Papers

We present a low entry barrier numerical code LazyTB that solves the Einstein equations in the ADM-formulation for a general spherically symmetric problem with an arbitrary number of fluids with user defined equations of state and optional interactions between the fluids mediated by drag-vectors. We present the ADM equations in terms of carefully chosen dimensionless variables that avoid some numerical instabilities by analytic cancellation of potentially diverging terms. We demonstrate the code by applying it to a number of examples including the standard LTB model, a model with radiation and dark matter, a polytropic dark energy model with a non-vanishing sound speed and a model with coupled interacting dark matter and dark energy. We also implement a suite of diagnostic tools, including ray-tracing algorithms, that allow extracting physical observables such as luminosity distances for observers at arbitrary locations from the simulations. The code is built to be easy to extend also beyond the late-universe applications considered in the examples of this paper. LazyTB is available at https://github.com/ollijvaisanen/LazyTB.

Tool calling, invoking external tools on demand, is central to agentic LLMs, yet the mechanism that decides whether a model calls a tool or responds directly remains poorly understood. Agentic prompts are long and heavily scaffolded, combining role instructions, tool schemas, format templates, and the user's request across hundreds of tokens, creating a noisy, highly entangled context in which no single controllable variable for mechanistic analysis is obvious. To obtain such a variable, we propose a method that converts complex agentic prompts into minimal contrastive pairs in which a single request verb determines the tool-call decision: replacing an execution-verb (e.g., write) with an analysis-verb (e.g., discuss) reliably flips the decision, suggesting it is mediated by a compact internal state. We construct 500 such paired prompts across Python, Java, and C++ (300 for mechanistic analysis, 200 held out for evaluation). We trace the decision to a vector, $\mu_\Delta$, that is both causally necessary and sufficient and generalizes beyond the discovery prompts to native multi-turn $\tau^2$-Bench trajectories and verb-free requests. Behavioral ablations show that the scaffold establishes a tool-call prior; Transcoder decomposition then reveals that analysis verbs suppress this prior through features signaling that tool use is unnecessary, whereas execution verbs largely leave it intact. Downstream scaffold-reading attention heads and MLP features read out the resulting state, and the same mechanism recurs across seven models from the Qwen, Mistral, and Granite families. Our code is available at https://github.com/XijieGo/MI4ToolCalling.

Quantum machine learning is rapidly emerging as a promising and potentially more sustainable approach that can complement traditional, energy-hungry HPC, AI, and GPU resources-particularly for the demanding global challenges the world urgently needs to address. In recent years, the first prototypes of quantum processors have reached the market, are sometimes available via the cloud, and distributed quantum computing is beginning to move from a largely theoretical concept to a demonstrated reality. However, these devices are still noisy and qubit-limited. Therefore, it is desirable to design quantum machine learning models with a reduced quantum register and a limited number of quantum gates, avoiding overly deep and wide quantum circuits. Here, we explore this idea by proposing a novel divide-et-impera-based training protocol that splits quantum neural networks into smaller components and better governs their optimization. We benchmark our approach on real data and real-world prediction tasks in intertwined energy and environmental domains, such as the status of charging stations for electric vehicles and the global air quality index. Our results suggest a design principle for quantum machine learning algorithms across a wide range of applications, which can be more feasibly tested on state-of-the-art quantum processors or within modular quantum architectures being developed for future hybrid infrastructures interconnected via high-speed communication links.

Risk evaluation under distributional ambiguity is central to decision making in finance, economics, and operations research. Wasserstein balls provide a natural way to describe uncertainty around a reference distribution. We solve a natural yet open problem of robust optimization for the class of distortion riskmetrics with Wasserstein distance as the sole ambiguity constraint. This chosen objective class does not require convexity, monotonicity, and continuity of distortion functions, encompassing many common risk measures and deviation measures. First, we characterize conditions under which direct convexification preserves the worst-case value. Second, we develop a constructive method for exact worst-case evaluation when the direct convexification conditions fail. Third, we construct explicit approximate worst-case distributions and provide computable error bounds to assess their accuracy without solving the exact problem. We apply these results to distributionally robust portfolio selection and use numerical experiments to assess approximation accuracy and the resulting portfolio decisions.

