Papers

Large language models (LLMs) show considerable potential in simulating human attitudes and preferences. Prior work finds that LLM-generated responses can compress the range of attitudes found within populations and misrepresent particular subgroups in ways that vary across models and topics. We introduce Population Fidelity, an evaluation framework that distinguishes key conditions required for a set of LLM-generated responses to represent a population. It incorporates three dimensions: group-level accuracy, the amount of between-group variation, and the structure of that variation. We demonstrate the framework's utility in two ways. First, we reproduce a prior study of "machine bias" in LLM survey responses and apply the framework to its models and more recent ones, showing that poor representation reflects not only insufficient between-group variation but also variation assigned to the wrong groups. Second, we evaluate one proposed approach to improving models' population representativeness: cultural fine-tuning. We find that cultural fine-tuning can improve alignment with the survey center without improving the representation of within-population differences, a distinction that measures of aggregate agreement do not capture. We argue that representing a population requires models to reproduce several features of human attitudinal variation simultaneously. Our framework organizes these features and provides reusable code, data, and trained models for evaluating population fidelity across substantive domains and assessing proposed alignment methods.

Closed-form recourse moves a rejected user along the unit gradient $\hat g$ of the classifier score $f$ by the promised distance $d_p=|f(x)|/\|\nabla f(x)\|$, at which the linearized score reaches zero. We ask when this one-shot step succeeds and what additional model queries change. To leading order the step ends on the favorable side exactly when the path curvature $\kappa=\hat g^\top\nabla^2 f(x)\,\hat g$ is nonnegative. Across 80 shallow models, the fraction of rejected users whose step ends there and the fraction with $\kappa\ge0$ correlate at $r=0.985$, although on Fashion-MNIST the first falls below the second by 8.2 points on average. No rule that uses only the score value and gradient can be valid for every score with path curvature bounded by $K$ without overshooting some by order $Kd_p^2/\|\nabla f(x)\|$. When the curvature is also Lipschitz and the step is short, one evaluation of $f$ at the promised point attains the minimax rate among deterministic one-query rules that know the curvature bound and its Lipschitz constant, and split-conformal calibration makes such a rule reach the first crossing or abstain with probability at least $1-\delta$. Training with an asymmetric curvature penalty lets 99-100% of paths cross within the promised step on undershoot-prone shallow data, at about 4-22 times the overshoot of symmetric penalties (Fashion-MNIST, COMPAS). Because $\kappa$ and $d_p$ depend on how the score is scaled, part of this gain can be a longer promised step, and at matched validity a smaller audit of briefly trained models finds no uniform advantage over tuned inflation. Where a per-user line search along the ray is affordable, it is exact to grid resolution and preferable.

Protein abundance alone does not capture the molecular diversity generated by protein processing and post-translational modification, yet most single-cell protein assays do not resolve these proteoform states. Here, we develop RCAmp-scWB, a post-separation amplification strategy that performs rolling-circle amplification directly within the polyacrylamide gel after single-cell protein electrophoresis. Reaction-transport modeling identifies a balance between reagent access and confinement of the template-associated amplification product that supports signal amplification while retaining the electrophoretically encoded spatial readout. Using purified protein standards, RCAmp-scWB produced a 4.0-7.8-fold steeper concentration-response slope than conventional single-cell western blotting. Across six human cancer cell lines, RCAmp-scWB quantified protein abundance and resolved distinct Vimentin and PD-L1 proteoform states whose relative abundance and single-cell distributions were not captured by total protein measurements alone. Extension to individual small extracellular vesicles further revealed source-dependent shifts in Vimentin proteoform composition despite comparatively similar abundance of one major Vimentin species. By separating electrophoretic molecular discrimination from signal amplification, RCAmp-scWB enables proteoform-resolved analysis of heterogeneous cells and small extracellular vesicles.

