Chain-of-thought (CoT) reasoning has emerged as a powerful paradigm for extending the computational capabilities of transformer-based models. A growing body of recent work has begun to uncover the fine-grained computational power of transformers augmented with CoT, as well as their connections to classical complexity theory. In this work, we advance this line of research by establishing the first hierarchy theorem for CoT-based computation. Our main result shows that for any reasonable resource bound $r(n) \geq n$ and any $\varepsilon > 0$, \[ \mathrm{CoT}(r(n)) \subsetneq \mathrm{CoT}(r(n)^{1+\varepsilon}), \] where $\mathrm{CoT}(r(n))$ denotes the class of decision problems solvable by transformers using $O(r(n))$ CoT reasoning steps on inputs of length $n$. Our result shows that increasing the number of CoT reasoning steps provably yields strictly greater computational power, establishing CoT steps as a fundamental resource in transformer-based computation. Unlike classical hierarchy theorems, which are typically proved via diagonalization, our approach leverages known coarse-grained simulations between CoT-augmented transformers and Turing machines in both directions. Building on these connections, we adapt the classical padding technique from complexity theory to this setting to obtain a tight hierarchy. A key technical contribution of our work is the implementation of padding within the transformer-based CoT model.
The success of modern score-based generative models is largely driven by diffusion-based training, which learns a collection of time-indexed score fields corresponding to progressively noisier versions of the data distribution. While such models achieve impressive sample quality, leveraging them for sound probabilistic inference---particularly sampling from arbitrary conditionals of the model---remains challenging. This difficulty arises because conditioning information is only available for clean data and not for the higher noise levels required to generate exact conditional samples. In this paper, we introduce DIffusion-free SCOre matching (DISCO), a principled approach that sidesteps the need for time-dependent score fields altogether. Our method is based on an objective that, while reminiscent of diffusion-based training, estimates only a single score of the (slightly perturbed) data distribution, for which the exact conditional score is readily obtained. In experiments, DISCO is competitive with state-of-the-art diffusion models in terms of sample quality. More importantly, DISCO yields a more faithful representation of the underlying data distribution and---crucially---enables accurate sampling from arbitrary conditionals, outperforming standard heuristic samplers. This capability opens the door to principled and flexible probabilistic reasoning with score-based models.
This paper proposes a novel, lightweight convolutional neural network (CNN) designed for edge device deployment. The CNN is developed to recognize and classify threats or targets of interest. The model is equipped with a real-time hotspot detection algorithm, which enables it to process information quickly and accurately, resulting in improved inference time of up to 20 fps and a detection range of more than 400 meters with typical thermal situational awareness sensors. The proposed CNN has been rigorously tested and validated to demonstrate its high accuracy, sensitivity, and low false positive rate, providing a reliable solution for edge devices to detect potential targets. Additionally, the lightweight design of the CNN allows for easy deployment, making it an ideal solution for extending the security bubble for edge devices. The proposed model can be used for a variety of applications, including surveillance, security, and object recognition.
We introduce Multi-scale Closing Index (MCI), a new dissimilarity measure for evaluating the alignment of two 2D point sets. MCI is bounded between 0 and 1 and is based on multiscale mathematical morphology operations, with smaller values indicating greater structural agreement. The measure was motivated by the need to assess the quality of registration between point sets representing cell populations in biological images. To evaluate its behaviour under controlled conditions, we generated synthetic point clouds from Perlin-noise-based spatial structures, following established approaches for simulating biologically plausible spatial organization. We assessed MCI between those point clouds and different transformed versions, obtained by local perturbation, point removal, translation, rotation and addition of impulsive noise. Across these experiments, the dissimilarity MCI increased gradually and consistently with perturbation severity, while showing a clear discontinuity between clouds originating from the same underlying spatial structure and point clouds generated from different structures. We further compared MCI with commonly used point-set distances, including Hausdorff-based measures and Sliced Wasserstein distance. These experiments show the ability of MCI to capture structural agreement and quantify deviations between point sets, highlighting its potential as a complementary metric for evaluating two-dimensional point-set registration.
