability to handle the data deletion task with varying degrees of eigendecomposition to mimic the loss model memory. While both first and second-order methods realign with the ideal counterfactul in terms of performance and gradient, the second-order optimizer shows significant volatility in the optimizer state. This indicates residual information, supposedly deleted, that isn't detectable by first-order analysis. Various eigendecay treatments show that stability and information loss is regained only under controlled state pertubation where geometric information (or memory) is erased.

Systematic biases in General Circulation Model (GCM) outputs limit their direct applicability in regional planning, making bias correction a technically demanding but necessary step for both short-term and long-term impact assessment. Correcting precipitation is particularly challenging due to its non-Gaussian distribution, intermittent nature, and heavy-tailed extremes. However, traditional statistical bias-correction methods have limited ability to learn systematic patterns from large datasets or generalize to new locations. While machine learning (ML) provides greater flexibility, it can produce unpredictable and difficult-to-interpret results, limiting generalization across GCMs and locations. In this study, we propose a differentiable bias-adjustment framework called dCLIMBA, that learns a spatiotemporally adaptive parametric bias-adjustment procedure, rather than corrected precipitation directly, between historical CMIP6 model outputs and a gridded observation-based dataset, Livneh. Results demonstrate that the proposed method corrects the magnitude and distribution of extreme precipitation with particularly strong performance in the upper tail. The quantile distribution of precipitation was well reproduced across diverse U.S. cities, and spatial patterns were comparable to those from the widely used LOCA2 statistical downscaling product. In addition, the framework showed partial future trend preservation and promising attenuation of marginal biases in unseen regions. This work presents a modular and efficient bias-correction approach. The differentiable approach provides an easy-to-use option for connecting atmospheric-model outputs to on-the-ground impacts.

Despite MoE models leading many benchmarks, supervised fine-tuning (SFT) for the MoE architectures remains difficult because its router layers are fragile. Methods such as DenseMixer and ESFT mitigate router collapse with dense mixing or auxiliary load-balancing losses, but these introduce noisy gradients that often degrade performance. In preliminary experiments, we systematically pruned experts and observed that while certain super experts are activated far more frequently, discarding less used experts still leads to notable performance degradation. This suggests that even rarely activated experts encode non-trivial knowledge useful for downstream tasks. Motivated by this, we propose an auxiliary-loss-free MoE SFT framework that combines bias-driven sparsification with always-active gated condenser experts. Rather than enforcing balanced activation across all experts, our method encourages task-relevant experts to remain active while pushing long-tailed experts toward inactivity. The condenser experts provide a persistent, learnable pathway that alleviates gradient starvation and facilitates consolidation of information that would otherwise remain fragmented across sparsely activated experts. Analysis further suggest that this design better preserves long-tailed expert information under sparse routing. Experiments on large-scale MoE models demonstrate that our approach outperforms state-of-the-art SFT baselines such as DenseMixer and ESFT, achieving average gain of 2.5%+ on both mathematical reasoning and commonsenseQA benchmarks.

Android malware detectors built with machine learning often suffer from temporal bias: models are trained and evaluated without respecting apps' actual release times, inflating accuracy and weakening real-world robustness. We address this by constructing a time-stamped dataset of benign and malicious Android apps and introducing a timestamp-verification procedure to ensure temporal accuracy. We then propose a detection framework that uses Bootstrap Your Own Latent (BYOL) for self-supervised pre-training to learn obfuscation-resilient representations, followed by supervised classification. Under time-aware evaluation, the method attains 98% accuracy and 89% F1. We further characterize malware behavior by analyzing true positives and false negatives using VirusTotal and the MITRE ATT&CK framework. To support reproducibility and further innovation, we release our dataset and source code.