Action chunking provides temporal abstraction in reinforcement learning by selecting short action sequences instead of individual actions, but many existing approaches face two limitations in high-dimensional robotic control. First, many rely on value functions over action chunks, which can be difficult to learn as action dimensionality and chunk length grow. Second, executing chunks open-loop removes within-chunk feedback, limiting reactivity in contact-rich tasks. We present Action Chunking PPO (ACPPO), a PPO extension that uses a chunked actor while retaining a standard state-value critic, thereby avoiding chunked Q-functions. We further propose ACPPO-Corr, which augments the chunk planner with a stepwise feedback corrector that adjusts planned actions online within each chunk. Across 25 simulated robotics tasks from IsaacGym and Bi-DexHands, spanning locomotion, arm manipulation, and dexterous hand-object interaction, ACPPO-Corr achieves the strongest aggregate performance among evaluated methods and performs best on both decision-frequency-sensitive and decision-frequency-neutral task subsets. Ablations show that moderate chunk lengths work best and that corrector regularization is important for balancing chunk-level planning with local feedback. These results suggest that action chunking can be effective in online PPO when chunk-level planning is paired with closed-loop correction. The code is available at: https://github.com/hshhahn/ACPPO.

We introduce a new family of recursively constructed sparse matrices, termed Fractus matrices, and investigate their use in constructing low-density parity-check (LDPC) codes. Generated through a self-similar recursive process, these matrices yield regular sparse parity-check matrices while preserving key structural properties across successive iterations. This recursive structure enables an efficient encoding algorithm with computational complexity that is nearly linear in the block length. Decoding is performed using standard iterative message-passing algorithms, thereby retaining the low-complexity decoding characteristic of LDPC codes. The proposed construction produces Tanner graphs with girth six and guarantees a minimum Hamming distance of at least $\ell+1$. We establish several algebraic properties of Fractus matrices, including sparsity, regularity, recursive decomposition, and symmetry under the flip-transpose operation. In addition, we show that the family of Fractus matrices admits a natural lattice structure and that the associated LDPC codes inherit corresponding lattice-theoretic properties. These results establish a connection between order theory and coding theory. Overall, the proposed framework integrates recursive matrix constructions, efficient encoding, graph-theoretic analysis, and lattice theory into a unified algebraic approach to the design and analysis of scalable LDPC codes.

Lowest-energy excitons are usually expected to have nodeless $1s$-like envelope wavefunctions. We show that band topology can obstruct this expectation. The exciton envelope wavefunction is a section of the valence-conduction transition bundle, whose topology can enforce momentum-space zeros, with their parity or signed total index fixed by the corresponding characteristic class. We exemplify this behavior in a minimal $PT$-symmetric three-band model with a rank-two transition bundle characterized by Euler number $\nu^e=2$. By directly solving the Bethe-Salpeter equation with both contact and Rytova-Keldysh interactions, we find that the lowest exciton contains two zeros, each with index $+1$, and is less strongly bound than its topologically trivial counterpart. We further classify topology-enforced exciton nodal structures for real and complex transition bundles in dimensions $d \leq 3$. Our results establish the topology of the transition bundle as a direct constraint on exciton wavefunctions and spectra.

The growth of distributed energy resource (DER) integration introduces greater variability in distribution system operating conditions, creating a need for comprehensive datasets for developing and evaluating data-driven fault diagnostic methods. This paper presents DER-Fault, a simulation-based dataset generated in OpenDSS using the Iowa 240-bus distribution system with photovoltaic (PV) generation, electric vehicle (EV) charging, and vehicle-to-grid (V2G) operation. To capture annual load variability while maintaining a manageable number of simulation cases, 60 representative operating conditions are selected from 8,760 hourly load profiles, covering peak, off-peak, transition, typical weekday, and typical weekend conditions. Six DER scenarios with varying PV and EV penetration levels and V2G participation are considered. The dataset includes normal operation and ten short-circuit fault classes, with varying fault resistance. Pre- and post-fault voltage and line-current phasor measurements are recorded at selected measurement locations, resulting in 19,800 simulation cases. Technical validation demonstrates broad coverage of annual loading and DER operating conditions, distinct phase-specific responses corresponding to the simulated fault types, and a consistent reduction in voltage-phasor disturbance with increasing fault resistance. The resulting dataset provides a structured resource for developing and evaluating machine-learning and other data-driven methods for fault detection, classification, and localization in DER-integrated distribution systems.

