Papers

Current approaches to aligning language models often make it hard to know what behavior is being rewarded or to change that reward in a targeted way. In particular, standard preference-based methods collapse multiple considerations into aggregate human judgments, obscuring what drives the resulting reward, while principle-based methods specify high-level values without fully operationalizing them. To address this gap, we develop a rubric-based framework to transform a general-purpose constitution into an interpretable and tunable reward model, using constitution-guided AI feedback to estimate initial weights for the constituent rubric items. We then reweight those dimensions to construct modified rewards for training. Across experiments on political alignment and safety-helpfulness tradeoffs, reweighting individual dimensions predictably changes targeted behaviors largely independently while navigating tradeoffs between conflicting alignment objectives. We show that the same framework can mitigate label bias encoded in preference judgments – including sycophancy and demographic bias – by reducing their influence on the training reward. Our results demonstrate that constitution-derived, interpretable rewards can translate high-level alignment principles into more transparent and controllable model behavior.

Reinforcement learning with verifiable rewards (RLVR) is often limited by insufficient exploration: difficult problems can yield uniformly incorrect rollout groups and therefore little learning signal. We show that such failures need not reflect missing capability. Instead, finite sampling often concentrates on a problem-specific dominant reasoning strategy while leaving alternative strategies already supported by the model unexplored. Moreover, the accessibility of these strategies evolves during RL: some are internalized into autonomous behavior, while others become difficult to elicit before being absorbed. Motivated by these observations, we introduce Problem–Strategy Rollout Allocation (PSRA), which treats unguided and strategy-conditioned prompts as competing exploration arms and uses Bayesian sequential allocation to direct a fixed rollout budget toward arms most likely to yield informative, non-saturated groups. A preservation objective keeps useful strategy-conditioned routes accessible while successful guided behaviors are transferred to the unguided policy. Across Qwen2.5 models from 1.5B to 7B and two RL training corpora, PSRA consistently improves reasoning performance, reduces dead saturation, strengthens out-of-distribution transfer, and maintains larger gains under increased inference budgets.

We study local eigenvalue statistics and dynamical (de)-localization properties for long-range Anderson models, including the fractional Anderson model. These systems are random Anderson-type perturbations of operators with long-range (non random) hopping terms of the form $|T(n,m)| \sim \|n-m\|^{-(d+2\beta)}$ for $\beta>0$, on the $d$-dimensional lattice. In the presence of a strong enough random potential, these models exhibit dense pure point spectrum with polynomially decaying eigenvectors, almost surely. We show that in this strong disorder regime, and for $\beta>d/2$, the local eigenvalue statistics centered at any $E$ in the deterministic spectrum is a Poisson point process with intensity given by the density of states function $n(E)$. Moreover, we prove that, at strong disorder, there is no dynamical localization for these models, verifying a conjecture of Disertori et al. We achieve this by establishing explicit, sharp lower bounds on the Green's functions fractional moments which imply that large moments of the position operator are infinite. Hence, these models exhibit Poisson eigenvalue statistics and dynamical delocalization, that is, the absence of dynamical localization. In particular, this shows that in dimension $d=1$, the fractional Anderson model, a random perturbation of the fractional Laplacian $(-\Delta)^\alpha$ with $\alpha\in (0,1)$, exhibits Poisson eigenvalue statistics and dynamical delocalization if the disorder is strong and the exponent $\frac{1}{2}<\alpha<1$. This is in stark contrast with what is known for the usual Anderson model that has only nearest-neighbor hopping.

