Papers

Long-output reasoning shifts the KV-cache bottleneck from the fixed prompt to the generated trace. Existing reasoning-cache eviction methods largely treat cached entries as routing objects, estimating whether an old key will still be read, will recur, or can be replaced. This routing-only view overlooks two effects: low-attention entries can carry large value payloads whose removal changes future predictions, and newly generated states can appear stale before later queries have had a chance to read them. We introduce AvoKV-E, a training-free eviction policy that first delays eligibility for recent states and then ranks eligible entries using candidate-normalized read pressure, key redundancy, and value-payload potential. According to empirical evaluation across different models and datasets, AvoKV-E matches or exceeds redundancy-aware, recurrence-based, and thought-adaptive eviction baselines at matched active-KV budgets, with its largest gains in the tightest-cache regime. Component and counterfactual analyses further connect these gains to delayed observation, payload-aware scoring, redundancy, and scale-robust normalization. Together, the results show that long-reasoning KV eviction should preserve not only keys that are likely to be read, but also the value payloads that sustain the reasoning trajectory.

We introduce a set of consequence-based measures that quantify the misclassification arising from imperfect reliability in multi-item psychometric scales. Particular attention is given to the probability of individuals in extreme latent-trait percentiles being correctly identified from their observed scores. These cost functions provide a principled and interpretable way to characterise how inadequate reliability distorts classification and reduces the informational value of test scores. We also examine methodological issues in estimating reliability under common-factor models, with emphasis on McDonald's omega and the construction of accurate confidence intervals. To address the computational burden of model fitting, especially in small samples, we derive a modified version of Cronbach's alpha that closely approximates omega when the common-factor model holds. This estimator has comparable sampling variability to omega while requiring no parameter estimation, offering a practical and computationally efficient alternative. y

We construct hypocoercive Kolmogorov-type operators on the Euclidean motion group $\mathrm{SE}(3)=\mathbb{R}^3\rtimes\mathrm{SO}(3)$ using ZXZ Euler angles and study their long-time behaviour using the abstract hypocoercivity method. The operator $L=S-A$ decomposes into a symmetric part $S$, corresponding to a degenerate diffusion on the rotation component $\mathrm{SO}(3)$, and an antisymmetric part $A$, which captures transport and torque effects induced by the Lie group structure. The associated invariant probability measure is $\mu_\Phi=\gamma_\Phi\otimes\nu_3$, where $\gamma_\Phi$ is a probability measure on $\mathbb{R}^3$ with density $Z(\Phi)^{-1}e^{-\Phi}$ with respect to the Lebesgue measure, and $\nu_3$ is the normalized Haar measure on $\mathrm{SO}(3)$. As a consequence, if $\Phi\in C^\infty(\mathbb{R}^3)$ is bounded from below, $\gamma_\Phi$ satisfies a Poincaré inequality with constant $\Lambda>0$, and there exists $c<\infty$ such that \begin{equation*} |\nabla_\xi^2\Phi(\xi)| \leq c\bigl(1+|\nabla_\xi\Phi(\xi)|\bigr), \quad \xi\in\mathbb{R}^3, \end{equation*} then the semigroup generated by the closure of $L$ converges exponentially fast to equilibrium in $L^2(\mathrm{SE}(3),\mu_\Phi)$.

We study open billiard flows in $\mathbb{R}^3$ generated by reflections in the exterior of at least three ellipsoids with $C^3$ boundaries. Each obstacle is congruent to $$\tilde{K} = \{(x,y,z)\in \mathbb{R}^3 : x^2+y^2+(\beta z)^2 \leq r^2\},$$ with parameter $\beta>1$, small radii, and centers $O_i$ lying in the plane $\Gamma=\{z=0\}$. The configuration satisfies the no-eclipse condition (H). For any Gibbs measure on the non-wandering set of the billiard ball map, we prove that if $\beta>1/c_1^2$, for some constant $c_1>0$ determined by the geometry of the configuration, the two positive Lyapunov exponents are distinct and positive: $\lambda_1(\beta)>\lambda_2(\beta)>0$. Moreover, $\lambda_2$ is independent of $\beta$ and corresponds to the restriction of the billiard flow to the plane $\Gamma$.