Two-stage recommender systems first choose a candidate generator and then rank items within the generated set. Because the generator decides which items are available to the ranker, changing the generator changes both the policy value and the data support used to estimate that value. This creates an offline selection problem that standard single-stage objectives do not capture: a policy may look good under a retrieval score or a raw off-policy value estimate, but still be unreliable if it depends on weakly supported generator-item pairs. We propose CASP (Coupled Action-Set Pessimism), a support-aware offline selector for finite libraries of two-stage recommender policies. CASP combines doubly robust value estimation with a support-burden penalty. We show that stagewise rules that ignore downstream continuation value can be arbitrarily suboptimal, and we derive population, finite-class, and reconstructed-propensity guarantees for conservative selection. In simulations and a reconstructed MovieLens 1M application, CASP selects lower-burden policies when estimated value and support credibility are in tension.

Accurate classification of tropical tree species from unoccupied aerial vehicle (UAV) imagery remains challenging due to high species diversity and strong visual similarity among species at typical image resolutions (centimeters per pixel). In contrast, models trained on close-up citizen science photographs captured with smartphones achieve strong plant species classification performance. Recent advances in UAV data acquisition now enable the collection of close-up images that are spatially registered with top-view aerial imagery and approach the level of visual detail found in smartphone photographs, with the trade-off that such high-resolution photos cannot be acquired for many trees. In this work, we evaluate the performance of existing methods using paired top-view and close-up UAV imagery collected in a species-rich tropical forest. Through fine-tuning experiments, we quantify the performance gap between vision foundation models and in-domain generalist plant recognition models across both image types (high-resolution close-up versus coarser-resolution top-view imagery). We show that classification performance is consistently higher on close-up images than on top-view aerial imagery, and that this performance gap widens for rare species. Finally, we propose that self-supervised representation alignment across these two spatial scales offers a promising approach for integrating fine-grained visual information into canopy-level species classification models based on top-view UAV imagery. Leveraging high-resolution close-up UAV imagery to enhance canopy-level species classification could substantially improve large-scale monitoring of tropical forest biodiversity.

Web-scale 3D asset collections are abundant but rarely ready to ingest without cleanup, suffering from arbitrary metric scaling, incorrect pivots, brittle geometry, and incomplete textures, defects that limit their use in embodied AI, robotics, and spatial computing. We present AmaraSpatial-10K, a dataset of 10,071 synthetic 3D assets standardised for direct ingestion. Each asset ships as a metric-scaled, deterministically anchored .glb with separated PBR maps, a convex collision hull, a paired reference image, and multi-sentence text metadata. Alongside the dataset we introduce a reusable evaluation suite for 3D asset banks, a continuous Scale Plausibility Score (SPS), a keyword-based Concept Density metric, anchor-error auditing, and a cross-modal CLIP coherence protocol, and apply it to AmaraSpatial-10K alongside matched subsets of Objaverse, HSSD, ABO, and GSO. We check the annotations independently of the LLM/VLM pipeline that produced them: measured ABO object heights fall inside our scale intervals 88.7-90.7% of the time, and three non-author raters auditing a stratified sample of 314 assets judge 95.5% plausibly scaled and 99.7% correctly anchored. AmaraSpatial-10K improves CLIP Recall@5 by 3.4x over Objaverse (0.612 vs. 0.181, median rank 267 -> 3), achieves a 99.1% settling-stability rate under Habitat-Sim in static placement and collision tests, with ~20x lower per-load wall time, and as a drop-in Holodeck asset bank improves planned-scale matching and is preferred by blinded human raters in 27 of 40 paired scenes. Controlled ablations on the same asset bank attribute the retrieval gain to description richness.

Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural networks, benefit from updates like in SGD and Gradient Descent (GD) with a newly defined “gradient” that allows for complex parameters. This complex variant of the SGD/GD methods has already been proposed, but convergence guarantees without analyticity constraints have not yet been provided. We propose a variant of SGD (complex SGD) that allows for complex parameters, and we provide convergence guarantees under assumptions that parallel those from the real setting. Notably, these results extend to GD as well, and with the same set of assumptions, we confirm that some directional bias results extend from the real to the complex setting for kernel regression problems. We provide empirical results demonstrating the efficacy of the complex SGD in kernel regression problems utilizing complex reproducing kernel Hilbert spaces. In particular, we demonstrate we may recover superoscillation functions and Blaschke products from the Fock Space and Hardy Space, respectively, as the optimal functions for a particular choice of a loss function.