Sparse video understanding often requires selecting a small set of visual evidence under a fixed frame budget. Most sparse selectors allocate this budget globally, allowing all frames to compete with one another. For temporally localized events, this can be a poor inductive bias: useful evidence is often distributed across pre-event context, the event itself, and post-event consequences. We study fixed-budget evidence allocation for localized event videos and show that globally competitive Top-$K$ selectors can preserve recognition and grounding while producing unstable event evidence. On DoTA Video Anomaly Recognition, Global Top-$K$ obtains competitive recognition and temporal grounding, but low selector-event alignment at $K=12$ (Frame AUC $51.5 \pm 10.8$). We propose dKFD, a phase-structured differentiable selector that reserves evidence capacity across pre-event, event, and post-event phases after full-sequence temporal encoding. Under matched-budget multi-seed evaluation, dKFD improves Frame AUC by $+30.97$ over a matched Global Top-$K$ selector at $K=12$ ($p<0.01$), while yielding modest but statistically significant recognition gains and comparable temporal grounding. Mechanism ablations show that phase supervision is load-bearing: removing it reduces Frame AUC to $41.1 \pm 12.0$ even when phase-partitioned budgets are retained. Downstream diagnostics on VRU-Accident show consistent gains over learned Global Top-$K$ across VLM families, while dense captioning reveals a boundary condition where uniform sampling remains competitive. These results support phase-structured allocation as a controlled fixed-budget approach for event-centric sparse evidence selection, not as a universal video summarization strategy.

Developmental screening videos show how children perform specific behaviors, but clinical records usually contain outcomes rather than descriptions of what happened. We present SemReward-VL, which learns to describe item-specific behavior from these outcomes. A vision-language model generates a description, and a frozen language model scores its agreement with the clinical outcome, relevance to the item, abstention on unrelated video-item pairs, and clarity. Group relative policy optimization (GRPO) updates LoRA adapters using this semantic reward. On 13,379 videos covering 41 items, the method improves aggregate accuracy and the number of items with recall above 0.5. Errors remain in temporal direction, duration, and age-specific interpretations of behavior.

Modern cloud applications are built from loosely-coupled microservices that coordinate through well-defined APIs to service user requests. A single API request often triggers multiple downstream API calls, some executed sequentially and others spawned asynchronously in parallel. To certify safe and secure inter-service interactions in such applications, security and compliance teams must enforce policies not only over nested call/return structure, but also over the parallel structure of an execution: which calls may run concurrently, how many parallel branches can be spawned, and what combination of branch outcomes are allowed. However, existing runtime enforcement mechanisms typically model executions as sequential or purely nested traces, and cannot capture the parallel structure introduced by asynchronous API calls. Furthermore, since application implementations may not be accessible to security and compliance teams, the policy enforcement mechanism should be decoupled from the service implementation. We introduce SafePar, a specification and monitoring framework for policies over concurrent microservice executions. A SafePar policy constrains both the order of API calls and their series-parallel structure. To support seamless deployments, each policy is compiled into a series-parallel visibly pushdown automaton, a new model of computation we propose in this work, that drives a distributed runtime monitor implemented on top of the servicemesh layer. Our technique is blackbox and non-invasive: it requires no access or changes to the service implementation. Our experiments show that SafePar enforces rich concurrency-aware policies while incurring only millisecond-scale latency overhead.

Proper orbital elements have been used in diverse ways to study the dynamical architecture of transneptunian objects (TNOs), providing insights into Solar System evolution and migration theories. In this paper, we present the numerically-computed proper elements of all known TNOs. We then compare their distribution with the distribution of proper elements of a large synthetic sample generated to study the secular behavior of TNOs in the Classical belt region in an effort to better understand certain observed features, particularly features appearing in the inclination distribution of these TNOs. Our analysis indicates the presence of an inclination-dependent instability in the Classical belt from 42 < a < 45 au, which we find is caused by the g+s-g8-s8 = 0 secular resonance. The coincidence of this instability with the previously-noted inclination boundary of the Cold Classical belt near proper inclination of Ifree = 4 (deg) could suggest that the primordial Classical belt may have originally been more continuous between 4 < Ifree (deg) < 6 than we observe today. However, our analysis to account for the impact of secular resonant instabilities finds a best-estimate of the inclination width of the primordial Cold Classical belt near 1.5(deg), well below 4(deg), and slightly thinner than previous works have suggested. We conclude that the inclination boundary of the Cold Classical belt is not set directly by secular resonance or instability, and that this belt is generally unaltered by resonance or instability since the end of planetary migration.