Topological superconductivity has attracted broad interest because of its connection to Majorana fermions and quantum computation. Kagome materials provide a natural setting in which interesting electronic structures, topological surface states, and superconductivity may occur in nearby energy windows. Here we carry out a systematic first-principles search for binary kagome superconducting candidates with topological electronic states across several structural families $A_mB_n$ ($m$:$n$=3:1; 3:2; 1:1). The screening combines formation-energy and phonon-stability filtering, magnetic-ground-state searches, electron-phonon-coupling calculations, and topological electronic-structure analysis. We identify 286 nonmagnetic dynamically stable candidates for electron-phonon-coupling analysis, among which 84 have estimated transition temperatures above 3 K and seven exceed the $\sim 9$ K reference scale of existing ambient-pressure kagome superconductors. In addition, several systems are predicted to host abundant topological surface states near the Fermi level. NbBi is identified as a $\mathbb{Z}_2$ topological metal with clear Dirac-cone topological surface states and a kagome-derived flat band near $E_F$. Ti$_3$Si, with the largest estimated $T_\text{c}=15.2$ K in this dataset, shows nodal-line-derived drumhead surface states and selected nodes that survive spin-orbit coupling near $E_F$. Combining superconductivity with nontrivial topological electronic structures, the binary kagome compounds predicted here represent compact and chemically tunable candidate platforms for topological superconductivity and for exploring kagome-related quantum phenomena.

Unified multimodal models (UMMs) understand and generate both text and images, which lets a model produce its own training data. Existing self-improvement in UMMs keeps supervision on the visual side, where image understanding judges image generation. We propose recursive cross-capability self-improvement (RSI), a training loop in which the text and visual abilities of a UMM supply training data for one another. In each round, the model generates images and reads them to find where it falls short. It then writes programs aimed at these shortcomings, and execution verifies every result against its specification. Verified renders train image generation, while labeled renders and the model's own correct programs train visual understanding and program writing. Program execution thus acts as a source of truth outside the model, so errors do not accumulate across rounds. We study RSI on charts and build BasicChartBench to evaluate open models early in training. On requests worded differently from training, four rounds of RSI raise the score from 45.7% to 60.2%, while continued training stays at 46.3%. Verified construction carries most of the gain, and targeting the model's failures adds 3.5%. Along the way, the share of verified programs rises from 48.9% to 95.2%, and the reader's accuracy on edited renders rises from 55.6% to 87.4%.

Extracellular electrophysiology records a different set of neurons in every session. Neural foundation models embed each neuron and each session into their tokens, so every new session is an input they have never seen, and they fail to generalize to it. A tokenizer for new sessions needs a unit that every session shares and that carries behavior. Population activity offers such a unit. It evolves on a low-dimensional manifold that persists across neuronal turnover and across animals once sessions are aligned. This manifold changes regime at task events such as stimulus onset and movement onset. Within each regime the population occupies a state, the part of the manifold it spans between two events, and each state carries its own behavioral meaning. We propose Tokenization with States (TWS), which segments each trial, one repetition of the task, at these events and converts every state into tokens of population geometry, with no neuron or session embedding. On held-out International Brain Laboratory (IBL) sessions, TWS decodes movement even from regime boundaries that carry no information about the target, while a per-neuron foundation model pretrained on those sessions decodes at chance. Frozen after training on mice alone, TWS transfers to macaques and Utah arrays with only a linear probe. On reach direction, a target that its boundaries do not define, it achieves a Matthews correlation of 0.23, where the event time alone achieves $0.01$. For cross-session generalization, the token matters more than the model on top.

Intrinsic explainability remains a challenging problem, particularly in contexts where multilayer perceptrons (MLPs) require dynamic re-training within an optimization environment. This paper investigates how MLPs and their training dynamics can be represented and studied in non-Euclidean spaces; our representation features the Poincaré model of hyperbolic geometry. We aim to capture the geometric evolution of their weighted topology and self-organization over time. Instead of restricting the analysis to single checkpoints—as per established measure-based explainability methods—we construct temporal parameter graphs, i.e., snapshots over time $T$ steps of the optimization/training process for MLPs. This reflects the view that neural networks encode information not only in their weights but also in the trajectory traced during training. Drawing on the idea that many complex networks admit embeddings in hidden metric spaces where distances correspond to connection likelihood, we present a geometric and temporal graph-based metalearning framework for obtaining dynamic hyperbolic representations of the underlying neural parameter graphs. Our model embeds temporal parameter graphs in the Poincaré model ball, and learns from them while maintaining equivariance to within-snapshot neuron permutations and invariance to permutations of past snapshots. In doing so, the approach preserves functional equivalence over time and recovers the latent evolving geometry of the network. Experiments on regression and classification tasks with trained MLPs show strong meta-network performance, accompanied by hyperbolic temporal representations. This reveals how the network structure emerges over time under specific training environments, thus providing insights into the network's self-organization.