This paper presents a complete, end-to-end on-device vision machine learning pipeline, comprising data acquisition, two-layer CNN training with Adam optimization, and real-time inference, executing entirely on a microcontroller-class device costing $15-40 USD. Unlike cloud-based workflows that require external infrastructure and conceal the computational pipeline from the practitioner, this system implements every step of the core ML lifecycle in approximately 1,750 lines of readable C++ that compiles in under one minute using the Arduino IDE, with no external ML dependencies. Running on the Seeed Studio ESP32-S3 XIAO ML Kit (8 MB PSRAM), the firmware achieves three-class 64x64 image classification in approximately 9 minutes per training run, with real-time inference at 6.3 FPS. Key contributions include: correct batch-level gradient accumulation; pre-computed resize lookup tables for inference; dual-format weight export for SD-free baked-in deployment; a three-tier weight priority system (SD binary > baked-in header > He-initialization) resolved automatically at boot; a single-constant network reconfiguration interface; and PSRAM-aware memory management suited to microcontroller constraints. All source code and reference datasets are released under the MIT License at https://github.com/webmcu-ai/on-device-vision-ai

In this paper, we propose a Physics-Informed Neural Network framework for time-dependent simulations of pollution propagation originating from moving emission sources. We formulate a robust variational framework for the time-dependent advection-diffusion problem and establish the boundedness and inf-sup stability of the corresponding discrete weak formulation. Based on this mathematical foundation, we construct a robust loss function that is directly related to the true approximation error, defined as the difference between the neural network approximation and the (unknown) exact solution. Additionally, a collocation-based strategy is introduced to speed up neural network training. We also extend our model to the non-linear Burgers-type equations. As a case study, we investigate pollution propagation caused by snowmobile traffic in Longyearbyen, Spitsbergen, supported by detailed in-field measurements collected using dedicated sensors. The proposed framework is applied to analyze the effects of thermal inversion on pollutant accumulation. Our results demonstrate that thermal inversion traps dense and humid air masses near the ground, significantly enhancing particulate matter (PM) concentration and worsening local air quality. We compare our method to linear computational cost explicit dynamics solver using isogeometric analysis. We show that our method can solve non-linear non-stationary problem four times slower than IGA solver can solve the linear problem. It makes it particularly interesting to investigate the non-linear extensions with similar computational cost as the linear formulation.

Reward models in RLHF are trained to score only the final token of a response - a choice that discards rich signal from every intermediate position and produces models whose token-level outputs are noise. We argue this is a missed opportunity: a well-trained reward model's output at any token should represent the conditional expectation of the final reward given the response so far. We introduce Temporally Coherent Reward Modeling (TCRM), which induces this property via two regularization terms on top of the standard Bradley-Terry loss, with minimizers provably equal to conditional expectations. The regularizers correspond to Monte Carlo and TD value-learning objectives, establishing a direct connection to RL value functions. TCRM requires zero changes to architecture, data, or inference, yet unlocks three capabilities from one principle: interpretable token-level reward trajectories (middle-token pairwise accuracy improved from 50% to 88.9%, final-token accuracy preserved); state-of-the-art PRM performance on ProcessBench (44.9% average F1) among models trained only on outcome data; and unified reward/value modeling in PPO, reducing peak GPU memory by 27% and step time by 19% with matching LLM quality.

Trust Region Bayesian Optimization (TuRBO) is an effective strategy for alleviating the curse of dimensionality in high-dimensional black-box optimization. However, inappropriate lengthscale design can cause the local Gaussian process (GP) model within the trust region to degenerate, leading to suboptimal performance in high dimensions. In this work, we show that TuRBO's local GP may remain either excessively complex or overly simple as the dimension $D$ and trust region side length $L$ vary. To address this issue, we propose a straightforward variant, AdaScale-TuRBO, which scales the GP lengthscale with both the problem dimension and trust region size, thereby preserving kernel geometry and maintaining consistent prior complexity. Empirically, we show that AdaScale-TuRBO can robustly outperform standard TuRBO and other popular high-dimensional BO methods on synthetic benchmarks and real-world trajectory planning tasks.