Worked examples are a powerful form of instruction, but learners must infer how the demonstrated steps were produced. A naive simulation of this self-explanation process can generate thousands of numerical explanations that reproduce one observed change without capturing its underlying procedure. We propose structure-mapping-guided self-explanation as a computational account of the cognitive biases that reduce search effort and make this inference tractable. The model represents mathematical expressions as typed relational structures and uses structure mapping to identify corresponding source and target regions. For each changed target value, the corresponding source region serves as an anchor: it guides abductive search toward structurally relevant values and operations before broader alternatives, yielding ordered, executable candidate procedures with inspectable source evidence. Across 70 mathematical transformations containing 120 changed numeric components, the model recovered every intended procedure. It returned the intended procedure before any other computation producing the same target value in 104 subproblems (86.7%), compared with a median of 32 (26.7%) across 100 unguided runs that tested candidate calculations in random order. Our proposed model also tested 93.8% fewer combinations of values and operations than unguided search before reaching the intended procedures. These results provide an efficient, interpretable account of how relational structure can guide procedural learning and a testable hypothesis about human self-explanation from worked examples.

Automatic differentiation (AD) lets neural networks compute derivatives of governing equations to machine precision, and this precision has made it the computational backbone of physics-informed machine learning. Yet exactness in the mathematical sense is not the same as fidelity to the physics. Here I argue that a derivative can be numerically perfect and still be the wrong derivative for the problem at hand, because AD, by construction, has no notion of the physical structure a solution must obey. Convection and its associated directionality, diffusion, and dispersion are only the most visible instances of a much longer list that spans all branches of computational science and engineering, including conservation, thermodynamic consistency, symmetry, symplectic structure, positivity, monotonicity, and boundedness. Recognizing this broader gap reframes how the field should build the next generation of PDE-driven neural surrogates.

Three-dimensional dense convolutional networks are the strongest performers on volumetric medical image segmentation, but their parameter counts scale poorly: moving a dense k x k convolution to k x k x k multiplies its weights by k. We observe that depthwise separable factorization does not share this penalty. Because the cubic kernel term applies only to the depthwise stage while the pointwise projection, which dominates the parameter count, is unchanged, the same architecture grows by 5 % from 2D to 3D where a dense convolutional U-Net grows by 200 %. We exploit this asymmetry to build a 3D U-Net with 536,990 parameters, 24x fewer than an identical dense 3D U-Net. On MSD Task03 Liver (the Medical Segmentation Decathlon liver task, derived from LiTS), evaluated per case under five-fold cross-validation over all 131 public volumes, the model reaches a tumor Dice of 0.577 (95% CI [0.518, 0.633]) and a liver Dice of 0.947 (95% CI [0.941, 0.952]). Its liver Dice exceeds previously reported performance. Its tumor Dice exceeds their low-resolution configuration (0.4701) by 0.107 and their 2D configuration (0.5394), at approximately one twenty-fourth of the parameters and roughly half the in-plane resolution. Trained under identical conditions on a common held-out split, it exceeds a dense 3D U-Net on liver by +0.031 Dice (paired p = 0.006) and on tumor by +0.041 (95 % CI [+0.005, +0.081], paired p = 0.056), suggesting the factorization also acts as a regularizer in the small-data regime characteristic of medical imaging. We further show, on both LiTS and a 2D endoscopy benchmark, that a large fraction of the network's learnable spatial filters can be replaced by fixed shifts at no cost in accuracy, but that replacing all of them is measurably worse, the placement of spatial capacity matters more than its total amount.