Networks that behave alike now can still learn differently when training continues. Work on loss of plasticity and critical periods shows that the path to a state shapes what follows; it does not show whether the path carries information that a measurement of the state itself misses. We ask when the training history of a network predicts its future learning better than its current state. In a main study, small multilayer perceptrons were trained under three history regimes (42 histories), and future learning was measured at four checkpoints by a short probe: a copy of the network trained for 100 updates on a new task. Before the prediction result was read, the protocol checked the probe. It responded monotonically to a function-preserving rescaling of hidden units, repeated measurements agreed (intraclass correlation 0.940, [0.903, 0.997], in the least reliable class, mean of three repeats), and a re-initialisation of units was visible directly after it but not 100 to 200 updates later. A history state of at most four dimensions did not improve on a calibrated model of the current state (gain -21.4%, 90% interval [-91.9, 8.1]; required in advance: 10%). A companion screen on 1,560 synthetic regression runs asked the same question for a target further away, the final error of the run. There, history models forecast better than the current validation error after 12 of up to 240 epochs (compact state 30.3%, [15.8, 39.4], a contextual comparison) and were not distinguishable from it after 48. In both studies the history was informative only while the current state was not yet informative about the target; this reading was formed after the results.

We study which parameters of deep, unmasked, single-head attention are determined by its input–output function. For known positive nonconstant real-analytic normalizers, the function generically determines the effective scores and combined value map up to the signs induced by even normalizers. This proves the real-analytic case of a conjecture of Henry–Marchetti–Kohn, including softmax. We then classify exceptional fibers under explicit normalizer conditions, identifying when collapse makes later scores unobservable, and establish sharp Taylor orders for local identification. Near simultaneous query/key collapse, we compute the complete native Jacobian decay spectrum on separating finite input banks. For common first nonconstant normalizer degree $k$, layer $i$ has contact order $2k3^{i-1}-1$, with exact multiplicities and kernel dimension. High-precision and automatic differentiation calculations illustrate the resulting loss of numerical sensitivity.

A recently introduced anharmonic mean-field model unifiedly reproduced a broad range of low-temperature glass phenomena — including harmonic nonphononic spectral properties, linear micromechanics and strongly driven elasto-plastic dynamics — indicating that its underlying energy landscape is intrinsically glassy. Here, we apply a nonlinear modes framework to the model and derive analytic predictions for the asymptotic distributions of activation barriers $p(\Delta{U})\!\sim\!(\Delta{U})^{1/4}$ and the external force needed for the onset of plasticity $p(f_{\rm c})\sim f_{\rm c}^{2/3}$, for their extreme-value scaling and for $\langle\Delta{U}\rangle$ beyond the asymptotic regime. These predictions are expected to equally apply to the mean-field model and to finite-dimensional glasses. We develop efficient algorithms for sampling minima and saddles of the model's glassy potential energy landscape, and quantitatively confirm the theoretical predictions. This progress is enabled by identifying a subset of collective degrees of freedom that are physically relevant for activated glassy dynamics, which like the theoretical predictions should apply to realistic glasses.

