Science & Mathematics

Bitcoin-style Proof-of-Work (PoW) secures permissionless blockchains but spends substantial computation on hash puzzles which have no utility other than extending the chain. At the same time, we have seen that the rise of generative AI has created significant demand for computational resources that are unfortunately available only to a few players. We propose a solution that solves both problems at the same time. In particular, we present Proof-of-ML-Inference (PoML), a consensus protocol in which miners perform user-requested machine-learning inference as part of their consensus algorithm. We identify exactly what computational assumptions are needed for ML inference to safely replace hash work, formalize those assumptions, and give evidence that LLMs and diffusion models satisfy them. We then formally analyse the security of our protocol by reducing the security of our protocol to the security of the Bitcoin Backbone model. Finally, we empirically evaluate block-time stability, showing that, in a simulated environment, PoML maintains a block production rate close to its calibrated block-time target.

Benchmark compression reduces evaluation cost by selecting a small set of samples. Existing methods typically guide selection using a single metric, although benchmarks often assess models along multiple dimensions. We find that model rankings are often weakly correlated across metrics, indicating that different metrics capture distinct aspects of model performance. Samples selected for one metric do not reliably preserve scores and rankings on others when used for compressed evaluation. At 80\% compression, each of the five single-metric baselines yields higher reconstruction error than equal-size random sampling in over 70\% of cross-metric comparisons. To address this challenge, we present HoloCosm, which jointly minimizes normalized score-reconstruction error across source models and metrics while constraining ranking distortion. We evaluate HoloCosm across multiple compression rates on 15 language, multimodal, VLA, and agent benchmark configurations with 85 component metrics. With 80\% compression, HoloCosm outperforms Random, the strongest baseline overall: average NMAE drops by 35.3\% to 0.236, worst-component NMAE drops by 39.5\% to 0.330, and average Spearman correlation rises from 0.884 to 0.915. In addition, HoloCosm remains competitive with existing baselines in single-metric evaluation. We will release our code and experimental results.

Robotic manipulation in agricultural environments remains challenging due to variations in plant geometry, occlusion, and camera viewpoints. Pretrained vision-language-action (VLA) and generalist robot policies offer a promising approach to addressing these challenges by learning manipulation behaviors from multimodal observations and language instructions. However, adapting these policies to agricultural tasks requires domain-specific demonstrations, which are costly and time-consuming to collect on physical robots. In this work, we develop a simulation-to-real robot-learning framework for agricultural reaching and grasping that integrates task-specific demonstration collection and pretrained policy adaptation. A MuJoCo-based agricultural environment is developed with diverse tomato plant structures to support demonstration collection and controlled evaluation. Expert demonstrations are collected through joystick teleoperation, with a low-level controller used to execute robot actions. Two pretrained generalist robot policies, Octo and $π_{0.5}$, are adapted using simulated demonstrations, followed by further fine-tuning on a physical Franka Research 3 manipulator using real-robot demonstrations. The adapted policies are evaluated under in-distribution, viewpoint/spatial-shift, and out-of-distribution conditions in simulation, followed by physical-robot experiments. The influence of proprioceptive information on policy performance is also investigated. Results show that $π_{0.5}$ achieves higher task-performance scores than Octo and exhibits less degradation under distribution shifts. These findings demonstrate the potential of integrating pretrained generalist policies with task-specific demonstration learning for agricultural manipulation.

We develop a deep Pontryagin learning framework for high-dimensional continuous-time stochastic control problems that naturally accommodates jump-diffusions. In contrast to direct policy optimization, which repeatedly differentiates the objective through the entire time-discretized dynamics, our method separates adjoint learning from policy improvement by explicitly incorporating state-sensitivity information from the Pontryagin stochastic maximum principle. For a fixed Markov control, we first compute pathwise adjoint labels by backpropagating the reward through time along simulated state trajectories, and project these labels onto the Markov state through a supervised regression step. The control is then updated by enforcing the pointwise Hamiltonian stationarity condition. We prove that the resulting projected adjoint process satisfies a discrete-time Pontryagin principle and converges, as the time step tends to zero, to the solution of the corresponding continuous-time adjoint backward stochastic differential equation. Numerical experiments illustrate the accuracy, stability, and scalability of the approach.