Nutrition estimation is a fundamental task in consumer diet tracking, clinical dietetics, chronic disease management, sports and hospital nutrition, and broader food computing systems. The existing approaches have progressed along two largely separate axes, vision models that rely on calibrated RGB-depth captures and ingredient-aware methods that use textual cues but use limited multimodal fusion. We introduce NutriVision, an end-to-end framework that leverages visual geometry and ingredient semantics to estimate calories, mass, fat content, carbohydrates, and protein from a single RGB image and an optional ingredient list. It obtains the unavailable depth modality using DepthAnything-V3 and encodes ingredient descriptions using CLIP. It integrates three complementary mechanisms: (1) an Ingredient-Conditioned Frequency-Aligned Fusion Module (IC-FAFM), which uses textual guidance to reweight and align RGB-depth frequency components; (2) an Ingredient-Aware Mask-based Prediction Head (IA-MPH), whose gating and channel masks are conditioned on food identity; and (3) modality-specific Internal Semantic Modeling (ISM) blocks. On the Nutrition5k dataset, NutriVision achieves a mean PMAE of $\mathbf{13.60\pm0.10\%}$, outperforming our IGSMNet implementation by $0.89$ percentage points and OmniFood8k by $2.90$ percentage points (both $p<0.001$). The module-level ablations identify the ingredient-aware prediction head as the primary architectural contributor, improving mean PMAE by $1.50\pm0.17$ percentage points ($p<0.001$). These results demonstrate that ingredient-conditioned prediction and frequency-aware RGB-depth fusion provide measurable gains for single-image nutrient estimation. More broadly, NutriVision offers a practical route toward nutrition-assessment systems that exploit geometric and semantic cues without requiring specialized depth-sensing hardware

Radiological similarity depends on disease relationships and on fine details such as laterality, lobe, severity, size, and certainty. Broad biomedical similarity can overlook these qualifiers, particularly when several attributes vary together. We introduce QureRadEmbed, a 4B radiology-aware encoder trained with two complementary signals: RadSim supplies deterministic, attribute-decomposed ranking targets, while RadThought aligns reports with hierarchical evidence and reasoning descriptions. A three-stage curriculum combines these signals with report triplets, finding perturbations, and single- and cross-attribute contrasts. The final model achieves 0.996 mean ordering accuracy across ten controlled synthetic attributes and raises Spearman correlation with the designed joint-attribute targets from 0.501 to 0.976. On external findings-to-impression retrieval, Recall@1 reaches 10.5% on Open-I, 12.4% on testing XR, and 42.9% on testing CT, compared with 6.6%, 5.7%, and 31.4% for its backbone. Frozen embeddings support finding extraction with only 100 labeled testing-XR reports (macro-F1 0.481 versus 0.412 for the backbone). Whole-report comparison costs 8.8 seconds per 1,000 pairs in our benchmark, versus 2,755.1 seconds for the generative evaluator GREEN. Sentence-level comparison improves sensitivity to local discrepancies, although generative evaluation remains stronger on several expert-rated and subtle-error tasks. The results support reusable radiology-aware representations for search, structured report indexing, and efficient report comparison.

High-performance GPU kernels are essential to modern machine learning systems, yet automatically generating kernels that are both correct and efficient remains challenging. Existing LLM-based approaches face two major limitations: the scarcity of high-quality training data aligned with the model's current capabilities, and the inherent trade-off between kernel correctness and performance. To address these challenges, we propose KernelZero, a co-evolution framework that continuously improves GPU kernel generation through two specialized models: a Proposer that generates Torch modules from API sets and a Coder that translates them into CUDA or Triton kernels. KernelZero uses a frontier-driven module generation mechanism to continuously produce capability-aligned training modules based on the Coder's current weaknesses. It further introduces Correctness-Aware Group Relative Policy Optimization (CA-GRPO), which optimizes performance only after correctness becomes sufficiently reliable. By alternating the optimization of the Proposer and Coder, KernelZero forms an automatic curriculum that enables targeted and training-efficient capability improvement. Empirically, KernelZero-7B surpasses Claude-4.5-Sonnet on CUDA and DeepSeek-V4-Pro on Triton. On KernelBench Level 1 and 2, it achieves CUDA pass@1 scores of 75.8% and 69.6%, respectively, with pass@10 reaching 100% and 97%. On Triton, it achieves pass@1 scores of 77.2% and 72.5%, respectively.

