Science & Mathematics

Motivated by ten years of Learning-Based Control Invited Sessions at the IEEE Conference on Decision and Control (CDC), this tutorial paper reviews key advances at the intersection of machine learning and control. We focus on methods that combine the flexibility of machine learning techniques with the structure and theoretical foundations of control to design autonomous systems that are capable, reliable, and safe. We first introduce core notions for establishing stability and safety guarantees, then review approaches that learn dynamics models to improve control under uncertainty, and finally discuss data-driven methods that directly synthesize or learn policies, including reinforcement learning, imitation learning, and Bayesian optimization. We further discuss representative applications and open challenges. The goal is to provide an accessible entry point to the field and to support continued progress toward reliable learning-based control in real-world systems. To support learning and practical exploration, we share implementations and illustrative examples along with our discussion, together with additional resources on our website: https://learning-based-control.github.io/tutorial/.

Tables in real-world documents, including scientific papers, financial reports, and statistical summaries, frequently use merged cells, multi-level headers, and sectioned layouts. Yet the lightweight formats LLMs handle best (Markdown, CSV) cannot express these structures, while expressive formats (HTML, LaTeX) impose excessive token cost and parsing complexity. To enable systematic analysis of this trade-off, we introduce a taxonomy decomposing table structure into six atomic features (F1-F6) and corresponding complexity levels (L1-L6), and construct STB (Synthetic Table Benchmark), a controlled benchmark with 1,089 tables systematically distributed across complexity levels. Using this framework, we propose LTEM (LLM-friendly Table-Enhanced Markdown), a formally specified, minimal extension of Markdown that explicitly encodes spans and hierarchical headers. Experiments across five state-of-the-art LLMs show that LTEM achieves accuracy comparable to HTML, offers a favorable accuracy-token trade-off relative to HTML and LaTeX, and produces substantially fewer invalid responses than LaTeX; for table generation, LTEM is comparable to MultiMarkdown though HTML is best. We release our taxonomy, benchmark, and format specification to support future research on LLM-table interaction.

Large language models (LLMs) demonstrate impressive emergent reasoning capabilities, yet they remain constrained by fixed model parameters and finite context windows. Even when augmented with static retrieval, they can produce statements that are unsupported by, or even contradictory to, retrieved evidence. This leads to hallucinations, difficulty incorporating up-to-date information, and failures to correctly interpret or reconcile sources. Recent work addresses these limitations by tightly coupling step-by-step reasoning with interactive search, treating retrieval as an action within an iterative agentic loop rather than a one-shot preprocessing step. This study reviews frameworks that implement such reasoning-search loops by interleaving planning, querying, retrieval, integration, verification, and stopping. We analyze these systems through four architectural axes: retrieval coupling, controller design, knowledge source, and grounding strictness. We separately treat the learning signal as a cross-cutting dimension because prompting, supervision, preference optimization, and reinforcement learning can instantiate the same architecture while producing materially different search, stopping, and grounding behavior. We further distinguish benchmark difficulty from RSA-loop demand and synthesize controlled within-study ablations and quality-cost deltas, avoiding invalid pooling across heterogeneous model backbones, retrievers, corpora, and evaluation protocols. Our goal is to clarify the landscape of reasoning-search-augmented LLMs and outline a unified perspective on the design choices shaping future research.

Sharpness-Aware Minimization (SAM) has established itself as a widely used method for training deep neural networks. Despite its popularity, existing convergence guarantees for SAM-type methods require smoothness, a restrictive assumption. Generalized smoothness conditions have recently been proposed in the analysis of gradient methods but remain underexplored for SAM. To analyze the effect of SAM's perturbation under generalized smoothness, we use relative gradient distortion to quantify how the sharpness-aware direction departs from the original gradient. Under $(L_0,L_1)$-smoothness, we show that this distortion can become unbounded near stationarity for SAM and at large gradients for its unnormalized variant (USAM), with examples where SAM cycles and USAM diverges. We then establish a necessary condition for uniform distortion control among perturbations along the gradient whose nonnegative multipliers depend only on its norm. Motivated by this condition, we propose Curvature-Scaled SAM (CS-SAM), which scales both the perturbation and the descent step by suitable curvature upper bounds, and prove that it uniformly bounds the distortion. Under both $(L_0,L_1)$- and $(H_0,H_1)$-smoothness, we establish deterministic $\mathcal{O}(1/T)$ rates for the best squared gradient norm on nonconvex objectives, last-iterate $\mathcal{O}(1/T)$ rates for the function gap on convex objectives with a minimizer, and linear convergence under the Polyak-Lojasiewicz condition. With zero perturbation, our guarantees recover the rates for gradient descent with $(L_0,L_1)$- or $(H_0,H_1)$-based step-sizes. Minibatch experiments on computer vision tasks demonstrate competitive performance for both variants, with the $(H_0,H_1)$ variant achieving the highest mean best-test accuracy in all four settings against tuned SAM and USAM with constant and cosine annealing schedules.