For every fixed proper minor-closed class $\mathscr C$ and every $\epsilon>0$, we give a deterministic LOCAL algorithm that returns a dominating set of size at most $(2a(\mathscr C)+1+\epsilon)\gamma_f(G)$ on every $G\in\mathscr C$. Here $a(\mathscr C)$ is the supremum edge-to-vertex ratio in $\mathscr C$, and $\gamma_f(G)$ is the fractional domination number. The class also admits a deterministic $(1+\epsilon)$-approximation for fractional dominating set and a randomized algorithm that always returns a dominating set and has expected size at most $(1+\epsilon)\gamma(G)$. In each case, the number of rounds depends only on $\mathscr C$ and $\epsilon$. None of these algorithms requires the number of vertices or the maximum degree as part of the input. For planar graphs, this gives the deterministic guarantee $(7+\epsilon)\gamma_f(G)$. Together with the lower bound of Hilke, Lenzen and Suomela, it determines the infimum of the deterministic constant-round approximation ratios for planar minimum dominating set as $7$, settling a question that had remained open since their work. The corresponding infima, measured against the integral optimum, are $7$ for graphs of Euler genus at most any fixed $g\ge0$, $2t-3$ for $K_t$-minor-free graphs with $3\le t\le9$, and $2r+1$ for graphs of treewidth or pathwidth at most any fixed $r\ge1$. We also prove that, for every integer $r\ge1$, no deterministic constant-round LOCAL algorithm achieves an approximation ratio below $2r+1$ on the $r$-th powers of paths, even when every vertex knows the number of vertices. This gives a new proof that the limiting constants are optimal for planar graphs, graphs of bounded treewidth or pathwidth, and $K_t$-minor-free graphs with $3\le t\le9$. For triangle-free planar graphs, the corresponding infimum is $5$.

We introduce a novel second-order optimization framework for minimizing so-called variable projection functionals. We demonstrate that the proposed framework is especially usefulfor the training of variable projection based kernel methods. In particular, the problem of efficiently training variable projection support vector machines (VP-SVMs) is considered. We show the effectiveness of the proposed training methodology in a real-world application, namely we demonstrate how second-order trust region algorithms can be used to train VPSVM models to recognize road surface abnormalities based on 1D signals obtained from a tire sensor.

Predicting anharmonic vibrational spectra is a complex computational task, which becomes quickly infeasible as molecular size and the number of vibrational basis functions increase, leading to an exponential growth of the underlying Hilbert space. Here, we employ a sample-based quantum diagonalization (SQD) framework to compute anharmonic vibrational energies and spectra. The approach combines quantum state preparation and sampling with configuration recovery, diagonalization of the Hamiltonian projected in a subspace of basis configurations, and calculation of transition-dipole moments to obtain both vibrational energies and infrared spectra. We investigate two approaches for sampling, namely, vib-LUCJ and vib-SqDRIFT and apply the method to study the polyyne molecules C$_2$H$_2$ and C$_4$H$_2$, reaching representations requiring up to 104 qubits. Beyond energies, transition-dipole calculations reveal that infrared intensities and excited-state composition continue to evolve with basis size through anharmonic mixing and intensity redistribution, even when low-energy eigenvalues appear converged. These results show that sample-based quantum subspace methods can capture spectroscopic information in vibrational spaces far beyond the regime of full diagonalization. Moreover, our simulation identify multi-state recovery and scalable projected-space treatment as central challenges for further scaling sample-based approaches.

We present a holographic model of QCD to study the strong coupling constant $\alpha_s$ from the low-energy region to the high-energy regime. The approach uses a double-dilaton background, which breaks conformal and chiral symmetries, while large-$N_c$ corrections are incorporated to connect the holographic description with perturbative QCD. The model leads to an infrared fixed point and provides a smooth transition to the pQCD running. The resulting background also produces linear Regge trajectories for scalar, vector, and tensor states in reasonable agreement with experimental data.