In this work, we consider algorithmic harms that may arise as generative models are incorporated into machine learning platforms. We argue that existing harm taxonomies and threat models require extension to (1) address novel causal drivers of well-studied representational and quality-of-service harms; and (2) anticipate and mitigate endogenous harms, such as sanitization, which may arise when system inputs are misaligned with the system designer's objectives, or the generative model's inductive priors. To this end, we introduce an expanded taxonomy of algorithmic harms associated with the use of generative models in non-conversational recommendation systems. In addition, we offer a causal analysis of how problematic subsets of the (input, output) joint distribution can arise, in an effort to inform harms detection and mitigation efforts.

The Baroclinic Annular Mode (BAM) strongly influences extratropical circulation, yet its role in the global hydrological cycle remains unclear. Using ERA5 reanalysis and a global atmospheric river (AR) database, we show that BAM systematically reorganizes AR occurrence and extreme precipitation in both hemispheres. During high-BAM states, AR frequency increases along the flanks of major storm tracks and decreases near their climatological cores, redistributing preferred AR corridors. Relative AR-frequency changes locally exceed 50%, with the most zonally coherent patterns over the Southern Ocean. Extreme precipitation varies correspondingly, with 99th-percentile precipitation occurrence increasing by more than 50% across broad poleward storm-track regions. A large fraction of these extremes coincide with ARs, and AR-associated extreme precipitation shows similar BAM-related modulations. Low-BAM states show broadly opposite anomalies. These results identify BAM as a key mode linking large-scale circulation to global moisture transport and hydrological extremes.

The exploration of topological states has emerged as a vibrant frontier across diverse physical systems. Among these, the Möbius strip stands out as a canonical structure that has recently inspired intriguing optical physics.In this work, we extend this concept into the high-dimensional realm by using an optical analogue-the optical Möbius snail. Specifically, employing a skyrmionic beam as the input field, tight focusing yields a continuous family of Möbius strips that exists in three-dimensional space, giving rise to a snail-like polarization topological texture. Furthermore, we demonstrate full-field polarization tomography and achieve switchable control of this optical snail texture by tuning the Skyrme number of the incident skyrmionic beam. Our findings establish a direct bridge between low- and high-dimensional Möbius geometries, opening a new platform for exploring complex spatial topology and tailored light-matter interactions.

We study in this paper an unsupervised, two-step, model-informed deep learning framework for solving the phaseless inverse scattering problem. The objective is to reconstruct a compactly supported function that characterizes a scatterer from boundary measurements of the modulus of the total wave corresponding to multiple incident waves. In the first step, the phaseless data are transformed into an imaging function that is directly related to the underlying scatterer. Motivated by the contrast source method, we derive a coupled system of model equations using the Lippmann-Schwinger integral equation and a spectral-based equation involving the imaging function. In the second step, the unknown scatterer and contrast source function are each parameterized as independent feedforward neural networks, which are trained simultaneously at each iteration using the derived system of model equations. The Lippmann-Schwinger integral equation enforces the underlying physics as a model constraint, while the spectral-based equation incorporating the imaging function supplies geometric information on the shape and location of the unknown scatterer. The resulting framework achieves accurate and efficient reconstructions while maintaining robustness to measurement noise. Furthermore, transforming some aspects of the problem to the spectral domain enables an effective reduction in the computational cost, allowing us to recover the unknown scatterer quickly. Numerical experiments in both two- and three-dimensional settings demonstrate the effectiveness, stability, and practical potential of the proposed approach.