Omni-modal large language models (OmniLLMs) unify text, images, audio, and video, yet hallucinate when generation relies on the wrong evidence. Existing inference-time methods can reduce hallucinations, but rarely reveal which evidence sustains a generated commitment. We introduce OmniConfess, a training-free method for mitigating omni-modal hallucinations. It fixes a candidate response and re-scores it at token resolution under controlled channel-wise evidence interventions, producing a structured token-by-channel confession that reveals the response's evidential dependence. OmniConfess uses this confession to preserve grounded content and correct commitments driven by irrelevant or contradictory evidence. To evaluate OmniConfess, we construct OmniHalluBench, a 3,540-example benchmark built from six datasets spanning text, image, audio, and video settings and both judgment and free-form generation. Experiments show that OmniConfess mitigates hallucinations across heterogeneous modality and task settings. Our code and benchmark are publicly available at https://github.com/RongHuiQiang/OmniConfess.

The search for novel materials capable of robust spin-current generation remains an active area of research. Here, we investigate the intrinsic spin Hall and spin Nernst effects in Co- and Rh-based skutterudites and explore their enhancement through heavy-metal substitution and site-selective doping. Using first-principles calculations and Wannier-based tight-binding models, we analyze the spin Berry curvature and spin-transport responses of pristine MX$_3$, where M = Co, Rh and X = As, Sb, as well as chemically modified systems. Despite sizable momentum-resolved spin Berry curvature, the pristine compounds exhibit relatively small net spin Hall responses due to substantial cancellation across the Brillouin zone. Isoelectronic Ir and Bi substitution at 8$c$ Wycoff M site produces little enhancement near the E$_F$, whereas non-isoelectronic Pt substitution yields a relatively better response. Most interestingly, the incorporation of Pt at the interstitial $2a$ Wycoff site of RhAs$_3$ nearly doubles the spin Hall conductivity to $\sim400~(\hbar/e)(\Omega,\mathrm{cm})^{-1}$ near the E$_F$ when compared to Pt substitution at 8$c$ position. At 300 K, the same interstitially filled system exhibits a spin Nernst conductivity of $\sim1.46~(\hbar/e),\mathrm{A,m^{-1}K^{-1}}$ at the E$_F$, nearly an order of magnitude larger than that of $M$-site Pt substitution. The enhanced responses arise from Pt $5d$ states, strong spin-orbit coupling, and avoided crossings that generate pronounced spin-Berry-curvature hot spots. These results demonstrate that site-selective chemical engineering can effectively overcome momentum-space cancellation resulting in enhanced spin Hall and spin Nernst responses in skutterudites. Our results provide a possible route towards robust spin-current generation in this class of materials.

In our paper, we show that a two-qutrit Werner state admits a local hidden-variable model for all values of the parameter in a scenario involving two projective measurements per site, with three outcomes per measurement. To this end, we derive a simple sufficient condition under which a two-qutrit state satisfies the Collins-Gisin-Linden-Massar-Popescu inequality for arbitrary choices of Alice's and Bob's observables, and show that the Werner state always satisfies this condition. Next, we use the fact that any two-qutrit state satisfying the Collins-Gisin-Linden-Massar-Popescu inequality for arbitrary choices of Alice's and Bob's observables admits a local hidden variable model.

As Artificial Intelligence (AI) has evolved from task-specific models to foundation models and agents, the scope of trustworthy AI has expanded from model-level robustness to the reliability and safety of broader AI systems. This evolution has also expanded the attack surface from individual models to broader system-level interactions, including tool use, context, and interaction trajectories with dynamic environments. As a result, maintaining reliable and safe behavior under changing or deliberately manipulated conditions has become increasingly challenging. The search for effective attacks and defenses often relies on black-box feedback to navigate discrete choices among words, actions, system components, or their combinations. Multiple objectives and expensive candidate evaluations further limit what can be explored. Evolutionary Computation (EC), with its population-based, gradient-free search and flexible variation and selection mechanisms, is well suited to these settings. This survey reviews how EC has been applied to trustworthy AI across three directions: evolutionary attacks, evolutionary defenses, and trustworthy self-evolving AI systems. Unlike prior reviews that treat trustworthy AI, EC, and self-evolving systems largely separately, we connect these lines through a common evolutionary perspective. For self-evolving AI, we examine how trustworthiness governs the generation and retention of updates that shape subsequent adaptation. We further synthesize evaluation methods and benchmark resources from both trustworthiness and evolutionary-search perspectives. Finally, we discuss key challenges and future research directions toward more effective and reliable use of EC in trustworthy AI.