National-scale magnetic resonance imaging (MRI) repositories increasingly integrate data from different studies and institutions. However, subject identifiers assigned to study participants are typically specific to individual datasets, so the same person may appear under different identifiers when these datasets are aggregated, a problem we define as identity duplication. Such duplication can create leakage between training and test data and inflate apparent performance in downstream biomedical studies. Existing methods do not provide an end-to-end, image-based workflow to address this problem. In this work, we present HAPPEN, a human-in-the-loop pipeline for auditing identity duplication in T1-weighted brain MRI repositories. It combines SHA-256 fingerprinting for exact-duplicate detection with embeddings learned through supervised contrastive learning to retrieve near-duplicate candidates: pairs of non-identical scans that may originate from the same person. Retrieved pairs are reviewed as candidates in a locally hosted interface rather than automatically classified as duplicates. We deployed the workflow in a national-scale aggregated repository containing 95,129 scans and assessed end-to-end recovery of 54 pairs of subject records identified as duplicates using genome-wide genotype data. Transferability was assessed by locally deploying the same workflow on 22,386 scans at an independent institution without model retraining or image transfer. Deployment in the study repository identified 1,316 exact-duplicate scan groups and 1,275 near-duplicate groups of subject records supported by human review. Of these groups, 56% and 82%, respectively, crossed dataset boundaries. All 54 genetic-reference pairs were recovered. The external team independently completed the full workflow using a locally selected operating threshold and review standard.

Shallow models are special cases of deep models, and deep models theoretically have the potential to outperform the shallow ones. However, the existing empirical asset pricing literature provides strong benchmarks for shallow models. Residual learning allows neural network models in asset pricing to go deeper by preserving and refining their shallow counterparts. The out-of-sample Sharpe ratio for value-weighted long-short portfolios of deep residual models (2.07) is higher than that for the corresponding shallow ones (1.92) and more than twice that of the deep feedforward models (0.89). We show that model depth is a source of additional economic value in asset pricing. Residual learning can be used to deepen other neural-network-based asset pricing models if they contain intermediate layers. Our design also provides one way to scale asset pricing models, making native "large asset pricing models" more feasible.

Late-stage shell interactions, including shell mergers, can mix material across adjacent burning shells and imprint chemically inhomogeneous structures in the hydrostatic O-rich layers before core collapse. Whether such inhomogeneities survive the explosion and remain observable in the resulting supernova remnant is not well understood. We investigate the spatial and compositional structure of the O-rich ejecta in Cassiopeia A using deep Chandra X-ray observations. Principal component analysis of narrow-band images reveals O-rich ejecta spanning a compositional sequence from Ne-rich through NeSi-rich to O/Si-rich material. Spatially resolved spectroscopy of 20 representative regions confirms systematic depletion of Ne and Mg toward the O/Si-rich component. Notably, the composition of the O/Si-rich ejecta over a broad elemental range from O to Ca is simultaneously well reproduced by O-layer material in 17-20 $M_\odot$ one-dimensional presupernova models that experienced strong shell-merger-induced burning and mixing. In contrast, the Ne-rich ejecta retain substantially higher Ne and Mg abundances and resemble less strongly processed O-shell material. These chemically distinct components are spatially segregated on remnant-wide scales, with Ne-rich ejecta preferentially concentrated toward the north and O/Si-rich ejecta more prominent in the southeast. Our results suggest that late-stage shell burning and mixing in the progenitor of Cassiopeia A were spatially heterogeneous. The remnant-wide distribution of ejecta with different burning histories further indicates that part of this asymmetric presupernova structure may have survived the explosion and remains imprinted in the present-day remnant.

Large neural networks often acquire capabilities that small models fail to learn. Does this stem from large models learning more representative features, or from being more robust to unaccounted-for adverse effects introduced during training? We define and quantify one such adverse effect, primacy bias, as the extent to which exposure to early data distributions impairs later learning. We show that small models can allocate learning capacity inefficiently toward early distributions, whereas sufficiently overparameterized models are robust to this effect. This inefficiency is particularly consequential in pretraining, where foundation models often encounter heterogeneous data distributions sequentially rather than jointly. As a result, small foundation models can struggle to learn distributions encountered late in training, which is particularly harmful when later data emphasizes desirable capabilities such as code, mathematics, and reasoning. Motivated by these findings, we introduce Exposure Therapy (ET), a simple regularization that promotes more efficient allocation of learning capacity during sequential pretraining. We demonstrate that ET improves foundation models' performance on late data distributions as well as overall capability in models up to the billion-parameter scale. Overall, our results suggest that some benefits of large foundation models may arise from greater robustness to adverse training effects, rather than from learning more representative features, and that improved training algorithms can recover some of these advantages in smaller models.