We present OLIVE (OnLine InterVEntion). At each iteration, the evolving student policy generates a new prefix, the teacher continues it autoregressively, and the student is updated using cross-entropy computed on the teacher-generated tokens. Each design choice targets a corresponding limitation of existing distillation methods: (1) sequential covariate shift in offline supervised fine-tuning (SFT) on fixed teacher trajectories, (2) fragmented supervision under prefix failure in token-level on-policy distillation (OPD), and (3) the need for access to teacher token probabilities in distribution-matching distillation. OLIVE achieves higher reasoning performance than OPD (with a top-16 KL approximation) at comparable GPU-hour cost. Our asynchronous implementation further reduces OLIVE's total training time by 23.8%. We evaluate OLIVE on both hard reasoning tasks and agentic tasks which reflects modern post-training scenarios, and it consistently outperforms existing distillation methods under the same training budget. By regenerating prefixes from the evolving student, OLIVE continues improving after offline distillation plateaus while better preserving the general capabilities and plasticity of the student. Using only text from GPT-5.4-mini, continuously training with OLIVE outperforms offline SFT from the same teacher by 13% on ScienceWorld. These results support OLIVE as an effective and efficient approach to online language-model distillation.

Latent reward models (LRMs) enable efficient alignment of video diffusion models by scoring intermediate states directly in latent space. However, we find that optimizing against a fixed latent reward rapidly leads to latent reward hacking: the predicted reward stays high while perceptual and motion quality deteriorate. Our analysis identifies distributional escape as the central cause: within a few hundred updates, the generator moves beyond the reward model's training support, where its scores no longer reflect video quality. Based on this insight, we introduce CoRe, a co-evolving reward framework that treats latent-space alignment as a dynamic interaction between the generator and the reward model. Rather than optimizing against a stationary proxy, CoRe continually refits the reward model on the generator's current samples while anchoring it to real-video preferences, so the generator cannot gain reward by drifting away from the data. On Wan2.1-T2V-1.3B, experiments show that CoRe consistently improves generation quality over both the pretrained model and prior alignment methods, while avoiding the quality collapse of fixed-reward optimization.

Photosystem II (PSII) contains a diverse array of pigment-protein subunits with specialized roles in the antenna network. We investigate the functional significance of this subunit diversity in two structurally similar yet functionally distinct PSII subunits: minor light-harvesting complex CP29 and major light-harvesting complex LHCII. We combine two-dimensional electronic-vibrational spectroscopy with lifetime density analysis and structure-based kinetic modeling to assign spectral features to exciton states, providing molecular detail to probed spectral features. We show how the distinct pigment compositions of CP29 and Lhcb1, a monomeric subunit of the major LHCII trimer, reshape excitonic connectivity and energy transfer pathways in the complexes. Compared to Lhcb1, energy transfer pathways in CP29 are more spatially connected and reversible, suggesting CP29 evolved to distribute excitation between the core and periphery of the PSII antenna. We find that small structural modifications from a common framework tune CP29 and Lhcb1 to complementary roles in the PSII supercomplex.

Full-page blind restoration of historical Manchu manuscripts is challenging due to scarce annotations, unknown degradation regions, and fragile connected strokes. Generic restoration models may improve visual quality but often modify intact content, leading to over-restoration. We propose SAGE-Restore (Stroke-Aware Gated rEstoration), a selective restoration framework that first assesses where restoration is needed and then uses this assessment to guide restoration candidate generation and pixel-level selection. Its encoder predicts patch-level repair probabilities from complementary appearance and stroke-structural cues to condition restoration candidate generation, while the corresponding repair logits are refined into a pixel-level soft gate that selectively controls where the restoration candidate is applied. We further introduce a fidelity-aware evaluation protocol that jointly measures degraded-region recovery, intact-content preservation, and their balance. SAGE-Restore achieves the highest R-Recovery (0.463) and RFS (0.626), while maintaining high U-Fidelity (0.968), demonstrating an effective balance between restoration and content preservation.