Identifying the bug-inducing commit (BIC) is a fundamental step in regression debugging and a key input to emerging BIC-aware fault-localization pipelines. In practice, BICs are commonly obtained with bisection. Standard bisection selects the median commit of the remaining good-bad interval, thereby balancing commit count. This strategy is optimal under the assumption that each commit is equally likely to be the BIC. This paper shows that this assumption does not match real-world BIC histories. We construct a dataset of 8,172 bug reports from GCC, the Linux kernel, and MariaDB. We find a strong temporal skew: across the studied systems, 50% of BICs lie within the most recent 0.69% of the report-time commit history. Motivated by this observation, we introduce BISCEPTER, a probability-driven bisection approach that uses historical BIC latency as a lightweight prior. Instead of selecting pivots that split the number of remaining commits, BISCEPTER selects weighted-median pivots that split estimated BIC probability mass, while preserving the same good-bad oracle and interface as standard bisection. We evaluate BISCEPTER on three large-scale systems. The evaluation results show that BISCEPTER reduces bisection iterations by 25.75% on average (up to 55.55%) compared with standard median bisection, while improving over the baseline in 91.26% of test cases. Robustness experiments further demonstrate that the benefit remains stable under noisy historical data. We expect that our research can effectively save effort in debugging software in practice and, more broadly, benefit future software engineering research by bringing insights about BIC distribution.

LLM agents often fail mid-task due to invalid tool calls, repeated actions, or poorly grounded reasoning, and learning from these failures is a path to reliability. We find that how failure knowledge reaches the agent matters as much as what it contains. Failure lessons are conditional: kept in the agent's context, they misfire when their failure is absent, and removing them from an evolving playbook improves performance. Runtime interventions, in contrast, act only when a failure occurs but do not learn from their repairs. We argue that failure knowledge is conditional knowledge and should be conditionally exposed, and instantiate this principle in Sentry, a failure-management layer that runs alongside the agent. When Sentry detects a failure, it retrieves matching lessons from an external playbook to guide recovery, verifies without access to task rewards whether the agent recovered, and stores a new lesson only if it did; the full playbook never enters the agent's context. Across multiple agentic benchmarks, Sentry outperforms the strongest runtime-intervention baseline on every benchmark, by 37% on average, and the strongest context-evolution baseline by 39% on the two benchmarks where both are evaluated; combining Sentry with context evolution yields further gains. Learned lessons transfer to held-out tasks, and controlled experiments show that exposing the full playbook to the agent lowers performance even when relevant lessons remain available on demand.

Branson's $Q$-curvature is a natural fourth-order counterpart of scalar curvature in conformal geometry. In analogy with the classical recovery of the Ricci tensor from the linearized scalar curvature, Lin and Yuan introduced a symmetric $2$-tensor $J_g$ through the formal adjoint of the linearized $Q$-curvature and established its explicit decomposition in terms of the Bach tensor and auxiliary curvature terms. In this paper, we study the associated fourth-order geometric flow $\partial_t g = -2J_g$ on closed Riemannian manifolds of dimension $n \ge 4$. We establish short-time existence and uniqueness using a biharmonic DeTurck gauge and derive global and local integral smoothing estimates under curvature bounds. In dimension four, we prove long-time existence assuming a uniform Sobolev inequality and sufficiently small total $L^2$ curvature energy throughout the maximal interval of existence. Under uniform curvature and Sobolev bounds, time integrability of the $L^2$-norm of $J$ implies smooth convergence in fixed coordinates to a $J$-flat metric. Explicit Einstein and product solutions illustrate the evolution and show that small curvature energy alone does not prevent degeneration. Positive initial Yamabe constant and positive total $Q$-curvature give a uniform positive Yamabe lower bound throughout the smooth four-dimensional flow, whereas in higher dimensions total $Q$-curvature can decrease even near flat metrics. Finally, we prove that every closed four-dimensional $J$-soliton is trivial, its metric is Bach-flat with constant $Q$-curvature, and its soliton vector field is Killing.