Acoustic "ping" testing of bullion is empirical: it compares a coin's ringing frequency with frequencies recorded for the same coin type, so it cannot assess a specimen absent from the reference library. This work replaces the comparison with an absolute measurement, computed from the measured resonance and geometry through a physical model rather than retrieved from a library. Free-plate flexural resonance is calibrated on five machined aluminium discs ($a/t=2.58$--$10.75$), recovering an empirical finite-thickness coefficient $β=0.895\pm0.047$ that reduces the worst-case departure from thin-plate theory from 8.9% to 0.75%. A fill factor, the ratio of a coin's displaced volume to its nominal cylinder, supplies the effective thickness that relief hides from calipers, extending the calibration to struck coins. The readout is the plate wave speed $c_{p}=\sqrt{E/ρ(1-ν^{2})}$, a material constant, conditioned on an assumed Poisson's ratio. On six struck 0.999 copper rounds not used in the calibration it recovers a Young's modulus of $119.1\pm6.7$ GPa, inside the accepted 110 to 128 GPa. The recovered wave speeds form distinct observed groups across the measured specimens, with the strongest independent validation provided by these copper rounds. The $(3,0)/(2,0)$ mode ratio falls below its thin-plate value in thirteen of sixteen specimens (one-sided sign test, $p=0.011$), as finite-thickness theory predicts. Weighing displaced mass to 0.1 mg rather than 0.1 g cut per-specimen volume uncertainty from 1.6% to 30% to 0.5% to 2.6% and shrank an apparent 11% design-dependent bias to a 4.7% residual on one deeply relieved silver design. The readout is now limited by tabulated elastic constants and the assumed Poisson's ratio, not by the acoustics, which are reproducible to 0.15%.

Random-Forest wrapper feature selection can use out-of-bag (OOB) predictions as a built-in validation signal, but the criteria that decide each forward step accumulate OOB estimation noise. We propose TOP-Gain (Truncated Out-of-bag Probability Gain), which scores a candidate feature by the mean sample-level increase in the OOB probability of the true class, with decreases truncated at zero. Under a simple noise model, truncation removes about two-thirds of the noise variance contributed by unaffected samples while preserving the signal, and it makes the ranking of candidate features markedly more reproducible. In a pre-registered benchmark on 26 OpenML-CC18 datasets, TOP-Gain achieved the best mean rank in area under the ROC curve (ROC-AUC), accuracy and Macro-F1 among 15 methods; it was significantly better than 13 of 14 baselines and matched the accuracy of VSURF with 21 times less single-core computation. Within an identical wrapper, it selected significantly more stable feature sets than net-gain, Brier, log-loss and accuracy criteria without loss of accuracy. A confirmatory study on 24 further datasets replicated the advantage over all baselines. The accuracy gains were broad rather than tied to specific dataset characteristics, and, as pre-registered, the stability gain grew as relevant features became sparser

Recent advancements in Vision-Language Models (VLMs) enable end-to-end visual grounding via language prompts and generative decoding, demonstrating largely improved zero-shot and open-vocabulary detection capabilities. As a result, VLMs are rapidly being deployed at the edge in safety-critical real-world systems. However, the physical adversarial robustness of edge VLMs has not been systematically studied, and the fundamental differences in output with modern object detectors create methodological challenges for fair evaluation. To compare the two families directly, we evaluate every selected representative model on one outcome: whether an adversarial patch worn on a person evades detection of the model. We report this by introducing a unified metric, conditional attack success rate (cASR), counted only on images the model still localizes under a matched gray occluder, and partition every failure into omission (no box), substitution (a box on the patch), and displacement (a box on neither). We benchmark the physical adversarial vulnerability of compact grounding VLMs against a range of object detectors, and find that the VLMs can be as vulnerable as the detectors. We disclose that failure mode is largely associated with the output format of a model rather than its architecture family. Of the three, only omission is visible to a downstream system; displacement and substitution return confident, well-formed boxes, making them potentially more dangerous failures. Further, we find that, under distribution shift, VLMs that primarily failed by omission instead shift to failing more by displacement/substitution. Thus, a grounding VLM can inherit the detector's vulnerability while showing the possibility to adopt more dangerous failure modes. Our code and data are available at https://github.com/ericliang1/physical-adversarial-robustness.