Shallow-water UAV imagery provides centimeter-scale observations of benthic environments, but water-induced distortions complicate interpretation. To our knowledge, we present the first systematic zero-shot benchmark of unified multimodal large language models (MLLMs) for both assessing water-induced distortions and restoring shallow-water imagery within the same model framework. We evaluate five open-weight unified MLLMs with frozen pretrained weights and without access to paired reference images or descriptions of the true seabed. The benchmark contains 1,000 image pairs: 600 semi-synthetic UAV scenes created by applying synthetic water distortions to real shallow-water imagery and 400 fully synthetic through-water scenes. Three independent human annotations cover five distortion types. We evaluate four assessment prompts (P0-P3), from direct instruction to structured task decomposition, on all 1,000 images and four diagnosis-guided restoration prompts (R0-R3) on a common 100-image subset. Assessment varies substantially by model and prompt, with systematic prediction biases and a best pooled balanced accuracy of 0.654 for distortion presence. The best pooled PSNR gain is +0.255 dB, no unified MLLM improves pooled LPIPS, and some outputs alter scene structure or hallucinate content. Two restoration-only baselines also show limited transfer: InstructIR achieves a pooled PSNR gain of +0.040 dB, while PromptFix degrades all four pooled metrics under every prompt. These results show that recognizing shallow-water degradation does not imply reliable physical restoration and provide a reproducible baseline for future work.
OpenAI's agents breached Hugging Face in July 2026, and the same company released more than seven hundred AI-generated manuscripts of mathematical proofs in October 2026. The first event is read as a failure in security, while the second is read as a success in mathematics. We read both through the hybrid framework of our paper (Kim and Kang, 2026, arXiv:2611.01914), in which coding, proving, and learning from data are derivations by one and the same deductive mechanism, distinguished by the kinds of premises from which they are derived. Under this framework, the AI systems behind the two events ran the same loop, in which a statistical proposer produces candidate exploits or proofs and a deductive verifier settles each one by a derivation. What separates the events is the logical form of the statement wanted by each of the two domains, security and mathematics. The safety of a program is a $\Pi_1$ statement, for it says that no exploit exists, which is not assured by any finite list of tests that have been passed by the program. By contrast, the provability of a sentence is a $\Sigma_1$ statement, for it says that a proof exists, which is assured by a single instance, namely a proof that has been checked by the deductive verifier. The theorem behind both is Turing's Undecidability Theorem: the halting set is $\Sigma_1$ but not decidable, so its complement is $\Pi_1$ and not $\Sigma_1$, which is to say that membership has a finite witness but non-membership has none. We prove that attaching a statistical proposer to a deductive verifier does not change this undecidability result, however good the proposer is. We then discuss what does assure safety and where the residual risk goes.
Large language models (LLMs) have shown promise for automating data science workflows. Benchmarks such as DataSciBench (2026) and StatQA (2024) have advanced the evaluation of their capabilities across data science and statistical tasks. Assessing their reliability requires examining both the quality of their responses and their consistency across repeated runs, task types, and difficulty levels. With this aim, we introduce DS-QA, a benchmark comprising 100 data science and statistics questions drawn from UK university courses, spanning 16 datasets and three difficulty levels. We develop a three-layer evaluation framework that combines general response properties (runtime, verbosity and text similarity), coarse-grained metrics (accuracy, code executability and completeness), and task-specific metrics. We evaluate OpenAI models using a Monte Carlo protocol with 100 repeated runs. The results reveal substantial variability in responses to data visualisation and supervised learning tasks, particularly at medium and hard difficulty levels, highlighting the importance of evaluating consistency alongside response quality. We also find that an increase of 0.1 in the word verbosity ratio corresponds to an increase of about 0.013 in the token verbosity ratio.