The well-known inequality of Fiedler ensures that the spectral gap $r-\lambda_2(G)$ of a connected non-complete $r$-regular graph $G$ is bounded from above by the vertex connectivity $\kappa(G)$ of $G$. We prove that, for integers $t\geq2$ and $r>2t^2$, every connected $r$-regular graph with vertex connectivity at most $2t$ has spectral gap at most $\frac{1}{2}(r+t+2-\sqrt{(r-t+2)^2-4t(t-1)})$. We show that this bound is nearly optimal for each fixed $t \ge 2$ and sufficiently large $r > 2t^2$ such that $r+1$ is divisible by $t$. We further prove that if $r>(2t-1)(2t-2)$, then every connected $r$-regular graph whose vertex connectivity is odd and no more than $2t-1$ has spectral gap at most $r-\min\bigl\{\xi(r,t),\nu(r,t)\bigr\}$ for some explicitly given functions $\xi(r,t)$ and $\nu(r,t)$. If $r\geq6t^2$, then this minimum equals $\xi(r,t)=\frac{r(2r-4t+5)}{2(r-t+2)}$. In particular, when $\kappa(G)=2t-1$, this gives $r-\lambda_2(G)<t=(\kappa(G)+1)/2$, which improves Fiedler's bound by nearly a factor of two. Our upper bounds in their parameter ranges improve two known bounds on the spectral gap of regular graphs.

Lower-limb exoskeletons have made considerable progress in reducing energy expenditure during walking. However, designing optimal assistance strategies remains challenging, particularly given inter-individual variability in anthropometry and biomechanics. This study explores energy-optimal lower-limb joint-assistance strategies using predictive simulations with musculoskeletal models. Subject-specific models of six able-bodied subjects, with BMI-based muscle strength scaling, were used in predictive simulations to generate gait at self-selected walking speeds. Ideal actuators were incorporated to simulate various combinations of joint assistance at peak levels of 25 Nm and 50 Nm to examine the effects of assistance on gait and metabolic savings. The effects of each assistance configuration were assessed through cost of transport (COT), joint kinematics, muscle activations, assistive torques, and joint-level power metrics to characterize the biomechanical and energetic impacts of different assistance strategies. At 50 Nm, combined H+K+A (hip-knee-ankle) assistance resulted in the greatest mean COT reduction of 48.50 +/- 4.55%, with individual reductions ranging from 42.22% to 54.65% across the subjects. Among single-joint conditions, assisting the hip was most effective, reducing COT by 31.77 +/- 5.21%; the knee and ankle produced smaller, comparable reductions (19.17% and 17.02%). H+A (hip-ankle) assistance (44.60 +/- 7.08%) emerged as the most effective two-joint assistive configuration. Increasing the torque bound increased positive assistive power primarily at the hip and ankle, while knee assistance showed little sensitivity and delivered positive power near pre-swing. These results support H+A assistance as an efficient two-actuator target, while identifying the knee's atypical pre-swing power strategy as a candidate for targeted experimental validation.

Real-world interaction networks are inherently dynamic: edges form and dissolve as node behavior shifts over time. Most snapshot-based contrastive methods encode temporal dependencies implicitly in encoder weights, without an explicit model of how node representations evolve, making them brittle under distribution shifts. We propose KAIROS (Koopman-Aligned Invariant Representations for Open Dynamic Systems), a self-supervised framework that embeds a differentiable Koopman operator within a dynamic graph contrastive learning loop to linearize temporal evolution in the learned embedding space. A dual-view encoder pairs raw node features with a graph-diffused structural view and is optimized with multi-granularity contrastive objectives across temporal windows. For anomaly detection, KAIROS uses the Koopman prediction residual together with temporal inconsistency and local neighborhood deviation to separate irregular behavior from predictable graph evolution. Evaluated on nine dynamic graph benchmarks, KAIROS achieves state-of-the-art anomaly detection results on all nine datasets, with gains of up to 23.15 ROC-AUC points over prior work, while remaining competitive for unsupervised node classification. These results show that explicit dynamics modeling provides a scalable and effective inductive bias for temporal graph representation learning.

Post-fault ascent replanning for launch vehicles requires rapid joint trajectory-guidance replanning under uncertainty to maintain closed-loop constraint satisfaction. In particular, propulsion performance cannot be promptly and fully identified after a fault, leaving persistent parametric uncertainty throughout the remaining flight. A fast stochastic ascent replanning method is developed to address this problem. To efficiently account for the cross-time correlation induced by persistent parametric uncertainty, a fast system level synthesis formulation is developed with a Riccati-based solution structure. The resulting feedback synthesis is complemented by a task-oriented terminal weighting method that shapes terminal covariance according to post-injection correction demand. These components are integrated with nominal trajectory replanning, chance-constraint tightening, and online feedback realization to establish a real-time joint stochastic trajectory-guidance replanning framework for launch vehicles. Nonlinear Monte Carlo simulations show that the proposed method effectively suppresses the influence of persistent parametric uncertainty and maintains stable convergence and high injection accuracy across parameter sweeps, with subsecond solution times. Compared with conventional ascent guidance, the empirical constraint-violation rate is substantially reduced.