Research on why people contribute to open source software (OSS) and related open collaboration platforms spans more than two decades, but its findings conflict, and studies often treat the work people contribute and their intention to keep contributing as interchangeable. Drawing on self-determination theory and motivation crowding theory, we meta-analyze 41 studies. The main analysis pools 178 correlations of eight antecedents with contribution effort and continuance intention from 29 independent samples (N = 9,632). Seven antecedents relate positively to effort, all eight relate positively to intention, and each relates at least as strongly to intention as to effort. Contrary to a common assumption, intrinsic motivation is not more strongly related to effort than extrinsic motivation, but its gap between intention and effort is larger. Reputation relates to effort mainly on platforms with a reputation system, and we find no sign that monetary rewards crowd out enjoyment. The findings inform how platforms can turn contributors' intentions into work.

The scarcity of high-quality annotated visual data remains a critical bottleneck for autonomous-driving perception. Simulators provide training data at scale, but the limited realism of synthetic videos compromises perception performance in real-world applications. To address this limitation, we propose NeuralSRender, a sim-to-real video translation framework that enhances the photorealism of synthetic videos while maintaining geometric consistency with the source scenes. Built on a pretrained video diffusion transformer (DiT), NeuralSRender uses a lightweight projector to inject geometric and material priors from G-buffers, and LoRA enables parameter-efficient adaptation. The model is trained in two stages: it first learns G-buffer conditioning from synthetic videos with accurate G-buffers, then adapts to real-world appearance using real videos with estimated G-buffers. During the second stage, an additional LoRA module is trained while the projector and first-stage LoRA remain frozen to reduce interference from estimation noise. NeuralSRender introduces only 1.45\% parameter overhead and can be trained on consumer-grade GPUs with 24 GB of memory. To support training and evaluation, we introduce GenReal, a large-scale driving video dataset comprising synthetic and real-world videos with corresponding G-buffers. Experiments demonstrate improved photorealism with competitive geometric consistency. Training perception models on our translated videos instead of raw simulator renders improves detection $\mathrm{AP}_{50}$ on nuImages from 35.1 to 40.6 and segmentation mIoU on Cityscapes from 32.4 to 40.8. Our code, data, and model weights are available at: https://github.com/WHU-USI3DV/NeuralSRender.

We consider the problem of allocating indivisible goods to agents with additive valuations, under two classic notions of fairness and efficiency: envy-freeness up to any good (EFX) and Pareto optimality. While some of the earliest work on EFX showed that Pareto optimal EFX allocations may not exist if agents can have zero value for some goods, it has remained open whether the same is true when all values are positive. We present a simple instance in which every good has positive value to every agent, but no Pareto optimal EFX allocation exists. We then generalize to a family of instances showing that Pareto optimal $α$-EFX allocations may not exist for any $α> 2/3$.

Vision-language-action (VLA) navigation models translate visual observations and instructions into actions. Navigation success assesses whether an agent reaches the goal. However, reaching the goal successfully does not establish whether the model genuinely follows the instructions or relies on visual cues or navigation history. We introduce NavBind to diagnose instruction-action binding: whether changing the instruction influences the probabilistic distribution of the actions, with the navigation context fixed. We construct 3,252 route-fork contexts by recombining route-aligned instruction segments from R2R-CE and RxR-CE. Each context pairs full instructions that share the description of the route already traveled but specify different branches. Both are evaluated under the same agent state and navigation history. We compare generated local action sequences, the likelihoods of fixed reference action sequences under both instructions, and changes in visual attention and attribution. Across the evaluated models, higher reported navigation success does not imply that the model more faithfully follows the instructions.