When an envy-free allocation of indivisible goods does not exist, monetary transfers can restore envy-freeness. Existing work on fair division with subsidies, however, typically assumes that these payments are provided by an external source, an assumption that may be unrealistic in many applications. We address this limitation by allowing only monetary transfers between agents, with each agent's payments constrained by their individual budget. We show that while it is polynomial-time tractable to determine whether a given allocation can be made envy-free by payments under individual budgets, the general problem of computing such an allocation from scratch is NP-hard, even when agents have relatively large budgets. Motivated by this intractability, we conduct a parameterized complexity analysis, establishing fixed-parameter tractability with respect to the number of goods or to the joint parameter number of agents and good types, and we provide efficient algorithms in several special cases. For explicitly listed items, our type-based algorithm answers the envy-freeness part of an open question of T. T. Nguyen and J. Rothe, "Complexity Results and Exact Algorithms for Fair Division of Indivisible Items: A Survey."

Semi-supervised learning (SSL) relies on two core mechanisms: self-training under the Teacher-Student (T-S) framework and joint optimization of labeled and unlabeled losses. Despite their effectiveness, we find both mechanisms introduce distinct optimization pathologies. First, parameter coupling enforces strict synchronization between teacher and student, where strong regularization on the student degrades the teacher's fitting ability, thereby limiting the permissible generalization intensity. Second, the imbalance in gradient update consistency between labeled and unlabeled losses drives the shared parameters to prematurely converge to labeled-dominated local minima, creating a bottleneck for global optimization. To address both issues, we propose the Pioneer Student (PiS), an auxiliary branch that operates in an independent parameter space and periodically transfers accumulated knowledge back to the T-S model. Extensive experiments show that PiS is a universal plug-and-play module that consistently improves mainstream SSL methods.

Organizations have long sought to make workers' expertise reusable by others. Agentic AI changes the nature of such reuse by enabling AI systems to act on workers' knowledge with limited human involvement. This raises the question of how this shift shapes workers' willingness to share their expertise. We conducted an experiment with knowledge workers who created materials incorporating domain knowledge and decided whether to authorize human or AI reuse. We find that AI and human reuse differ primarily in whether workers choose to share their knowledge, rather than in what they choose to share. Participants' reasoning shifts from prosocial considerations when sharing with humans toward concerns about loss of control, replacement, and downstream governance when sharing with AI. These findings suggest that AI reuse may intensify tensions between organizational knowledge reuse and contributors' interests. We discuss implications for workplace AI and knowledge management policies that preserve workers' rights and agency.

Skeleton-based reasoning prompting is a promising training-free approach for structuring LLM reasoning, but prior work largely assumes an English-centric setting. We propose the Language-Aware Skeleton Exploration Framework (LASEF) to study skeleton-language choice in multilingual mathematical reasoning. Across math benchmarks, model scales, and languages, we show that English skeletons yield a small positive tendency on average, most visible for smaller models and low-resource languages. However, few language-level gains remain significant after correction, and English is not universally optimal. Combining greedy decoding, multi-rollout evaluation, translation ablation, and cross-benchmark validation, we further find three patterns of skeleton-language effects: directionally consistent, evaluation- and benchmark-dependent, and asymmetric negative. These effects cannot be fully explained by generation quality alone. Overall, skeleton language is a context-dependent design variable that requires multi-level exploration. All resources are released at https://github.com/lhsstn/LASEF.