Time-to-event outcomes are often collected together with auxiliary outcomes that may provide additional information about baseline risk. We develop a semiparametric approach for incorporating such information into Cox regression without specifying a joint likelihood. The survival outcome follows a Cox proportional hazards model and a continuous auxiliary outcome follows a partially linear model, with separate nonparametric baseline covariate effects linked through a quadratic penalty. When these effects coincide and the outcome scores satisfy the information identities and a first-order orthogonality condition, we derive the sandwich covariance of the penalized estimator and show that, for any fixed penalty level, the asymptotic variance of the Cox regression estimator is no greater than that under separate estimation. We further characterize departures from the shared-effect setting. Local differences of order \(n^{-1/2}\) induce an explicit mean shift in the limiting distribution, yielding a direct bias–variance trade-off, whereas fixed differences generally alter the population target under nonvanishing penalization. These results motivate an adaptive penalty that borrows information when the fitted covariate effects are close and approaches separate estimation when a persistent difference is detected. Simulations and a real world data analysis demonstrate the validity and effectiveness of the proposed method.

By eliminating the win condition in the game of Connect Four and extending the board to infinite height, a rich state space of positions is obtained. We investigate the number of positions reachable on an $n$-column board after $k$ color-alternating moves. For fixed $k$ we demonstrate polynomiality, derive a partial formula for the polynomial coefficients, and precisely characterize the asymptotic behavior as $n \to \infty$. We then turn our attention to the fixed-$n$ case and show that, under a natural addition operation, positions reachable in an even number of moves form a monoid with a highly symmetric finite generating set; by examining certain free submonoids, we bound the exponential growth rate as $k \to \infty$.

Let $u=(u_n)_{n\ge0}$ be a binary sequence, and define \[ X_0=1,\qquad X_{n+1}=2X_n+u_n \qquad(n\ge0). \] Let $A_u$ be the set of all nonempty finite subset sums of the sequence $(X_n)$, and let $L_u(N)$ denote the maximum length of an arithmetic progression contained in $A_u\cap[1,N]$. We prove that there are absolute constants $c>0$ and $N_0\geq 1$ such that, for every binary sequence $u$, \[ L_u(N)\ge \exp\!\left(c\sqrt{\frac{\log N}{\log\log N}}\right) \] for all $N\geq N_0$. Moreover, if the random variables $u_n$ are independent and uniformly distributed on $\{0,1\}$, then, almost surely, \[ L_u(N)\ll_u N^{2/3}\exp\!\left(C\sqrt{\log N\log\log N}\right), \] where $C>0$ is an absolute constant. Furthermore, every eventually periodic binary sequence satisfies $L_u(N)\gg_u N^{1/2}$.

Contemporary neural inference architectures rely on dense floating-point weight matrices stored in high-bandwidth memory (VRAM), incurring severe memory-wall bottlenecks and preventing native execution inside deterministic virtual machines like the Ethereum Virtual Machine (EVM). Verifying termination and arithmetic invariants for recursive dynamical systems over continuous domains is generally undecidable in the Blum-Shub-Smale model. Here, we present the formal verification and bare-metal empirical validation of WERR (Waves & Errors) and Phase III Orbital Error Dynamics (OED), a non-tensor decision paradigm that procedurally synthesizes non-linear decision boundaries on demand from a 24-byte coordinate seed $\Theta = (c_x, c_y, \text{zoom})$ along the boundary of the Mandelbrot set ($\partial\mathcal{M}$). By projecting the recurrence $z_{n+1} = z_n^2 + c$ onto the modular residue ring $\mathbb{Z}/9\mathbb{Z}$ and the fixed-point domain $\mathbb{Q}_{16.16}$, we establish ten machine-verified theorems in Lean 4 (v4.34.1) with Mathlib4 and zero unproven conjectures (sorry): proving $\mathcal{I}_3 = \{0,3,6\} \subset \mathbb{Z}/9\mathbb{Z}$ ideal closure, universal fuel-bounded halting ($\le 9$ and $\le 12$ steps), absence of $\mathbb{Q}_{16.16}$ square overflow below $2^{63}-1$, non-constant boundary escape sensitivity, and a parametric EVM gas bound ($\le 22,557 \le 24,000$ gas). Evaluated on a 40-core Dual Intel Xeon server, the vectorized 36-iteration CPU kernel processes 100,000 decisions in 6.49 s (15,397 decisions/s, 0 Bytes VRAM, 15.15x speedup), while a sigmoidal outlier gate suppresses 100.00% of adversarial spikes while preserving 89.60% of clean baseline signals.