Time-series multispectral imaging is widely used to assess turfgrass condition; however, extracting plot-level vegetation index (VI) values remains labor-intensive when camera positions vary between acquisitions and automated plot tracking is unreliable. We developed an open-source software tool comprising (i) a graphical user interface (GUI) for the interactive placement of orientation-adjustable regions of interest (ROIs) with $N$-way subdivision to match plot geometry and (ii) a batch-processing script that computes plot-level mean VI values from single-band floating-point rasters and exports measurements and ROI coordinates in JSON format for reuse. Saved coordinates can be reapplied to measure NDVI, NDRE, and SAVI from identical pixel regions within a single time point without re-delineating ROIs. In a demonstration using rail-mounted multispectral turfgrass imagery (18 images), plot-level mean values were extracted in a single session, with coordinates reused directly for NDRE and SAVI rasters. The system reads non-georeferenced pixel-coordinate rasters natively, does not require GIS expertise, and supports reproducible VI quantification where static sensor deployment is impractical.

Frontier LLMs can copy random text almost flawlessly, yet they often overrun or truncate long blocks of repeated characters. In repeated strings, matching local content no longer reliably identifies where copying should continue or when it should stop. Nevertheless, we show that a two-layer transformer with $O(\log\log N)$-bit precision and $O(\log N/\log\log N)$ width can copy every string up to a chosen design horizon $N$ and terminate correctly under arbitrary repetition. We use RoPE-style rotations of attention values and outputs (VO-rotations) with small prime periods to encode distances from delimiter anchors modulo those primes. By the Chinese Remainder Theorem, these periodic encodings jointly distinguish all required distances, allowing one retrieval rule to select either the next source token or the end marker. In contrast, we prove a width-independent impossibility result for copying under sequential finite-precision softmax accumulation. It applies to transformers whose only positional input is an additive attention bias that eventually becomes constant, including NoPE and a recursive implementation of ALiBi. Once an identical-token run exceeds the resulting saturation threshold, further repetitions leave the logits unchanged. If this threshold grows sublinearly with $N$, these models cannot both complete a long all-identical copy and stop correctly, a pattern resembling the termination errors of frontier LLMs. In synthetic copying experiments, baseline transformer models fail on long repeated strings even within the training range. Trained VO models, by contrast, generalize beyond the training lengths with near-perfect accuracy up to length $\approx5005$, the selected primes' period product.

We develop an error model for a Non-Volatile Memory (NVM) device that represents the effects of physical faults experienced in a CubeSat mission in Low Earth Orbit (LEO). The CubeSat carries an off-the-shelf low-power Ferroelectric RAM (FRAM) chip and runs repeated read/write tests according to a predefined pattern. We compare every memory snapshot received from the satellite with a reference bitmap to identify bit errors. We visually analyze erroneous values distributions in the memory snapshots and we understand that they are frequently distributed according to regular spatial patterns. We define a generative deep learning technique to automatically learn these spatial patterns and to synthetically generate additional error patterns mimicking the observed ones. The model is capable at producing memory errors for general application-level experimentation. Our preliminary validation indicates that when comparing the model output with the data we collect, 0.92 of the generated bit flips correspond to bit flips in the memory snapshots and the model captures 0.91 of the observed bit flips. A comparison of the spatial distribution of bit flips in 10,000 generated error patterns also provides a Wasserstein distance of 0.073, indicating that the two distributions differ by roughly 7% of the maximum possible displacement of their probability masses.

Large Language Models (LLMs) have significantly advanced natural language processing and artificial intelligence applications through their capabilities in reasoning, text generation and knowledge retrieval. However, LLMs are still vulnerable to two important challenges: hallucination, generating factually incorrect or fabricated content, and response deviation, meaning systematic deviations from ground-truth responses. These limitations raise serious concerns regarding reliability and trustworthiness in academic and research environments. This study offers a thorough comparative analysis using a variety of metrics of ten advanced LLMs ChatGPT, Gemini, Claude~3.5~Sonnet, LLaMA~3, Mistral, Grok, Perplexity, DeepSeek~V3, Falcon, and Gemma based on a benchmark consisting of 70 carefully designed academic prompts across four complexity levels: Basic, Explanation, Advanced, and Tricky, evaluated in February 2025 on specific model versions. Each response was independently evaluated by three reviewers using five metrics: Accuracy, Precision, Recall, Response Deviation Index, and Hallucination Index. Perplexity and DeepSeek~V3 achieved the highest overall accuracy, while Gemini demonstrated strong recall and a well-balanced performance profile across all five metrics. LLaMA~3 showed strong resistance against hallucinations through a conservative method of generation. Advanced-level prompts proved most challenging across all models, while Tricky prompts were handled more reliably owing to their binary true/false structure. Falcon achieved perfect precision and zero hallucinations, but at the cost of the lowest recall and the highest response deviation. The results show a fundamental trade-off between response completeness and factual reliability, intensified by prompt complexity.