Anemia affects over one billion people globally and remains severely under-diagnosed in low-resource regions where laboratory blood tests are inaccessible. This paper presents AnemiaVision, an end-to-end web-based system for non-invasive anemia screening from smartphone photographs of the palpebral conjunctiva and fingernail beds. The proposed pipeline fine-tunes a pre-trained EfficientNet-B3 backbone with a redesigned three-layer classifier head incorporating BatchNorm, GELU activations, and high-rate Dropout (0.45/0.35). Training employs four orthogonal accuracy-boosting techniques: TrivialAugmentWide for policy-free image augmentation, RandomErasing for spatial regularisation, Mixup (alpha=0.2) for inter-class smoothing, and cosine-annealing scheduling with linear warmup. Early stopping is governed by peak validation accuracy rather than validation loss to prevent premature termination on high-variance epochs. The deployed Flask application integrates persistent patient-history management backed by PostgreSQL on Render, with an automated database-migration entrypoint ensuring zero data loss across redeploys. Ablation experiments demonstrate that accuracy-first early stopping contributes +1.6% and Mixup contributes +2.8% to final validation accuracy. Overall, the proposed system achieves a validation accuracy of 96.2% and AUC-ROC of 0.98, compared with 44.9% validation accuracy and AUC-ROC of 0.58 from the three-epoch CPU-only baseline. Sensitivity for the anemic class reaches 0.96, making the system suitable as a first-line screening tool for community health workers in rural settings. The system is publicly accessible and source code is openly available.

Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models better learn these long-tail skills, we find a counterintuitive result: across a wide range of compositional reasoning tasks, such as state tracking and multi-step arithmetic, training under power-law distributions consistently outperforms training under uniform distributions. To understand this advantage, we introduce a minimalist skill-composition task and show that learning under a power-law distribution provably requires significantly less training data. Our theoretical analysis reveals that power law sampling induces a beneficial asymmetry that improves the pathological loss landscape, which enables models to first acquire high-frequency skill compositions with low data complexity, which in turn serves as a stepping stone to efficiently learn rare long-tailed skills. Our results offer an alternative perspective on what constitutes an effective data distribution for training models.

History-dependent sampling can reduce long-run Monte Carlo variance by discouraging redundant revisits, but existing schemes typically encode history through empirical measure on finite state spaces, which is infeasible in high-dimensional discrete configuration spaces or ill-posed in continuous domains. We propose Score-Repellent Monte Carlo (SRMC) framework that summarizes trajectory history by a running average of score evaluations in $\mathbb{R}^d$, where $d$ is the dimension of the score and state representation. This history is converted into a surrogate target through an exponential score tilt, indexed with $\alpha$ that represents the strength of repellence in controlling the magnitude of the history-based repulsion. The surrogate family is normalization-free in the standard MCMC sense, yielding a generic wrapper: at each iteration, any base kernel targeting $\pi$ can instead be run on the current surrogate $\pi_{\theta_n}$ while the history is updated online. We analyze the coupled evolution of the history recursion and Monte Carlo estimators using stochastic approximation with controlled Markovian noise, establishing almost sure convergence and a joint central limit theorem. We further identify regimes in which the asymptotic covariance decreases as $\alpha$ increases, with scaling $O(1/\alpha)$, extending the near-zero-variance effect of finite-state history-dependent samplers to general state spaces with constant memory. Experiments on continuous targets and discrete energy-based models demonstrate improved estimator variance and mode coverage, while retaining $O(d)$ memory usage and modest per-iteration overhead.