We prove a dimensional strengthening of the colorful Helly theorem. Let $\mathcal{C}_1,\dots,\mathcal{C}_{d+1}$ be finite nonempty families of convex sets in $\mathbb{R}^d$. If $C_1\cap\cdots\cap C_{d+1}\neq\varnothing$ for every choice of $C_i\in\mathcal{C}_i$, then $\sum_{i=1}^{d+1}\dim(\bigcap\mathcal{C}_i)\geq0$, where $\dim\varnothing=-1$. We also obtain a dimensional strengthening of a theorem of Kim and Lew, in which the intersections are taken over unions of color classes. For simplicial complexes, we introduce the link-Leray dimension, defined as the Leray number of the link for a face and as $-1$ for a nonface. Using this invariant, we prove a matroidal extension of the dimensional colorful Helly theorem for $d$-Leray complexes. We further establish a corresponding strengthening of the topological Kim–Lew theorem in two ranges of parameters. As a special case, we recover the topological colorful Helly theorem of Kalai and Meshulam. Finally, we construct counterexamples to the unrestricted topological extension, even under a stronger local condition.

Dexterous robotic hands typically reproduce human hand morphology but inherit its one-sided grasping workspace, requiring wrist or arm reorientation to grasp from the opposite side. Existing reversible hands generally rely on non-anthropomorphic, soft, or task-specific finger arrangements, whereas conventional five-digit anthropomorphic hands remain designed primarily for palmar-side grasping. This paper presents an anthropomorphic, human-scale (200 mm length), lightweight (220 g), 3D-printed, 17-DoF robotic hand built on a bidirectional antagonistic tendon-routing mechanism, in which flexion/extension (except the coupled joint) and abduction/adduction at joints are actively driven without passive return springs. The proposed routing mechanism allows all degrees of freedom to cross their neutral configuration and form grasp closures on either the palmar or dorsal side. Experimental evaluation demonstrates an average motor-to-joint transmission error of 3.0%, an average joint transmission bandwidth of 13.2 Hz, a maximum fingertip force of 29 N, and a positioning repeatability up to 0.15 mm. The hand further achieves a Kapandji score of 8, successfully performs all 33 GRASP Taxonomy grasp types, and performs palmar- and dorsal-side grasping tasks, validating bidirectional operation in a compact, human-scale platform.

Does representation learning stop when the training loss stops improving? We study this question for matrix Muon, whose polar-normalised updates have a step length set by the gradient's rank rather than its norm. Near the edge of stability, full-batch Muon on teacher-student problems enters approximately period-2 loss oscillations that persist for thousands of steps: the cycle-mean loss stays flat or rises, yet the weights keep moving and the learned features continue to align with the teacher subspace. For linear teacher-student learning toys, we derive explicit cycle and alignment formulas and conditional plateau and decay bounds. For a population mean-field ReLU model, we prove that, under stated dimension, initialisation and small-head conditions, the leading eigenspace of the average gradient outer product (AGOP) recovers the teacher subspace exactly during a loss plateau, before the loss later drops. In all 33 ReLU, GELU and SiLU teacher configurations we study, direction-only alignment metrics show the student AGOP aligned with, or still aligning to, the teacher subspace during the period-2 oscillations; projected head refitting on selected configurations shows that the learned directions are useful for prediction, and further measurements distinguish AGOP alignment from weight-mass concentration. In deep residual ReLU students, freezing the downstream layers while the first layer trains with full-batch exact polar updates recreates a nearly flat cycle-mean loss with improving input-AGOP alignment; freezing and unfreezing switch between this plateau and loss decrease, and the effect is sensitive to momentum and to the choice of orthogonaliser.