Aerial visual localization is crucial for autonomous drone navigation in urban environments where GNSS signals are often degraded. Lightweight textureless Level-of-Detail (LoD) city models provide a geometric map alternative to textured assets. Existing silhouette-based methods rely on image-space alignment, which can leave different camera poses indistinguishable and favor incorrect poses when segmentation errors distort the building outlines. We present PlanarCityLoc, which moves beyond silhouette overlap by leveraging the planar geometry of building facades and roofs. Following geometry-aware initialization, we match image-side planar patches to LoD model planes and use the resulting 3D-to-2D correspondences to refine pose with Perspective-n-Point (PnP). The framework uses off-the-shelf geometry and segmentation models without dataset-specific training or fine-tuning. Experiments on UAVD4L-LoDv2 and Swiss-EPFLv2 achieve state-of-the-art localization recall among the evaluated off-the-shelf LoD-based methods. By grounding image-space alignment in 3D planes, PlanarCityLoc enables more accurate aerial localization with lightweight, textureless city maps.

To prepare for future outbreaks, researchers need to know what studies have been done and what data they use. Mapping a large literature by hand is slow, while large language models alone can misstate or conflate sources. We present EpiLens, a lightweight, open-source retrieval-augmented generation package that applies a fixed retrieval template and output schema to every paper in a corpus and links outputs to source passages. We build a corpus of 2,297 papers from the sources of a multi-pathogen parameter study and evaluate EpiLens's paper-classification workflow against 214 manually labelled papers. Without task-specific training data, the classifier matches or exceeds the tested supervised and zero-shot baselines across four tasks. The study's early extraction sheets cite published sources for 327 estimates. We link each estimate to a cited document or to corpus studies included by a review. Then, we use the classifier's labels to compare the papers associated with different parameters and pathogens. EpiLens labels more papers linked to reproduction numbers than fatality risks as model-based (54% versus 22%, compared with 62% versus 24% in the manual labels). The gap is consistent with the frequent use of transmission models to estimate reproduction numbers and persists within each of five pathogens compared. Beyond the contrast between parameters, the model-based share of papers linked to incubation-period estimates differs by pathogen: 55% for SARS-CoV-2 versus 6% for mpox.

Neural Posterior Estimation (NPE) fits an amortized conditional density estimator to a simulated training set of complete-data realizations. NPE's training objective, log-likelihood, favors posterior approximations that assign arbitrarily high density to the training points, and typical families of amortized conditional density estimators (e.g., normalizing flows, Gaussian encoders) are flexible enough to oblige. The resulting policy of extreme overconfidence translates poorly to held-out data. Early stopping and other regularizers can prevent this degeneracy, but they are limited to selecting posterior approximations along an unfavorable optimization trajectory set by in-sample residuals, where the posterior mean is underfit while the posterior variance is overfit. To avoid this trade-off, we propose Cross-Fitting NPE (CF-NPE), which uses sample splitting to separate conditional-mean estimation from the estimation of the posterior's higher moments. Using $K$-fold cross-fitting, CF-NPE fits $K$ posterior-mean regressors and then fits a conditional density estimator to the resulting out-of-fold residuals. In experiments with synthetic data and in a cosmological application, CF-NPE achieves higher held-out log-likelihood than standard NPE and typically improves calibration. CF-NPE is most useful in high-dimensional, simulation-limited settings.

Complementary-label learning (CLL) trains a classifier from labels that name a class an instance does not belong to. Such labels are cheap to collect from crowdworkers or vision-language models (VLMs), making them attractive for large-scale annotation. However, both sources can mistakenly assign the true class as the complementary label. Such annotation errors are particularly harmful in CLL because the model is explicitly trained to suppress the correct answer. Optimal transport (OT) data valuation identifies harmful samples by comparing training data with a clean validation set, but transferring it directly to CLL creates a semantic mismatch: label $c$ means not class $c$ in the training but class $c$ in the validation. We show that this makes the OT label groups noisy mixtures whose behavior depends on the noise rate. The transferred score is informative only at sufficiently high noise, becomes uninformative at the crossover rate $1/M$ for $M$ classes, and reverses below it, where practical CLL annotation typically operates. We propose CAVA, which introduces a complementary label cost and a label margin that isolates the contribution of each complementary label to the transport potential. The margin keeps a consistent direction across noise rates, detects diagonal noise with a parameter-free threshold of closed-form precision, and allows detected samples to be recycled as ordinary-label supervision. On synthetic and human-annotated benchmarks, CAVA separates diagonal noise almost perfectly where directly transferred OT valuation performs worse than random. With only a fraction of the clean validation data, it also improves every CLL objective we evaluate, showing that OT-based valuation becomes reliable once the semantics of complementary supervision are modeled explicitly.