Diffusion models produce high-quality synthetic data but suffer from slow inference. We propose 3D Variable-Step Denoising Diffusion Probabilistic Model (VS-DDPM) a framework engineered to maintain generative quality while accelerating inference by several factors. We tested our approach on four tasks (missing MRI, tumor removal, MRI-to-sCT, and CBCT-to-sCT) within the BraTS2025 and SynthRAD2025 challenges. Designed for high efficiency under hardware and time constrains imposed by both challenges. VS-DDPM achieved state-of-the-art (SOTA) performance in missing MRI synthesis, yielding Dice scores of 0.80, 0.83, and 0.88 for the enhancing tumor, tumor core, and whole tumor regions, respectively, alongside a structural similarity index (SSIM) of 0.95. For MRI tumor removal, the model attained a root mean squared error (RMSE) of 0.053, a peak signal-to-noise ratio (PSNR) of 26.77, and an SSIM of 0.918. While the framework demonstrated competitive performance in MRI-to-sCT and CBCT-to-sCT tasks, it did not reach SOTA benchmarks, potentially due to sensitivities in data pre and post-processing pipelines or specific loss function configurations. These results demonstrate that VS-DDPM provides a robust and tunable solution for high-fidelity 3D medical image synthesis. The code is available in https://github.com/andre-fs-ferreira/SynthRAD_by_Faking_it.

The promise of data-driven materials discovery remains constrained by the scarcity of large, high-quality, and accessible experimental datasets. Here, we introduce a generalizable large language model (LLM)-powered pipeline for automated extraction and structuring of materials data from unstructured scientific literature, using concrete materials as a representative and particularly challenging example. The pipeline exhibits robust performance across a broad range of LLMs and achieves an $F_1$ score of up to 0.98 for diverse composition–process–property attributes. Within one hour, it extracts nearly 9,000 high-quality records with over 100 attributes from a corpus screened from more than 27,000 publications, enabling the construction of the largest open laboratory database for blended cement concrete. Machine learning analyses underscore the importance of large, diverse, and information-rich datasets for enhancing both in-distribution accuracy and out-of-distribution generalization to unseen materials. The proposed pipeline is readily adaptable to other materials domains and accelerates the development of scalable data infrastructures for materials informatics.

Verification is becoming central to both reinforcement-learning-based training and inference-time control of large language models (LLMs). Yet current verifiers face a fundamental trade-off: LLM-based verifiers are expressive but hard to control and prone to error, while deterministic executable verifiers are reliable and interpretable but often limited in capability. We study the following question: given a development set of LLM outputs and labels for a target objective, such as correctness, can we automatically induce a minimal set of Python verifiers whose joint satisfaction closely matches that objective? We propose AutoPyVerifier, a framework that uses an LLM to synthesize candidate verifier functions and then refines them through search over a directed acyclic graph (DAG). By navigating the DAG, AutoPyVerifier systematically explores the space of deterministic executable verifiers and selects a compact verifier set whose joint satisfaction best approximates the target objective. Across mathematical reasoning, coding, function calling, and instruction-following benchmarks for several state-of-the-art LLMs, AutoPyVerifier improves target-objective prediction by up to 55.0 F1 points over the initial LLM-generated verifier sets. Additional analyses show that the most useful verification targets vary by benchmark and model, and that the DAG-based search shifts the learned verifier sets toward more structural and semantically grounded checks. We further show that exposing the discovered verifier set to an LLM as an external tool improves downstream accuracy by up to 17.0 points. We release our code

Understanding and representing complex climate variability is essential for both scientific analysis and predictive modeling. However, identifying meaningful climate regimes from raw variables is challenging, as they exhibit high noise and nonlinear dependencies. In this work, we explore the use of Masked Siamese Networks to discretize climate time series into semantically rich clusters. Focusing on daily minimum and maximum temperature, we show that the resulting representations: (i) yield clusters that reflect meaningful climate states under our modeling assumptions, offering a simplified representation for downstream use; (ii) enable sampling and analysis of specific climate scenarios; and (iii) exhibit statistical associations with El Niño events, underscoring their scientific relevance. Our findings highlight the potential of self-supervised discretization as a tool for climate data analysis and open avenues for incorporating richer climate indicators in future work.