Whether gravitational caloric theory admits spherical black-hole solutions beyond Schwarzschild remains open. A well-defined black-hole solution requires both a regular horizon and a nonsingular exterior extending to infinity. To investigate this question, we cast the vacuum equations for a purely radial caloric field in a general static spherically symmetric metric into a three-dimensional autonomous system, which facilitates the global classification of solutions. We show that the regular asymptotic geometry can be Minkowski or conical, with the latter requiring a specific relation between the model parameters. Within this parameter slice, Schwarzschild is the only asymptotically flat black hole, whereas non-Schwarzschild black holes with conical infinity exist. These black holes can remain arbitrarily close to Schwarzschild from the near-horizon region to the conventional weak-field region (e.g., Solar System scales), yet retain an order-unity solid-angle deficit or excess at infinity. The asymptotic solid angle depends on a single model parameter and is independent of the caloric field amplitude. At fixed locally inferred mass, the caloric amplitude sets the conical transition scale, with weaker fields shifting the transition outward. We derive the local metric corrections and use the resulting periapsis shift to formulate an orbital test of the transition scale.

Large Language Models (LLMs) have been widely applied to software vulnerability detection. However, their performance is often limited by insufficient use of control-flow and data-flow information. In this paper, we propose GRAML, a framework that combines graph evidence, vulnerability description generation, and multi-task training. GRAML first performs static analysis on C/C++ programs to extract critical source lines and typed line relations as structural evidence. It then uses this evidence to guide GPT-5 through the Tree-of-Thought-guided Vulnerability Reasoning (ToT-VR) process and generate vulnerability descriptions. These descriptions are further combined with Detection, Localization, and Assessment samples to build a unified four-task training dataset. We evaluate GRAML on an in-distribution (ID) test set and six out-of-distribution (OOD) datasets. The results show that GRAML achieves average F1 scores ranging from 66.67% to 68.70%, outperforming state-of-the-art baselines by up to 30.92%. Ablation experiments further show that ToT-VR and graph-guided vulnerability descriptions improve detection performance compared with standard Chain-of-Thought (CoT) reasoning and raw Code Property Graph (CPG) serializations. These findings provide practical guidance for building more reliable and secure software engineering systems with large language models.

This paper presents a lightweight and versatile learned optimizer that dynamically recombines gradient history, represented as averages over disjoint time spans. The optimizer reduces the prediction space to one scalar coefficient per gradient average, shared by multiple parameters. Progressively averaging older gradients minimizes memory cost of long history, while keeping their contributions independently accessible. A 37k-parameter network trained in 0.87 GPU-hours generalizes zero-shot to unseen tasks, lowering validation loss by 9.1% and 0.4% on BERT-Tiny and GPT-Tiny, and improving test accuracy over Adam by 3.5 %p on a Vision Transformer and by 2.7 %p on average across nine graph models, with FLOPs overhead as low as 0.3%.

This paper proposes and analyzes a numerical method for coupled wave-heat systems that arise, for example, in visco-elasticity with memory, thermo-elastic wave propagation with finite thermal speed, and Maxwell's equations coupled to dispersive material laws. Motivated by the widespread use of explicit leapfrog schemes for wave problems and the parabolic time-step restriction for heat equations, we design a second-order scheme that combines leapfrog time integration for the wave part with a Crank–Nicolson step for the heat part. The coupling is arranged in a Strang-splitting–type fashion so that the overall scheme remains explicit in the coupling and is subject only to a CFL condition of hyperbolic type, rather than the more restrictive parabolic constraint. We introduce an abstract space discretization that covers a broad class of wave–heat systems and accommodates both conforming and stabilized non-conforming discretizations. Using a general error decomposition, we derive error estimates for the fully discrete scheme under the desired CFL condition. Numerical experiments for our model applications confirm the theoretical results.