Large language models (LLMs) can predict human brain activity across a variety of brain regions during natural language comprehension. Typically, however, LLM-brain alignment is measured using one model for different regions of the brain, and then model performance is summarized across regions. This one-model-fits-all approach ignores the functional specialization of brain regions. In this study, we assess whether a model oriented toward a particular cognitive domain aligns better with the brain system dedicated to that domain. Through prompting and fine-tuning, we first build expert LLM variants for six domains: sensory, spatial, numerical, reasoning, social, and abstract processing. We then examine whether each expert best predicts activity in the brain region associated with the corresponding cognitive domain. Consistent with our hypotheses, each expert's representations align more closely with the brain system most associated with the matching domain than do other experts. This holds under both prompting and fine-tuning, across three base models and three fMRI datasets. In a series of control analyses, we show that this model-brain alignment is specific to cognitive domain interventions; non-cognitive and surface-level interventions do not result in comparable alignment. Specializing models shifts regional alignment while leaving aggregate prediction accuracy largely unchanged, suggesting that summarizing alignment across regions may obscure regional differences in performance for specific models.

A goal that is close in space can be far away in time. Obstacles, terrain, and the agent's own capabilities determine how long it takes to get there. Yet, critics in contrastive and survival reinforcement learning do not measure the distances in their representation space in units of time. We therefore introduce ChronoSRL, which gives the critic's embeddings an explicit temporal geometry. The distance between state-action and goal embeddings is trained to match the time that the agent takes to reach the goal (goal-reaching time), while goals that were not reached, and goals from other trajectories, are pushed at least one discount horizon away. Furthermore, reaching a goal quickly once does not mean that reaching it is reliable in general, so the policy should not follow the temporal distance directly. Instead, we build on survival reinforcement learning and predict from our temporal embeddings not only the full distribution of goal-reaching times but also the time spent near the goal. Thereby, the policy is trained to favor actions that reach the goal sooner and more reliably and that keep the agent near it. ChronoSRL learns faster and reaches higher performance than contrastive, action-chunked contrastive, and survival reinforcement learning baselines on seven standard locomotion and navigation benchmarks, even with much smaller networks. To test the limits of self-supervised reinforcement learning, we introduce velocity tracking, goal-position reaching, and box climbing tasks with a quadruped robot in a realistic sim-to-real locomotion setup, and show how the shaping terms that are typical for robotics can be naturally incorporated into our framework. ChronoSRL is the only one of the tested self-supervised reinforcement learning methods that learns to stay at the commanded velocities and goal positions, and climbs the highest boxes.

Many learning tasks require stability to small transformations while retaining sensitivity to larger ones. We introduce transversal pooling neural networks, which generalize spatial max pooling to affine group actions. We establish equivariance to a chosen subgroup and derive explicit stability bounds for individual pooled wavelet coefficients under affine perturbations of the input. Experimentally, we demonstrate the utility of our networks in low-data environments and for predicting tropical cyclone intensification.

Influence maximization is a central algorithmic challenge in network analysis, aiming to identify a set of $k$ seed nodes in a graph with $n$ nodes and $m$ edges that maximizes the expected cascade of information under standard diffusion models. The seminal work of Borgs, Brautbar, Chayes, and Lucier (SODA'14) yielded a fundamental breakthrough\footnote{The conference version of their paper originally claimed a runtime of $\tilde O_{\epsilon}(n+m)$, but this was subsequently corrected to a runtime of $\tilde O_{\epsilon}((n+m)k)$ in an updated version of the paper that is available online. We validate the necessity of this additional factor $k$ in Section~\ref{sec:lowerbound} by demonstrating that if their algorithm is restricted to a runtime budget of $\tilde{O}_{\epsilon}(n+m)$, the approximation ratio deteriorates to $O(k^{-1/4})$.} for this problem by achieving an $\tilde O_{\epsilon}((n+m)k)$ time algorithm for approximating the solution within a factor of $1-1/e-\epsilon$. In the years since, numerous efforts have attempted to improve the runtime of this algorithm; however, these works have been successful in only shaving logarithmic factors or improving the dependence on $\epsilon$, leaving the existence of an almost linear-time algorithm as an open question. In this work, we resolve this long-standing open question. We present a novel algorithm that approximates the influence maximization problem within a factor of $1-1/e-\epsilon$ in time $\tilde{O}_{\epsilon}(n+m)$, effectively removing the multiplicative dependence on $k$ from the time complexity.