Diffusion models achieve remarkable success in time series generation. However, slow inference limits their practical deployment. We propose E$^2$-CRF (Error-Feedback Event-Driven Cumulative Residual Feature caching) to accelerate frequency domain diffusion models. Our method exploits two structural properties: (1) spectral localization, where signal energy concentrates in low frequencies, and (2) mirror symmetry, which halves the effective frequency dimension. E$^2$-CRF uses a closed-loop error-feedback system that adaptively caches transformer KV features across diffusion steps. We trigger recomputation using event-driven residual dynamics instead of fixed schedules. Our method selectively recomputes high-energy or rapidly-changing tokens while reusing cached features for stable high-frequency components. E$^2$-CRF achieves ~2.2 speedup while maintaining sample quality. We demonstrate effectiveness on 5 datasets. Our caching strategy naturally aligns with the diffusion process's structure-to-detail progression. We include sufficient-condition error and complexity bounds under standard regularity assumptions (Appendix), alongside empirical validation. Our code is available at https://github.com/NoakLiu/FastFourierDiffusion and is also integrated in https://github.com/NoakLiu/FastCache-xDiT.

Indoor positioning is an essential technology for a wide range of applications in GNSS-denied environments, including indoor navigation and IoT systems. Combining convolutional neural networks (CNNs) and magnetic field-based features offers a low-cost, infrastructure-free solution for precise positioning. While magnetic fingerprints are a promising approach for indoor positioning, models trained on raw 3D magnetometer data are highly sensitive to device orientation. We address this by using two rotation invariant features derived from the 3D magnetic field: the norm (Mn) and the projection onto the gravity axis (Mg). We train a lightweight 7-layer dilated CNN (MagNetS/XL) on magnetic sequences to directly regress (x, y) positions. Using the MagPie dataset (three buildings, handheld trajectories), we systematically evaluate fixed and random rotations of test and/or train data. Raw 3D inputs (Mx, My , Mz) exhibit isotropic error increases under fixed 90{\deg} rotations and further degrade with growing random rotations. In contrast, 2D (Mn, Mg) inputs maintain rotation invariant accuracy and surpass the 3D inputs once rotation exceeds building-specific thresholds for three reference buildings: 0{\deg} for Loomis (large), 5{\deg} for Talbot (medium), and 6{\deg} for CSL (small). MagNetXL achieves or exceeds state-of-the-art accuracy on the MagPie dataset, and MagNetS delivers similar performance with roughly one third of the parameters, favoring mobile deployment. These results show that the robustness gained from rotation invariant inputs outweighs the loss of input dimensionality in realistic usage, allowing mapping and localization without orientation alignment or added infrastructure.

Traditional “row-count $\times$ quality coefficient” approaches fail to capture the nonlinear utility of data for Large Language Model (LLM) capabilities. We present a utility-aware data valuation framework that moves from static accounting toward utility-based pricing. The framework combines token-level information density and data quality, empirical training contribution estimated by influence functions, proxy models, and Data Shapley values, and cryptographic mechanisms based on hash commitments, Merkle trees, and tamper-evident training ledgers. Preliminary evaluation includes a smoke-scale multi-domain study and a synthetic duplication test. Results show that proxy-based empirical gain achieves strong ranking agreement with proxy-defined realized utility and substantially outperforms row-count and token-count baselines in the tested setting, while the prototype provides a controlled sanity check of the valuation pipeline and its sensitivity to duplication-based manipulation.

Feature selection in high-dimensional genomic data ($d \gg n$) demands methods that are simultaneously accurate, sparse, and stable. Existing approaches either require manual threshold specification (mRMR, stability selection), produce unstable selections under data perturbation (Lasso, Boruta), or ignore biological structure entirely. We introduce StackFeat-RL, a meta-learning framework that optimises the hyperparameters of an iterative dual-criterion feature selection algorithm via REINFORCE policy gradients. The dual criterion, requiring both coefficient consistency and selection frequency, guards against two failure modes missed by single-criterion methods, while iterative accumulation provides convergence guarantees via the law of large numbers. On COVID-19 miRNA data (GSE240888, 332 features) and three Alzheimer's disease classification tasks (GSE84422, 13237 genes; Normal vs.\ Possible, Probable, and Definite AD), StackFeat-RL achieves the highest predictive accuracy among all evaluated methods, including ElasticNet, Boruta, mRMR, and stability selection, while requiring 3–4$\times$ fewer features. Keywords: feature selection, reinforcement learning, REINFORCE, elastic net, biomarker discovery, Alzheimer's disease, dual-criterion selection, protein interaction networks