We present very long baseline interferometry (VLBI) observations of GRB221009A obtained with the global-VLBI network at 5 GHz between 231 and 750 days after the burst. The quality of our observations allowed us to measure the sub-milliarcsecond full-width at half maximum of the source surface brightness distribution with a one-sigma equivalent error of 13% and 30% at 231 and 391 days post-burst, respectively. By fitting the temporal evolution of these new size measurements alongside those previously published in the literature at 5 and 8 GHz with a single power law $\propto t^a$, we find a slope of $a = 0.52^{+0.14}_{-0.12}$. Using the public code VegasAfterglow, we model the 5 GHz size evolution considering the afterglow emission of the forward shock produced by a jet decelerating in either a homogeneous interstellar medium (ISM) or into a surrounding medium with a wind-like density profile. The model constrains the collimation-corrected Sedov ratio, that is, the ratio of the jet kinetic energy $E_\mathrm{jet}$ to the density of the surrounding medium ($n$ in the ISM scenario, or $A_\star$ in the wind scenario), in the range $\log[(E_\mathrm{jet}/n)\,\mathrm{erg}^{-1}\,\mathrm{cm}^{-3}] = 54.2^{+0.4}_{-0.5}$ for the ISM scenario and $\log[(E_\mathrm{jet}/A_\star)\,\mathrm{erg}^{-1}] = 51.7^{+0.4}_{-0.2}$ for the wind scenario. Among the works in the literature that fit the light curves and spectra of GRB221009A based on the standard afterglow model, and which can be reproduced with VegasAfterglow, none has best-fitting parameters that are compatible with these constraints within $2\sigma$. Moreover, we show that their predicted size evolution is not compatible with the observed one. Our results highlight the importance of size measurements of GRB afterglows as an independent probe of their dynamics, structure, and emission mechanisms.

We develop two methods in quantitative homological algebra: A declarative approach to integral cohomological filling problems and a quantitatively controlled replacement of normed chain complexes by their homology complex. Both methods are connected through so-called chain extensions. As applications, we obtain transparent proofs for uniform integral simplicial cohomological fillings for subdivisions of simplicial complexes, for uniform integral cohomological fillings of certain finite coverings, and for lower bounds of the $\ell^1$-semi-norm on product spaces.

Membership inference on large language models (LLMs) aims to determine whether a given text sample was included in an LLM's training data, without access to its training corpus. Despite recent progress, existing benchmarks suffer from three limitations: limited coverage of training stages, insufficient distributional alignment between members and non-members, and lack of rigorous filtering of non-members against the training corpus. To address these limitations, we propose OLMo-Detect, a multi-stage, confounder-controlled benchmark built upon the fully open OLMo 2 pipeline. OLMo-Detect spans pre-training, mid-training, and post-training, explicitly aligns members and non-members on three key axes, and rigorously filters non-members via infini-gram. To assess robustness to distribution shifts, we further introduce OLMo-Detect (Shifted), a variant where members are misaligned with non-members. We evaluate 15 unsupervised and 3 supervised membership inference attacks (MIAs) across the OLMo 2 family, finding that: (i) overall performance is limited: the best unsupervised and supervised MIAs both reach an AUC of only 0.68, and supervised MIAs degrade under cross-domain evaluation; (ii) MIA performance peaks at mid-training and is lower at pre-training and post-training, a pattern driven by data type rather than a stage effect: curated math data is far more detectable than other types; (iii) overall scores improve from 1B to 13B but plateau at 32B; and (iv) no unsupervised MIA is robust to distribution shifts, with AUCs shifting by up to 0.42. Finally, we find that our findings on OLMo 2 generalize to OLMo 3 and non-OLMo models.