Visible cameras fail at night and thermal sensors fail under saturation, blur or loss of contrast, yet most RGB-thermal (RGB-T) detectors mix the two streams with fixed weights and cannot tell when one modality has become unreliable. TriNetra is a reliability-aware surveillance framework built around this problem. The proposed solution computes a frame-level Thermal Reliability Coefficient (TRC) from five label-free image cues, uses it to gate the thermal features of a dual-branch YOLOv8m detector whose visible branch, neck and head are frozen and COCO-pretrained, and passes the same score to a ByteTrack-based tracker that feeds a rule-based behaviour analyser. On the M3FD benchmark (2,940/630/630 split) the detector reaches 87.6% precision, 79.4% recall, 70.0% mAP@50 and 47.8% mAP@50:95 on the test split, with 17.0 M of its 42.9 M parameters trained. TRC stays near 0.78 on clean frames (standard deviation 0.012), decreases with the severity of thermal saturation and blur, reaching 0.53 and 0.69 at full severity, and is insensitive to RGB-thermal misalignment. With identical weights, the adaptive gate matches a fixed gate on clean data (70.0% versus 69.8% mAP@50) but keeps 43.6% mAP@50 when the thermal stream is corrupted, against 38.4%, 29.2% and 25.0% for a fixed gate, full thermal admission and a closed gate; the 5.1-point gain over the fixed gate has a 95% bootstrap confidence interval of +3.6 to +6.5 points. In tracking, the TRC-gated association performs on par with ByteTrack on a synthetic benchmark with exact ground truth and on 14 M3FD clips, and is slightly less stable under thermal saturation, so its measured benefit is confined to the detector. The limitations of the current evaluation are reported together with the results.
Current solutions for assessing the risk of anterior cruciate ligament (ACL) injury typically rely on expensive motion-capture labs that require substantial resource investment or subjective evaluations of specific athletic stress tests by experts. The Drop Vertical Jump (DVJ) and the Single Leg Hop (SLH) are two examples of such tests typically used to track progress in ACL rehabilitation. In this paper, we develop an unsupervised learning model that runs entirely on a smartphone for two tasks, based on an autoencoder architecture with multiple layers of graph convolutional networks, which utilizes pose estimation data to determine a person's injury risk status. Our model accurately predicts athletes at high risk of injury for both athletic stress tests, with average sensitivities and specificities of 78% and 78% for the DVJ, and 75% and 74% for the SLH. Our findings support the development of a widely accessible smartphone solution for real-time screening of ACL injury risk.
We propose a fixed-point acceleration method for optimization over probability measures, applicable to a variety of machine learning problems. We represent probability measures as pushforwards of a reference distribution through a neural network map and equip the parameter space with the induced pullback Wasserstein metric. This geometric structure allows natural gradient descent to be interpreted as a fixed-point iteration on a Riemannian manifold. We accelerate this iteration using Riemannian Anderson mixing method, which exploits historical residuals to capture approximate second-order information without forming Hessians. In the present parametric setting, the manifold is represented by Euclidean coordinates endowed with a point-dependent metric, simplifying retraction and vector transport. We evaluate the method on multimodal sampling, PDE-based inverse problems, aggregation dynamics, Bayesian logistic regression, and generative modeling. Across the tested tasks, Anderson mixing reduces the number of natural-gradient iterations and achieves competitive performance relative to SGD and Adam in terms of both loss-gradient evaluations and wall-clock time. These results suggest that fixed-point acceleration is an efficient tool for improving the computational efficiency of training on parametric Wasserstein methods.
Event cameras offer high temporal resolution and dynamic range for uncooperative spacecraft pose estimation, but models trained on synthetic event streams must generalize to the noise, background activity, and contrast variation of physical sensors. We present a comparative systems study of two independently developed approaches to synthetic-to-real, event-based 6-DoF spacecraft pose estimation. The first is a modular pipeline that combines learned keypoint detection and unlabeled target-domain adaptation with geometry-based pose recovery and temporal smoothing. The second directly regresses translation and rotation from global and cropped event representations using an apparent-scale cue, physics-motivated synthetic corruptions, and feature-consistency regularization. We evaluate both systems under the same SPARK 2026 hidden-test protocol on the real-event split of SPADES, with predictions for all test frames. The results reveal a component-wise reversal concealed by the aggregate challenge score: direct regression reduces orientation error by 22.7% (1.1767 to 0.9101 rad) and obtains a 13.4% lower composite score, whereas the modular pipeline reduces relative translation error by 78.7% (0.1335 to 0.0285). Archived configurations and a qualitative failure case identify plausible explanations for these complementary error profiles, without isolating their causes. These findings motivate a testable hybrid design that combines direct orientation estimation with geometry-constrained translation recovery.