Major depressive disorder (MDD) severely impacts daily activities and quality of life. Detecting MDD involves multimodal data, such as interview recordings and sensor measurements. This is particularly challenging, as these heterogeneous modalities often demand distinct, customized prediction pipelines. Existing efforts to address this challenge have explored both manually engineered multimodal architectures and agent-assisted pipeline development. Despite their progress, it remains challenging to autonomously revise pipelines based on experimental feedback and carry verified improvements forward into subsequent designs. To this end, we propose Multimodal Exploration via Recursive Self-Improvement Agents for Major Depression Analysis (MERID). The framework develops depression pipelines through experience-based recursive self-improvement (RSI). Grounded State Construction (GSC) grounds experience by aligning multimodal records with subject-level depression targets. Coupled Pipeline Exploration (CPE) jointly modifies representations, fusion, and predictors to build successor pipelines for classification and severity estimation. Evidence-Guided Evolution (EGE) guides revisions through feedback and verifies gains under uncertainty in small depression cohorts before inheritance. Extensive experiments on depression benchmarks show that MERID achieves the best results on multiple tasks compared with multimodal and agent-based baselines. Further analysis highlights the value of acoustic and linguistic cues for depression detection. Our code is available at https://github.com/DiscoAILab/MERID

We obtain a general decay rate between Kaluza-Klein (KK) gravitons, resolving an ambiguity in the literature concerning these decays. The amplitude is determined not only by the mass $m_n$ of the decaying particle, but also by the momentum $q$ of the decay products in the parent's rest frame, and is suppressed relative to the expression commonly used in the literature by $(q/m_n)^2$. Phase space gives a general $q^5$-dependent decay rate obtained earlier in Randall-Sundrum models. We identify the cancellation that gives this result as a consequence of the massless 5D graviton, and argue for its universality even with scalar-induced KK violation by absorbing non-minimally coupled scalar fields into the warp-factor. This has significant implications for the potential for cascading dark matter models, and can be used to rule out existing Dark Dimension models, because the rapid cascade that was needed to evade constraints is severely suppressed. The amplitude is established by an explicit calculation that accounts for the backreaction of fields and branes and applies broadly to non-minimal diffeomorphism invariant two-derivative couplings between scalar fields and gravity.

Let $X\subset\mathbb P^N$ be a smooth complete intersection of two quadrics. We find formulas in the Grothendieck ring of varieties for the class of $X$ and for the class of its Fano scheme of lines, thereby proving the first two cases of a conjecture of Belmans et al. We also find a formula for the class of the relative Fano schemes of linear subspaces (of any dimension) in the fibers of quadric fibrations over curves, under a simple degeneration assumption. As consequences, we compute the rational Chow motive of the relative Fano scheme, and we provide evidence for a conjecture of Shah on a residual category in a semiorthogonal decomposition of the relative Fano scheme of lines.

Our recent research on Langevin dynamics with self-harmonic drift and classical spins has revealed a strong connection to “Stochastic Localization," a concept attracting attention in the fields of mathematical geometry and data science. Roughly speaking, the former can be viewed as a version of the latter in which the $n$-dimensional Euclidean space - the domain of the probability distribution function appearing in the latter - is “compactified” to the surface of an $n$-dimensional sphere. By comparing the two frameworks, we argue that this compactification is a consequence of requiring the drift to be autonomous. The relationship between the two approaches may expand the scope of Stochastic Localization.

Collective patch-foraging experiments in the laboratory provide a controlled setting in which social information use can be quantified. Here, we consider a go/no-go task in which groups choose between two patches differing in food reward probability. We use agent-based simulations, underpinned by an augmented collective drift-diffusion model, to investigate alternative mechanisms for representing and integrating social information. We consider two representations, continuous (counting representation) and discrete (pulsatile representation), and two integration mechanisms, biasing the decision threshold (threshold modulation) and modifying the accumulated belief (belief modulation), yielding four distinct social models, in addition to a non-interacting model. We first characterize the collective dynamics generated by these models across cognitive parameters and experimental conditions. The temporal dynamics of group accuracy provide informative signatures of the underlying mechanisms. We then assess model selection and parameter identifiability using Bayesian inference and Wasserstein distance minimization, applied to group-accuracy and departure-time distributions. Bayesian inference using distributions of group accuracy provides the most reliable identification across the conditions considered. Importantly, model selection and parameter identifiability are associated with different aspects of collective behavior: model selection is closely linked to the presence of oscillations in the temporal dynamics, whereas parameter identifiability is more closely related to the global accuracy value. Thus, the information available for distinguishing the underlying cognitive mechanisms is not necessarily the same as that required to recover their parameters. Our results further show that identification depends not only on model structure but also on the experimental conditions.