Embodied agents interacting with the same physical process may maintain heterogeneous, asynchronous, and observer-relative representations. Rather than assuming that such representations should always be globally aligned, we investigate which distinctions among them must actually be resolved for coherent interaction. We formalize this question through relational sufficiency: an interaction-specific relational-evidence map defines the representational ambiguity left unresolved by comparison, and sufficiency holds when each residual ambiguity fiber lies within an interaction-equivalence class. When this condition fails, additional sensorimotor anchors must separate precisely the ambiguities that can change the interaction-relevant outcome. For smooth systems, we derive a local first-order lower bound on the number of inde- pendent scalar anchors required, given by the dimension of directions that are invisible to relational evidence but visible to the interaction-relevant map. We instantiate the theory in two variants of an asynchronous hand-off scenario that share the same observer agents, representations, transports, and relational evidence. Relative synchronization requires no additional anchor, whereas hand-off at an absolute time requires exactly one. The analysis there- fore provides a task-relative stopping condition for representational alignment: residual disagreement need not be eliminated when it is invariant with respect to the interaction.

The center of mass of a Bose–Einstein condensate in a harmonic trap oscillates at the trap frequency independently of the interactions. Without interactions a parity-time-symmetric gain-loss gradient leaves this frequency unchanged, and a cloud of the ground-state width is translated rigidly while the atom number is periodically modulated. With interactions the protection is lost, because the gain and the loss change the number of atoms; the modulated atom number drives the width of the cloud, and the width acts back on the center of mass. At small gain the period grows quadratically with the gain strength, with a coefficient that in the Thomas–Fermi regime is set by the size of the cloud alone. The family of periodic orbits continued from the Kohn oscillation can be followed up to a critical gain, where it comes into resonance with highly excited states of the trap, and over the computed families this critical gain decreases with the amplitude of the oscillation and with the size of the cloud. A five-variable moment model reproduces the period and the width of the cloud along the orbits nearly up to the critical gain.

Direct approaches to discrete parabolic Carleman estimates often rely on weighted identities tailored to the discrete operator. We prove an abstract transfer theorem that derives such estimates for fully discrete backward Euler schemes with conforming spatial reconstructions from a continuous Carleman inequality together with suitable weighted approximation and compatibility properties. For a class of time-independent positive self-adjoint operators, the key construction assigns to each discrete state a shifted continuous auxiliary problem whose discrete solution is exactly the prescribed state. Weighted space-time error estimates, uniform over the full discrete load space, then transfer the inequality while preserving the residual and observation terms of the original scheme. This separates the PDE-specific Carleman analysis from the numerical verification required for each discretization. We verify the hypotheses for the heat equation discretized by consistent-mass $P_1$ finite elements on locally graded meshes in two and three dimensions and by standard Cartesian finite differences in any fixed dimension. For the heat equation, the transferred estimate is valid for Carleman parameters up to the scale $\min\{h^{-4/5},(\delta t)^{-2/5}\}$. For bounded real-valued space-time potentials, the resulting estimates yield relaxed observability and approximate null controls with uniformly bounded cost and exponentially small terminal errors under independent spatial and temporal refinement; weak accumulation points of the reconstructed controls are continuous null controls.

Programmable logic controllers (PLCs) coordinate industrial equipment by reading sensor inputs and issuing control commands. Evaluating whether large language model (LLM)-generated PLC programs satisfy task requirements and safety constraints requires observing how their commands affect device and workpiece states. We introduce PLCWorld, a common closed-loop execution environment and benchmark that couples Structured Text (ST) execution with simulated plant responses and sensor feedback. Grounded in control relations identified in industrial PLC programs and engineering documentation, PLCWorld contains 100 synthetic tasks and 473 registered task-condition pairs across Motion Control and Material Handling, with difficulty defined by control-dependency scope. A common protocol reports Task Success and Safety Violation separately. Validation combines practitioner review, reference and alternative programs, targeted counterexamples, specification-evaluator alignment checks, and comparisons with independent ST runtimes. Reference and alternative programs satisfy their applicable cases, while all 542 targeted counterexamples activate their designated evaluator rules under at least one registered condition. Execution Gap relates submission-profile acceptance to subsequent task failure or observed Safety Violation. Across the constructed task groups, direct GPT-5.5 achieves 82.70% Task Success on Easy cases but 25.10% on Hard cases. Evaluations of six LLMs and four adapted generation-and-verification workflows further expose differences between completion, safety, and generation cost. Our code, simulation environment, benchmark tasks, and baseline implementations are publicly available at https://yunji0516.github.io/PLCWorld/.