Coronary ostia and centerlines are key reference points for automated analysis of coronary computed tomography angiography (CCTA), from surgical planning to intraoperative vessel tracking. However, the only public ostium annotations cover 77 non-gated aortic scans, not CCTA, while CAT08 and ASOCA (32 and 40 CCTA scans) mark the ostia only implicitly, as centerline start points. This work enriches ImageCAS, the largest public dataset for coronary artery segmentation, with ostium annotations for its 1000 patients and centerline graphs rooted at these new ostia, making it, to the authors' knowledge, the largest public dataset for ostium localization and the only one with centerlines following the official ImageCAS masks and starting at annotated ostia. Three annotators marked each ostium in the first 500 volumes; in the next 500, the candidates of a model trained on the first batch were corrected (human-in-the-loop). Six 3D localization models, trained on ImageCAS, CAT08 and ASOCA, were benchmarked on 58 held-out volumes (50 ImageCAS, 4 CAT08, 4 ASOCA). SwinUNETR-V2 and nnResUNet localized all ostia without failure (>5 mm error), with median errors of 0.70-0.87 mm. Trained on CAT08 and ASOCA alone, SwinUNETR-V2 fails on 34% of right and 53% of left ostia, whereas adding 250 ImageCAS volumes removes all failures. The centerlines were extracted by a deterministic, quality-controlled minimal-path procedure; on ASOCA, they cover a median of 99.5% of the reference length, with a median per-patient mean distance of 0.22 mm between matched reference points and centerlines. Annotations, centerlines, code, and weights are available at https://hal9000-lab.github.io/.
Digital twins of intensive care patients should update forecasts from new data and predict treatment responses, but few studies test whether routine records support either. We propose ICare-DT, a Transformer-based twin that updates a latent patient state hourly from new measurements without retraining. We trained it on 140,473 eICU-CRD stays to forecast vital signs crossing their training-set means. On test data, later forecasts beat the twin's own hour-6 forecasts of the same windows in all 12 settings (+0.073 to +0.153 AUROC). On validation data, controls that withheld or swapped the new hours traced the gain to the patient's own measurements. Without refitting, the model kept its gain on a second database (8 of 9 settings, +0.025 to +0.114 AUROC) in a prespecified evaluation of the previously analyzed MIMIC-IV test split. Refitted within MIMIC-IV, a twin state fine-tuned on clinical endpoints gave gradient boosting a significant gain for acute kidney injury (+0.0035 AUROC; hypotension +0.0010, not significant). To test response prediction, we built a benchmark that replaces the treatments in real records with simulated doses and injects responses of known size, visible only at measurement times. Ridge models supervised with injected effects recovered them from real records only through frequently measured variables (heart rate) read at their measurement times. We asked standard learners to predict these effects for a dosing regime no patient had received. No standard learner outperformed predicting zero effect at an out-of-support query. When told how the simulated responses were generated, a separate learner recovered the effects from the same records without seeing their true values (R2 0.30 to 0.40 at one effect size). Routine records support forecasts that improve with each patient's new data, and our benchmark is a testbed for models that learn how responses are generated.