We study the dynamical behavior of tokens in transformers from a control-theoretic perspective. Our model includes the feed-forward layer present after the self-attention mechanism, with the self-attention mechanism interpreted as an interacting particle system and the feed-forward layer as an independent control. Our main theoretical result establishes that the feed-forward network can steer the tokens arbitrarily close to consensus regardless of the key, query, and value matrices. Our result are easily extended to convergence to many clusters and to multi-head attention. We conduct numerical experiments to verify our results, and compare thresholding behavior from our theory to real-world LLMs.

Pulsar halos are a class of extended gamma-ray sources, resulting from inverse Compton scattering of ambient photons by electrons and positrons believed to have escaped confinement in a pulsar wind nebula. First identified by HAWC towards PSR J0633+1746 and PSR B0656+14, a growing number of pulsar-powered gamma-ray sources is proposed as candidate halos. Using a model of isotropic diffusion, we assessed the ability of current-and-future generation imaging atmospheric Cherenkov telescopes to characterize the physical properties of such sources in the inner Galaxy. We constructed template-based pulsar halo models in the Gammapy library and fitted them to simulated H.E.S.S. and CTAO data of halos with different physical parameters. The sources were characterized spectro-morphologically using 2D Gaussian components. We assessed the statistical preference between the halo and 2D Gaussian hypotheses by the simulated data and quantified the impact of the diffuse Galactic emission. A multitude of the halos' parameters can be constrained simultaneously, including the pulsar's true age, its proper motion, the diffusion coefficient, the index of the injected particle spectrum and the injection efficiency. In some cases, the H.E.S.S. array can statistically distinguish between the halo model and a model containing 2D Gaussian components, while a significant improvement is seen with CTAO. The source's detection significance is drastically reduced with increasing intensity of the Galactic diffuse emission. If the latter is not modeled using the data-generating model, the halo parameter estimation is biased. A physically-motivated model of pulsar halos can facilitate the identification and characterization of this class of sources in high-level data analyses. The simulated halos exhibit properties that may already be found in surveys of current-generation telescopes with only a modest observation time.

The EU AI Act introduces extensive compliance requirements for organizations that develop, deploy, or integrate AI systems. Many of these requirements are directly relevant to security and privacy, while also addressing closely related issues such as data governance, transparency, accuracy, and robustness. However, stakeholders such as small-to-medium businesses and individual developers often lack the legal expertise required to interpret these obligations and translate them into engineering and governance practices. This disconnect creates challenges for implementing the EU AI Act and may lead to missing safeguards or misdirected development and deployment efforts. To address this, various automated EU AI Act compliance checkers (AIACCs) have emerged, claiming to streamline compliance assessments and provide practical guidance. In this paper, we present the first empirical study and assessment of AIACCs. We characterize 12 mainstream AIACCs across multiple dimensions, evaluate their legal coverage and alignment, and analyze checker-generated compliance reports for structure, determinacy, and actionability. We find that the quality of AIACCs varies significantly and that they currently can only serve as early-stage orientation tools. Specifically, we observe inconsistent interaction modes and user-friendliness, a tendency to overly simplify or omit key obligations, and a failure to provide determinate, actionable guidance. As a result, reliance on the current generation of AIACCs may foster a false sense of compliance. With our study, we provide a critical baseline of the current AIACC landscape. We further offer design principles for the implementation of more reliable compliance-support tools.