Source-Free Domain Adaptation (SFDA) aims to adapt a source-pretrained model to an unlabeled target domain without access to the original source domain. While early single-model approaches rely on self-refinement, they are inherently susceptible to confirmation bias and struggle to correct their own systematic errors. To overcome this limitation, recent methods introduce Vision-Language (ViL) models as external knowledge sources. However, these approaches operate in a largely unidirectional paradigm, using the ViL model primarily to supervise the source-pretrained model. This overlooks a key structural property: the two models exhibit distinct failure modes – where one produces an incorrect prediction, the other may produce a correct one, creating a natural opportunity for mutual correction within the target domain. Yet, without ground-truth labels, identifying which model is correct on any given sample is non-trivial, and naively exchanging predictions risks propagating errors across models. To address this challenge, we propose SafeCut, a novel approach that leverages the cut statistic as a label-free measure of prediction reliability to gate cross-model supervision. Our approach dynamically controls both the direction and strength of supervision based on relative reliability, selectively amplifying true corrections while suppressing miscorrections on a per-sample basis. We further provide theoretical justification showing that this reliability-gated mechanism guarantees a net-positive correction signal. Extensive experiments across diverse SFDA benchmarks demonstrate that SafeCut achieves state-of-the-art performance, highlighting the effectiveness of safeguarding mutual correction in SFDA via cut statistics.

Stochastic semiclassical gravity represents stress–energy fluctuations through the Einstein–Langevin noise kernel. We examine its Newtonian projection for specified closed, particle-number-conserving non-relativistic sources and distinguish the source covariance from a reduced matter channel. The connected one-particle covariance is state dependent and differs from the universal potential-noise law postulated in the Diósi–Penrose model. To relate the source spectrum to dephasing, we define a separate static probe subject to a prescribed Gaussian noise law. For a finite-variance source operator in an isolated non-degenerate eigenstate, the full connected spectral measure has a gap around zero. The probe dephasing exponent is then bounded and its long-time slope vanishes. Stationary doublets can instead carry static or low-frequency spectral lines, while a specified freely spreading Gaussian source gives a finite limiting exponent. Continuum results depend on preparation, normalisation, infrared regularisation and the order of limits. We also compare coherent and incoherent many-body preparations and establish no-signalling for fixed classical-noise channels. These results identify the spatial, temporal and dynamical assumptions needed to relate source fluctuations to a matter-decoherence model. They do not exclude Markovian limits in other number-conserving non-relativistic preparations.

Unstructured discharge notes in Electronic Health Records (EHRs) often carry signal complementary to structured medical codes, holding patient-specific evidence that standardized cohort-level codes alone cannot capture. However, this evidence in notes is frequently buried in lengthy, noisy text that is not intentionally written with any specific clinical prediction in mind. Summarization is an obvious mitigation, but generic summaries, tuned for fluency rather than the outcome, routinely omit decisive evidence while retaining plausible but uninformative detail. To this end, we propose RASPER, a Reward-Aligned Summarizer for Prediction in EHR, that optimizes note summarization directly against the downstream clinical task. RASPER employs a tunable LLM-based summarizer to extract task-relevant evidence from discharge notes and trains it via reinforcement learning from prediction feedback, using a reward derived from the downstream predictor's loss. To ground the summarizer, a longitudinal encoder converts structured codes into soft prompts that incorporate each patient's clinical context into note summarization. By rewarding the quality of the resulting multimodal prediction, RASPER encourages the summarizer to retain patient-specific evidence that complements, rather than duplicates, information captured by structured codes. RASPER consistently outperforms strong baselines on both readmission prediction and medication recommendation across MIMIC-III and MIMIC-IV.

Collective modes of the superconducting condensate encode fundamental information on the pairing interaction, yet their direct detection remains experimentally challenging. In multiband superconductors, the Leggett mode, i.e., a coherent oscillation of the relative phase between two condensates, is Raman-active and couples to light only nonlinearly in ordinary situations. Here we show theoretically that terahertz two-dimensional coherent spectroscopy (2DCS) provides a direct fingerprint of the Leggett mode (with frequency $\omega_L$) through sideband emission at the detection frequency $\omega_t = \omega_L\pm\Omega$ ($\Omega$ is the central frequency of the incident pulses) in the nonlinear 2D spectrum. The key insight is that the finite duration of the THz pulses is the physical mechanism that makes the mode accessible: the broad spectral content of a finite pulse provides the nonlinear frequency combinations needed to resonantly excite the mode at {\omega}L without any prior knowledge of its value or tuning of external parameters. We demonstrate robustness of this signature against temperature and quasiparticle relaxation, and show that sweeping $\Omega$ allows unambiguous identification of the Leggett mode.