RidgeFill shortens prefill by not computing most of a model's upper layers for the prompt. The lower layers run exactly up to a split; from the split layer's state a per-layer map predicts every later layer's input, and each late layer writes its cache from that prediction. The design follows YOCO and DeepSeek-V4.1-Flash, where the projection is trained into the model. RidgeFill retrofits it onto models that were never trained for it: the map is a ridge regression fitted once in closed form from one pass over calibration text, the layer's own projections run unchanged, and a chosen set of rows, the last few thousand tokens, and every decoding step run the full model. Nothing is trained and no token is dropped. Most of the work was in measurement, finding a repeatable methodology. Loss averaged over all tokens hides RidgeFill's error. Needle retrieval in the filled region, loss on tokens that depend on distant context, and splice tests that swap filled keys or values for exact ones show which component carries it: the keys on Llama-3.1-8B, half of it in their scale, and the values and the recurrent state on Qwen3.5-9B. On Qwen3.8-27B in a llama.cpp fork on an A100, time to first token is 1.25 to 1.31x faster at 16K to 120K tokens with the maps in VRAM; RULER changes by -1.2 and -1.4 points and LongBench v2 by -1.4; the 95 % intervals include zero but do not rule out losses of a few points. On Qwen3.8-Flash-Next in vLLM it is 1.50 to 1.60x faster than exact at 9K to 32K tokens, with RULER's needle tasks at 99.8 against 100.0 and perplexity on novel tokens 2.65 % higher [-0.02 %, +4.93 %]. On three 8 to 9B reference models, at the same split and tail as the identity fill, the fitted map retrieves 49.1 and 49.6 more filled-region RULER points on the two dense models (at that split Llama's loss is worse), and its long-document loss is +/-0.03 nats of the released SwiftKV checkpoint's.
Language-model systems can select prompts and parameter adapters repeatedly during deployment, using feedback to guide later choices. Earlier choices may change the context or environment inherited by later configurations. We study selection among preconstructed candidates and compare cumulative loss with the best fixed prompt--parameter pair used from the beginning. This excess loss separates into three terms: selection regret within the available family, the gap from restricting that family, and the benefit or harm of the actual deployment history. Selection is evaluated using the history each candidate would have produced if used throughout, which separates candidate quality from the effects of switching. When loss functions are fixed independently of selector randomness, past choices affect loss for only a bounded number of rounds, and every candidate's own-history loss is revealed, limiting switches yields sublinear expected regret within the selected family. We also quantify the costs and additional assumptions of independent probing and deployment-only feedback. Controlled experiments show that fewer switches can either lower or raise deployed loss, depending on whether inherited histories are harmful or helpful. With Qwen3.5-9B on Spider, text-only selection has lower within-family regret than joint selection, yet produces more failures because its candidate family excludes stronger configurations.
LLM-guided search loops propose a modified candidate, score it, and keep it if it scores better. When both candidates are re-scored at every comparison, as in the minibatch acceptance gates of prompt optimizers, keep-if-better is a reversible Markov chain if the score difference is logistic and the mutation operator is reversible, and its stationary law is the mutation equilibrium tilted by exp(beta f). For any continuous symmetric noise difference the same tilt is the stationary law of a small-step diffusion limit, with beta = 4F'(0); for a minibatch gate beta grows with the square root of the minibatch size. Caching the incumbent's score instead inflates the recorded score. We test the tilt as a prediction for LLM-guided program search, committing each prediction from calibration data before the search runs. The level after 150 steps rises with the minibatch size in six of seven settings, but its predicted value fails: on bin packing, search attains 62-88% of the predicted gain when the proposer edits the parent and 109-119% when it writes new heuristics. The attained fraction falls with the parent-child quality correlation of unselected mutation; a registered test on two new settings confirmed the direction, but not the quantitative agreement after a correction. Further registered tests found that runs started from a good program kept losing quality over 300 steps, more so from starts that search had selected, by a margin that passed its registered rule narrowly. Runs from different starts had not reached a common level, so whether the tilt describes the stationary law of LLM editing remains open. A registered test in prompt optimisation on frozen task-model scores failed: search exceeded the tilt, and the bin-packing relation did not transfer.