Large language model (LLM) assistants can now search the web and consult external sources while completing user requests. These sources can provide useful evidence, but they can also introduce additional content into the model's context. Can such passive exposure steer a decision even when the added content provides no reason to change it? We examine the stability of model decisions on the same tasks with and without such external content. Across all open-weight and closed-weight models we test, exposure systematically shifts decisions, with effects reaching nearly 50 percentage points in closed-weight models. The same pattern appears with real-world online opinions. The influence also extends beyond subjective preferences. Such exposure can steer models toward choices that violate explicit user requirements and increase their acceptance of false claims. In short, what enters an LLM's context can influence its decision even when it should not determine it.

This paper develops a theory of accommodation traps in workplace hierarchies. Workers with weak outside options face a higher relational cost of appearing unavailable, resistant, or difficult, and so adopt accommodative communication (extra deference, softened boundaries, visible flexibility) to preserve the employment relationship. This short-run strategy is also an informative signal: a friction-minimizing supervisor rationally infers that an accommodating worker is less likely to resist, and assigns that worker the invisible, low-promotability work. The signal harms the worker who sends it. Unlike agents in ratchet-effect models, who conceal information that would invite heavier demands, dependent workers reveal their low refusal cost, because the relational value of accommodating rises with dependence. The resulting inequality requires no productivity difference and no taste for discrimination, and the supervisor's beliefs are correct, so correcting beliefs cannot remove it. When visible work builds outside options and invisible work erodes them, the allocation becomes self-reinforcing, and even workers who start out identical are locked into unequal roles with probability one. The equilibrium is privately rational for every party yet socially inefficient whenever diminishing returns to outside options outweigh the supervisor's friction cost. Attaching recognition to invisible work, rotating it by rule, or limiting managerial discretion each weakens or breaks the link from communication to assignment that sustains the trap.

Chu proved that a symplectic structure $\omega$ on an even-dimensional Lie algebra induces a left-symmetric structure which is defined by $\omega(x\scriptstyle{\Delta}_{\omega} y,z)=-\omega(y,[x,z])$. El Bourkadi and Mansouri proved that a cosymplectic structure on an odd-dimensional Lie algebra $\mathfrak{g}$ induces the left-symmetric structure, which is defined by using a linear isomorphism from $\mathfrak{g}$ to $\mathfrak{g}^*$ associated with the cosymplectic structure. In this paper, for a non-degenerate bilinear form $\phi$ on a Lie algebra $\mathfrak{g}$, we give a necessary and sufficient condition for the product $\scriptstyle{\Delta}_{\phi}$ on $\mathfrak{g}$ defined by $\phi(x\scriptstyle{\Delta}_{\phi} y,z)=-\phi(y,[x,z])$ to be a left-symmetric structure. We also prove that the left-symmetric structure $\scriptstyle{\Delta}_{\phi}$ is complete if and only if the Lie algebra $\mathfrak{g}$ is unimodular. Moreover, we formulate the notion of double extension for non-degenerate bilinear forms and prove that a certain class of non-degenerate bilinear forms is obtained by double extension.

In this paper, we propose an unsupervised, two-step model-informed deep learning framework for solving the inverse source problem. In the first step, boundary measurement data are transformed into an imaging function that encodes information about the shape and location of the unknown source. Leveraging this information, we derive a Fourier-based model equation in the spectral domain that relates the imaging function to the Fourier coefficients of the source function. In the second step, this model equation is incorporated into the training of a model-informed neural network to recover the parameters of interest. The proposed approach enables fast and accurate reconstruction of the source function while maintaining robustness to noise. The effectiveness of the method is demonstrated through numerical experiments in both two- and three-dimensional settings. For the two-dimensional case, we further compare our approach with the traditional least-squares method to validate its computational efficiency and reconstruction accuracy.