The full shadow of a complex polynomial $P$ of degree $d\ge2$ is the closure of all zeros of $(P^n)^{(m)}$, $n\ge1$, $0\le m<dn$. We prove that it consists of a compact connected limiting core containing all roots and critical points of $P$, together with isolated transient zeros, each occurring at only finitely many powers. The core is the Hausdorff limit of the zero sets pooled over all derivative orders as $n\to\infty$ and the support of their limiting normalized root-counting measure. For $m/n\to\alpha\in(0,d)$, we establish weak convergence of normalized root-counting measures and Hausdorff convergence of zero sets to the limiting supports, both stable under coefficient perturbations. We exhibit quartics with infinitely many transients. A bounded operator constructed from polynomial differentiators realizes the full shadow, core, and transients as its spectrum, Fredholm essential spectrum, and discrete spectrum, respectively.

Data collection is often costly or logistically demanding, limiting both the questions researchers can pursue and how precisely they can answer them. Prediction-powered inference (PPI) can reduce the amount of data needed for precise parameter estimation by combining labeled data with machine learning predictions. However, ignoring dependence within clusters can produce confidence intervals that cover the true parameter less often than their nominal rate. We introduce Cluster-Robust PPI++, which provides standard errors in closed form and asymptotically valid confidence intervals under arbitrary dependence within independent clusters, requiring no bootstrap or resampling. Our central contribution is to accommodate partially labeled clusters, a common empirical setting in which clusters contain both labeled and unlabeled units. As units are dependent within clusters, partially labeled clusters violate the independence assumption of PPI++. We also show how precision increases depend on the labeling design, and derive a cluster-aware power tuning rule that minimizes asymptotic variance. In an application to television news, standard PPI++ confidence intervals have coverage below 60%, whereas Cluster-Robust PPI++ can achieve nominal 95% coverage.

Safety interpretability advances the study of Large Language Model (LLM) alignment from behavioral constraints driven by data or algorithms towards a deeper understanding of internal mechanisms. However, existing works have focused primarily on safety-related representations, attention heads, or neurons after alignment, while largely overlooking the safety mechanisms in pretrained-only models and their evolution across alignment checkpoints. To address this, we propose SafeEvo, an interpretability framework from the circuit (sparse subgraphs of an LLM) perspective. SafeEvo first applies an optimization-based extraction algorithm to identify weak refusal circuits in pretrained base LLMs that can independently express refusal behavior. Causally ablating these circuits completely eliminates the base model's refusal of harmful inputs. SafeEvo then traces the evolution of refusal circuits across successive alignment checkpoints and finds that their structures change progressively, suggesting that the alignment tax may result from refusal-circuit updates affecting utility-related parameters. To validate this, SafeEvo introduces Safety Circuit Alignment (SCA), which confines safety updates to the refusal circuits. Experiments across three LLMs and two alignment algorithms show that, on average, SCA outperforms vanilla alignment in three aspects: (1) stronger alignment, lowering harmfulness score by 63.21%; (2) less over-refusal, yielding a 58.44% decrease in refusal rates for benign queries; and (3) better utility, retaining 99.58% of the original model capabilities.

We study graph transformations and their effects on the eigenvectors of three fundamental graph matrices: the adjacency matrix $A$, the signless Laplacian $Q$, and the Laplacian $L$. We extend the Laplacian eigenvector edge and matching principles introduced by Merris to $Q$ and $A$. We also extend some of the known $L$ graph transformations to $Q$ and $A$ and prove that graphs admitting a common eigenvector $\mathbf{x}$ for $A, L$ and $Q$ are such that vertices corresponding to nonzero components of $\mathbf{x}$ have same degree. Following our previous work for $L$, we investigate bivalent graphs for $A$ and $Q$, that is graphs admitting an eigenvector with all components in $\{-1, 1\}$. In particular, for trees, we characterize $Q$-bivalence and establish that $A$-bivalence forces all vertex degrees to be odd.