Generalized Bayes product partition models provide a probabilistic counterpart to loss-based clustering. They update a prior over partitions through an exponentiated clustering loss rather than a likelihood, so allocation uncertainty can be quantified without a full generative model for the data. However, their performance depends on the space in which the loss is evaluated. For high-dimensional observations, a squared Euclidean loss on the raw features can be dominated by irrelevant coordinates or fail to reflect cluster structure lying near a nonlinear low-dimensional manifold. We propose an extension in which an autoencoder and the partition are learned together, so that the space in which the clustering loss is evaluated is shaped by the clustering itself. Our generalized posterior combines a reconstruction loss, which keeps the low-dimensional representation faithful to the observed data, with a within-cluster sum of squares in the latent representation, which encourages cluster separation. Posterior computation alternates between Gibbs sampling over partitions and gradient-based updates of the autoencoder network, with the learning rate estimated jointly. We illustrate the approach through simulation studies and applications to four benchmark datasets.
We present PoseRieFlow, a compact flow-matching framework for text-conditioned generation of whole-body 3D human poses. Prior text-to-pose methods either neglect articulated hands or model rotations in Euclidean space despite their non-Euclidean geometry. PoseRieFlow instead formulates generation directly on the product manifold of SMPL-H joint rotations, learning a text-conditioned vector field that transports samples from an isotropic $\mathrm{SO}(3)$ Gaussian prior to the data distribution along Riemannian geodesics. A part-tokenized Diffusion Transformer aggregates the 52 joints into eight body-part tokens, allocating a dedicated token and nonlinear projector to each hand, and restores per-joint resolution through part-specific decoders, shortening the sequence while improving kinematic fidelity over per-joint tokenization. With only 21.6M trainable parameters, PoseRieFlow supports expressive SMPL-H generation with detailed hand articulation at a fraction of the scale of recent LLM-based generators. On PoseScript, it attains the lowest whole-body kinematic error among all hand-producing methods, with consistent kinematic gains from the Riemannian formulation over its Euclidean counterpart at every practical inference budget, while distributional and retrieval metrics remain comparable between them.
We consider the Multiscale Single-Index Model (MSIM), first introduced by Oymak and Soltanolkotabi (2021), as a stylized model for hierarchical feature learning with scale separation. Each layer extracts a shared single-index feature at one physical scale and passes it to the next, giving a tractable setting in which to study how deep architectures learn local multiscale representations. Under non-degeneracy and delocalization assumptions on the link function and planted features respectively, for the two hidden-layer case ($K=2$), we analyze joint online spherical SGD under MSE loss, which is a canonical regression objective, in discrete time and show that it achieves weak recovery from random initialization in $O(d\log^2 d)$ samples, followed by strong recovery to accuracy $\varepsilon$ in $O(d\log(1/\varepsilon))$ additional samples. The main technical challenge arises from the non-Gaussian learned features observed by the second layer. We address this challenge through a quantitative Gaussian comparison using delocalization, combined with sharp trajectory-level control of the coupled SGD dynamics. This work is a companion to Bruna (2026, arXiv:2607.03347), which studies recovery under a correlation objective for general $K$.
Particle image velocimetry (PIV) reconstructs a flow field from the motion of tracer particles but the reconstruction quality is bounded by how well the flow structure of interest is resolved in the images. The acquisition position is typically fixed by the operator before the measurement. We cast camera placement as a sequential decision-making problem and train a reinforcement learning agent to control a 6-DoF manipulator equipped with a camera, enabling it to locate, frame and resolve a hydrofoil wake in a water tunnel. The agent commands the camera pose and observes the scene only through the velocity field and uncertainty estimated from time-separated image pairs. It is trained entirely in a photorealistic simulation of our water tunnel, with wakes generated by Computational Fluid Dynamics (CFD) simulations of hydrofoils with varying profiles, positions and angles of attack. After zero-shot transfer to the real water tunnel, the policy reliably locates and frames the wakes of randomly placed hydrofoils. It resolves the wake at a higher resolution than a fixed camera view and with lower error in the measured flow statistics, in roughly half the time of a full scan and with far fewer image pairs.