Neural network models are increasingly constructed from synapse-resolution connectomes, and the same circuit is now available in reconstructions from other animals and pipelines. We do not know whether such models are dependent on the reconstruction they are built from, and whether connectome differences are biological or measurement errors. We studied the Drosophila head-direction circuit in nine versions: four flies (male CNS, hemibrain, FlyWire, BANC) and five variants of the same fly varying only by thresholds, proofreading or synapse detection. Using wiring-based correspondences validated by anatomical labels, we place all differences on one scale. A change of synapse detection within one fly changed the circuit more than halfway to the smallest between-fly difference on four distance measures; proofreading differences were smaller but depended on the metric, and left and right halves of one fly differed no more than random halves. Networks trained on each wiring to hold a cued heading developed near-perfect ring attractors, but their error increased from below 1 degree to 10-28 degrees when all weights changed by 1%. Training on each wiring did not transfer to any other connectome, including other versions of the same fly; refitting thirty cell-type gains, we repaired filtering-level differences but remaining error depended on wiring distance. Training with noise lowered precision and gave only partial transfer. In imaging data, the fly compass drifted gradually in darkness. Connectome-constrained models should report the reconstruction they were built on and be tested for robustness across reconstructions.

norregel asks language models for numeric values in Norwegian statutes, regulations and parliamentary decisions (NOK amounts, percentages, multiples of the National Insurance basic amount (G) and age limits), each at a stated date. The 916 items were extracted mechanically from Lovdata's open data, and each carries the dated history of its provision, so an answer can be classed as correct, outdated, wrong or uninterpretable. We report a first and a second preregistered run on the same items. In the first run (five models, listed publicly only after local analysis), H1, that outdated answers are more frequent for values that took effect after a model's cutoff, could not be tested in substance, and H2 and H3 were inconclusive; Opus 5.5 and Sonnet 4.6 answered 46.7% and 40.2% of the 880 primary items correctly. The second run was preregistered and published before any of its calls, and eight models were analysed. Its pooled primary test supported H1 under the preregistered decision rule (d = 17.8 percentage points, 95% interval [7.7, 28.9], p = 0.0001). In the preregistered sensitivity analysis S8, which counts as outdated only the most recent value that differs from the key, d was 3.9 [-3.6, 12.7] (p = 0.1754), an interval that contains 0. H1 was supported in every other preregistered sensitivity analysis, but S8 is the only one that gives both groups one target value, so we do not regard the support for H1 as robust. The share of outdated answers equal to that most recent value (H2) was 56.1% [46.6, 65.0], an interval that contains 0.5, and the pooled test of a lower share correct in Nynorsk than in Bokmål (H3) was inconclusive. Several models, among them Haiku 4.5, gave mostly uninterpretable answers. Items and keys are withheld; item IDs, per-answer classes, code and results are on Zenodo.

Speculative decoding uses a target model to verify a tree of draft tokens in parallel. We study whether the resulting next-token distributions can help select the next tree. For unrestricted target models, we show that guaranteed exact reuse requires a distribution computed at the next round's complete context. We characterize when retaining this distribution requires sacrificing accepted tokens and establish conditions under which this loss persists across decoding rounds. Across six targets, we find that reranking first-token branches with a separately computed distribution at the current context improves expected acceptance over draft ranking, especially with small tree budgets. Drawing the first token from this distribution before allocating the tree further improves expected acceptance over pruning a preselected tree, even at equal mean tree size. In our experiments, both selection rules also decode faster than draft ranking when the separate target pass overlaps standalone drafting. Our findings show that making target probabilities available before tree allocation can improve the efficiency of speculative decoding. Our code is available at https://github.com/js-lee-AI/TargetRows.

We prove that for every open $ U \subseteq \mathbb R^n $ the spherical projection of every gradient trajectory $θ(t)$, $t \geq 0$, of a definable $C^1$-potential $F \colon U \to \mathbb R$ has finite length and, in particular, converges (directional convergence). In other words, every gradient trajectory of a definable $C^1$-potential has finite total angular motion. Here, definable means definable in an arbitrary o-minimal structure expanding the real field. Notably, the gradient trajectory in this result is an arbitrary solution of the gradient flow differential equation (whose solutions may not be unique) with no further assumptions: The gradient trajectory may be unbounded and diverge to infinity or it may be convergent. The established theorem therefore provides affirmative answers to both the gradient conjecture at infinity for definable potentials and the definable Thom gradient conjecture. We apply our theorem to the training of deep neural networks (DNNs) to conclude that, in the case of definable and continuously differentiable activation and loss functions, the spherical projection of the DNN training flow must always converge (directional convergence).