Large language models (LLMs) are increasingly used to drive scientific discovery. Understanding how LLMs make decisions from new data and memory of the literature is vital before trusting them to design experiments under tight experimental budgets. However, their decision strategies are invisible in the current performance scores used to evaluate research agents. Here, we benchmark five frontier LLMs in a Bayesian Optimization setting against published statistical baselines on seven combinatorial datasets spanning protein engineering, reaction optimization, molecular design, peptide self-assembly, and catalysis. Performance is paired with direct measurements of model beliefs and actions, enabling highly resolved behavior analysis. A prompt ablation that progressively strips context separates memorization from chemical reasoning and from bare categorical optimization. Prior chemical knowledge helps in expectation, but with high variance and occasionally even harms performance. No configuration tested decisively beats a mean statistical baseline across domains. Belief-movement and Martingale diagnostics, corrected here for a measurement-noise bias that mislabels rational agents as irrational, show that models overreact to incoming data rather than entrenching on their priors in the contexts studied here. Interestingly, while LLM actions are exploitative, models sincerely intend to explore and consistently act on that intent. This failure is a competence gap arising from context-stickiness. Removing in-context history restores exploration, indicating that priors and data must be decoupled to achieve effective LLM-driven discovery.

Speech therapists often face difficulties diagnosing impairments due to the lack of efficient tools for transcribing speech into the International Phonetic Alphabet (IPA). This work addresses this challenge with Broca, a Conformer-based deep learning system pretrained on 8 days of adult speech and fine-tuned on a 165-minute dataset of Italian child speech collected through a range of standardized diagnostic tests for children aged 3.5-6.5. Broca was optimized to handle phonetic variability in children's speech, including tone, accent, and speech errors, and achieved a state-of-the-art weighted Phoneme Error Rate of 13.36% on Italian speech. Remarkably, this performance was obtained using less than three hours of child-specific data, underscoring the model's efficiency and robustness in low-resource clinical settings. This work demonstrates that accurate, vocabulary-independent speech-to-IPA transcription can be achieved with minimal data, paving the way for more accessible, data-efficient tools to support speech assessment and diagnosis.

The hyperfine structure splitting for the triplet $2^{3}S(L = 0)-$state in the two-muonic helium ${}^{3}$He $\mu_{2}$ atom is determined to high accuracy. Such a structure arises as a result of hyperfine (or spin-spin) interaction between the triplet two-muonic shell and non-zero spin of the central helicon nucleus. Our result for the hyperfine structure splitting is $\Delta \approx 5.1623403103010 \cdot 10^{7}$ $MHz$, where the standard uncertainty has been evaluated as $\pm 10$ $Hz$.

Market microstructure studies how trading rules turn orders into prices and allocations. Those rules have been rebuilt repeatedly: for floor traders, electronic limit order books and high-frequency trading, batch auctions and dark pools, blockchains run by automated market makers and block builders, and now AI agents that discover, pay for, and compete over resources. This survey traces that evolution through one question: can a market allocate scarce goods efficiently and fairly without participants revealing everything they know and want? Each technological shift moved the binding constraint of market design from trader rationality to speed, to control over transaction ordering, to the dimensionality of what participants can report. Impossibility results persist; only their cost moves. We review evidence on high-frequency trading, trading venues, automated market makers, extractable value and algorithmic collusion, and identify allocation as the missing layer of the agent-commerce protocol stack.

I introduce a robustness criterion for settings where players may disagree about the distribution over signals induced by endogenously chosen information. In the spirit of Hansen and Sargent (2008), an information choice is evaluated by its worst-case payoff over beliefs within an $\eta$-entropy ball around the signal distribution it induces. I apply this formulation to buyer-optimal learning in bilateral trade (Roesler and Szentes, 2017). If trade is always efficient, disagreement raises the price and twists the buyer's demand curve while preserving full trade. When trade may be inefficient, the same characterization holds conditional on trade with an endogenously amplified disagreement level.