Uterine contractions in fetal MRI are typically identified manually and discarded, limiting insights into contraction dynamics. We formalize Uterine Contractile Activity Detection (UCAD) as a weakly-supervised learning problem and introduce STORK, a multi-instance learning model trained on dynamic MRI series using only coarse, series-level labels. STORK factorizes 3D spatio-temporal convolutions into parallel branches across temporal hyperplanes to capture coherent tissue motion without the cost of full 4D convolutions. Per-frame embeddings, combining intensity and Demons-estimated displacement fields, are aggregated by a linear mean-pooling head. This ensures that frame-level contraction scores can be recovered post-hoc without frame-level training supervision. Evaluated on around 700 multi-vendor dynamic fetal MRI series, STORK achieves a series-level AUROC of 95.0% and AUPRC of 94.6%, substantially outperforming 3D ResNet and ConvNeXt baselines. Grad-CAM analysis suggests that the model draws on predictive features extending beyond the placenta into the uterine tissue, offering an automated tool for richer phenotyping of uterine behavior.

Asynchronous RL accelerates large language model post-training by decoupling rollout generation from optimization, but trains on stale trajectories. Existing methods primarily correct token-level policy mismatch through importance-ratio control in the actor objective. We show that this policy-side correction alone is insufficient: advantage estimates also inherit mismatch from behavior-policy continuations, which we term advantage staleness. We derive exact bias and variance decompositions for a general two-channel actor update, revealing nonseparable coupling between policy-weight and advantage-estimation errors: their interaction induces multiplicative bias terms, while squared policy weights amplify advantage uncertainty in gradient variance. This motivates the hypothesis that policy- and advantage-side correction should be coordinated. We introduce Coupled Off-Policy Correction (COPC), an actor–critic method combining token-level ratio masking with two-sided clipped-ratio weighting of TD residuals for return and advantage estimation. Joint parameter sweeps across staleness levels support this hypothesis: the effect of one correction parameter depends on, and can reverse with, the other. COPC achieves the highest reported performance on tool-integrated mathematical reasoning and search, outperforming the strongest reported asynchronous baseline in each setting. It also offers a broad high-performing parameter region and improved training stability. In search, COPC remains stable throughout training, while most evaluated asynchronous baselines collapse late in training. These gains persist at 64-step policy staleness. COPC adds minimal step-time overhead over asynchronous PPO and retains a $1.7\times$ step-time speedup over synchronous PPO.

We establish the free-boundary version of Schoen-Simon's regularity and compactness theory for stable minimal hypersurfaces in a complete $(n+1)$-dimensional Riemannian manifold-with-boundary, following the intrinsic PDE scheme introduced by the first-named author. The key step is to prove sheeting theorems in the two possible scenarios in which local weak flatness can occur near a point on $\partial M$: flatness with respect to $\partial M$, and flatness with respect to a reference hypersurface-with-boundary meeting $\partial M$ orthogonally. We obtain these theorems via $\varepsilon$-regularity results for geometrically adapted tilt functions that quantify flatness while keeping track of the ambient geometry. These tilt functions satisfy nonlinear elliptic PDEs on the hypersurface which are amenable to an intrinsic analysis via De Giorgi iteration, made possible by the weak Caccioppoli-type inequalities obtained from stability. Both results apply to immersed hypersurfaces with a singular set of locally finite $(n-2)$-dimensional Hausdorff measure. When specialised to embeddings, they yield compactness and regularity: a sequence of stable free-boundary embedded minimal hypersurfaces with uniformly bounded area and singular sets of locally finite $(n-2)$-measure admits a subsequence converging to a free-boundary minimal hypersurface that is smoothly embedded away from a singular set of Hausdorff dimension at most $n-7$. Convergence is smooth and graphical, possibly with multiplicity, away from this singular set. As an application, we extend to arbitrary dimension the free-boundary Almgren-Pitts existence theory developed by the second-named author with X. Zhou and prove that every compact Riemannian manifold-with-boundary of dimension $n+1$ contains a free-boundary minimal hypersurface smoothly embedded outside a singular set of Hausdorff dimension at most $n-7$.