Next-latent prediction fits a map from the current embedding to the next one. LeNEPA carries this objective to time series, replacing the stop-gradient of next-embedding prediction with the isotropy penalty of LeJEPA. A world model is a transition kernel that can be rolled out. The one-step regression identifies a conditional mean, and a mean is a kernel only in special cases. For a linear-Gaussian Markov latent, the mean transition and the innovation covariance are fixed by the one-step problem, and the open-loop squared error at horizon $K$ equals the trace of the sum of the pushed-forward innovation covariances. That error grows with $K$ after the one-step fit is exact. If the conditional mean is nonlinear, composing it is not the multi-step conditional mean. If the observation is a non-injective function of a Markov state, a memoryless one-step map does not determine future observations, while a short window can. An isotropy penalty is a function of the embedding marginal, so its partial derivative in the transition weights is zero. On a scalar autoregression with coefficient $0.9$, the one-step mean squared error is $0.998$ and the $16$-step open-loop error is $5.10$. On a hidden rotation, an eight-step window reaches $16$-step error $0.056$, while the current scalar alone reaches $0.778$. Raising the isotropy weight from $0.1$ to $10$ leaves eight-step latent error inside $[0.78,0.85]$ on three seeds.

We prove Tachibana-type rigidity theorems for closed manifolds under weakened partial-sum conditions on the eigenvalues of curvature operators. Specifically, an Einstein manifold of dimension $n\geq4$ is locally symmetric if its curvature operator is $\frac{2(n-1)}{3}$-nonnegative. The corresponding thresholds are $\frac{2(n+1)}{3}$ for the primitive curvature operator of a Kähler-Einstein manifold of complex dimension $n\geq2$, and $\frac{2(n+2)}{3}$ for the curvature operator of a quaternionic-Kähler manifold of real dimension $4n\geq8$.

We present a system that aids the design of 3D obstacle course games by providing designers with rapid feedback on how obstacles can be solved. Our core contribution is a system for querying for solutions (sequences of player actions) to an obstacle that adhere to designer-specified constraints (e.g., avoid a region, travel through a given waypoint, only perform two jumps, etc.). To solve a wide range of obstacle designs quickly, we author a high-performance implementation of the GoExplore algorithm for exploratory search, and guide search with an obstacle solving agent trained offline using reinforcement learning (RL). To further accelerate search, the system carries out exploration using a custom GPU-accelerated obstacle course game simulator that generates playthrough experience at nearly 14,000$\times$ real time, 60-fps gameplay. Through design studies, we demonstrate that the use of constrained solvability queries in a rapid design loop is sufficiently expressive to help designers understand ways an obstacle can be solved or why it cannot be solved. We also show how the tool can let designers answer higher-level questions such as identifying undesirable solution paths and assessing the difficulty of solutions. This allows them to pursue new design directions they did not originally anticipate. Human playtesting of obstacles designed using our system confirms that human players indeed play the obstacles in the manner the designers intended. We release code for our interactive tool, simulator, training setup, and procedural level generation system at https://zandermajercik.github.io/interactive-obstacle-course-feedback/.

Unified multimodal models (UMMs) combine image generation and visual understanding in a shared backbone. Since generation and understanding are inverse tasks, recent studies self-train UMMs by letting the two branches cooperatively supervise each other. We introduce MATE (Mutually Adversarial self-Training with Evolving data), a reinforcement-learning-based post-training framework in which the two branches instead challenge each other, and the challenges evolve as the model trains. MATE lets generation and understanding take turns to be challenger and solver. Given an image, the understanding branch proposes several candidate descriptions that the generation branch must turn back into similar images, and vice versa. The candidates are screened for consistency with the image or prompt they were proposed from, and the solver is trained on the candidate it handles worst. The adversary thus comes from the model's own outputs, and no separate adversary is trained. Moreover, the candidates that defeat one branch become the sources of the next challenges to the other in the next epoch, which keeps the challenges evolving with the model and turns the training into self-play in data space. On Janus-Pro-1B, MATE improves GenEval by 2.4 points, DPG-Bench by 1.7 points, and the average over nine understanding benchmarks by 0.7 points, while strengthening consistency across repeated image-text cycles.