Reinforcement learning for instruction-guided image editing requires reward models that provide reliable, accurate, and efficient feedback. Direct scalar prediction compresses multidimensional editing preferences, whereas generative evaluators can expose their judgment through explicit reasoning. However, broad scoring criteria do not specify all instance-dependent editing and preservation constraints, and generating long reasoning trajectories is costly for online optimization. We introduce CheckDistill, a pointwise reward modeling framework that internalizes instruction-adaptive checklists. We decompose each editing condition into atomic, independently verifiable requirements and construct four-dimensional scoring labels together with structured verification evidence. After supervised score initialization, a privileged teacher conditions on checklists, item-level judgments, and dimension-level rationales to supervise the student's own scoring trajectories. A reliability-weighted on-policy self-distillation objective adjusts supervision at score tokens according to agreement between the teacher's expected scores and reference labels, while retaining candidate probability weights in a truncated token support. The deployed student directly predicts four score distributions without checklist inputs or explicit reasoning and aggregates their expectations into a scalar reward. CheckDistill achieves aggregate accuracies of 72.30%, 56.67% and 82.90% on MMRB2, MER-Bench and EditReward-Bench, respectively, exceeding the compared open-source baselines on all three metrics.

Nonlinear state-space system identification has attracted decades of interest, yet remains challenging because of the interplay among unknown parameters, nonlinear dynamics, and latent state variables. Its difficulty increases dramatically when the state and parameter dimensions increase. To address this challenge, we develop an ensemble Kalman inversion (EnKI)-based approach. This approach leverages EnKI to perform maximum a posteriori parameter estimation through successive local Gaussian approximations, enabling an iterative and incremental search for unknown parameters. The search combines Monte Carlo sampling with Kalman-type updates to evolve an ensemble of parameter samples, thereby offering empirical stability and the ability to handle strongly nonlinear models. The EnKI search is coupled with state estimation conditioned on the latest parameter estimates. This enables parameter identification along with latent state recovery. To improve scalability for large datasets, we further develop a cascaded EnKI (CasEnKI) method, which assimilates subdatasets sequentially to accelerate computation. We validate the proposed methods using a lithium-ion battery model with ten state variables and 18 unknown parameters. Simulation results show that the EnKI approach offers high identification accuracy and empirical stability in parameter search. Further, experimental results illustrate the computational efficiency and scalability of the CasEnKI method for large battery datasets.

Muon, a 2024-born optimizer for language models, differs from the 2015-born spectral gradient descent mainly in its fast, GPU-friendly Newton--Schulz polynomial for orthogonalizing the gradient matrix. Accordingly, a line of research proposes faster polynomial iterations for gradient orthogonalization, such as Polar Express and Gram Newton--Schulz, both built on quintic polynomials. In this paper, we introduce Polar Switch, a new approach to polynomial gradient orthogonalization. Using simple polynomial circuits, Polar Switch reaches a given high polynomial degree at a lower FLOP cost than quintic iterations. We define a circuit as a short sequence of symmetric matrix products on a few square buffers, and circuits with $k$ products form a restricted family of odd polynomials of degree up to $2^{k+1}+1$. We choose the sequence of products in each circuit, their coefficients, and how the circuits are composed by numerically minimizing a worst-case bound on the polar approximation error. This minimization is subject to a FLOP budget that accounts for symmetric matrix multiplication kernels and a rounding constraint for numerical stability in half precision. Our two recommended Polar Switch methods have 15.5--18.7\% lower runtime than Polar Express on square matrices and 8.6--16.2\% lower runtime than Gram Newton--Schulz on rectangular matrices with aspect ratios 3.25, 3.5, and 8, with comparable approximation accuracy. In pretraining Modded-NanoGPT \#91, Qwen3-0.6B, and Gemma 3-1B, Polar Switch reaches final validation losses similar to those of established orthogonalization methods. Across the more than 14 million matrices that each of the two recommended methods orthogonalized in these runs, the estimated output spectral norms never exceed the designed bounds by more than 3\%, demonstrating their numerical stability.