Papers

We modify a construction of Bradač \cite{Bradac26} using a vertex ordering to give, for every prime power $q$, an explicit $K_5$ free graph with more than $q^7$ vertices and independence number below $600q^4$. This shows $$r(5,t)=\Omega(t^{7/4}).$$ Additionally, pruning a graph defined by the Coulter and Matthews polynomial $X^{14}$ \cite{CM}, we give a deterministic polynomial time construction proving $$r(5,t)=\Omega\bigl(t^{20/11-\varepsilon}\bigr)$$ for every fixed $\varepsilon>0$. These results improve the constructive lower bound $\Omega(t^{5/3})$ of Kostochka, Pudlák and Rödl \cite{KPR}.

Fuzzing is effective at finding bugs in deep learning (DL) compilers, but existing fuzzers repeatedly trigger faults they have already uncovered. Current fuzzers diversify the generated programs, and downstream tools deduplicate bug reports post hoc, but neither stops a fuzzer from generating programs that re-trigger known defects. We present Reprise, a DL compiler fuzzer that suppresses reports of known defects during test generation. Reprise uses a deliberately lightweight generator that builds graphs in a unified intermediate representation (UIR) with local operator signatures. Instead of diversifying programs, Reprise distills each discovered defect into a semantic graph pattern that captures the operators, value constraints, graph context, and data flow required to trigger it. During graph synthesis, it regenerates any node that completes a known pattern, so known defect triggers are avoided before compilation and execution. We evaluate Reprise on three DL compilers: TVM, PyTorch Inductor, and ONNX Runtime. Against its unguided variant, patterns written for the dominant known defects reduce crash reports by 90.2% on TVM (254 to 25) and by 93.8% on PyTorch Inductor (594 to 37), with comparable branch coverage and 1.0-17.9% fewer executed tests. These results come from one run per configuration and concern the defects the patterns were distilled from. Reprise also found 25 previously unknown bugs across the three compilers, 24 of them within one month, of which 7 have been fixed and 12 more confirmed by developers. The replication package has been provided at [11].

We propose a stochastic optimization framework in which football performance is modeled as the result of an efficiency-driven production process under uncertainty. The model incorporates economic inputs, a latent efficiency variable evolving according to a stochastic differential equation, and a control variable representing investment in sports development. We derive the associated discounted Hamilton–Jacobi–Bellman (HJB) equation, characterize the optimal investment policy, prove a verification theorem under explicit growth conditions, and show that a bounded investment budget is required for the control problem to be well posed. We relate our efficiency measure to the stochastic frontier and data envelopment analysis (SFA/DEA) traditions used elsewhere in sports economics, and clarify what a dynamic control formulation adds relative to those static approaches. The theoretical results are illustrated with a numerical solution of the HJB equation – validated by a grid-refinement convergence study – and Monte Carlo simulations. A cross-sectional analysis of the 24 AFCON 2025 national teams, based on GDP, population, and FIFA ranking data, estimates country-specific conditional log-efficiency residuals using heteroskedasticity-robust inference. We show that these residuals are mechanically and strongly correlated with FIFA points by construction, quantify this dependence, and interpret the results accordingly. Teams such as Senegal and Morocco consistently outperform their GDP-implied potential, whereas others, including South Africa and Tanzania, tend to underperform. While these patterns are broadly consistent with observed AFCON outcomes, the estimated residual also captures unobserved factors, such as institutional quality, diaspora talent, and demographic structure, that are not included in the model.

Indirect prompt injection (IPI) hides adversarial instructions in content that large language model (LLM) agents read at runtime. As agents compose heterogeneous capability units, including Tools, MCP servers, and Skills, the carriers of injection multiply, and defenses built to recognize attack patterns fall behind them. We instead shift defense from covering attack patterns to one stable point: whatever the carrier and however the injection propagates, harm materializes only at the execution boundary, where the agent turns internal state into an external action or released output. Safety there turns on two conditions, both settled by the trusted task rather than by the run: whether the proposed effect is authorized, and whether the runtime information reaching it is endorsed by that task. We present APEX, an active defense that enforces both at this boundary from a single authorization contract compiled before untrusted execution: evidence-gated prevention admits an effect only when the contract justifies it, while deception-based exposure makes unendorsed use reveal itself before the effect commits. Protection therefore follows from what the task permits rather than from how an attack is built, and applies uniformly across capability units without attack-specific policies or taint tracking. Against 13 baselines, APEX attains 0% attack success on five of six benchmarks and 0.56% on the sixth, holds 0% under adaptive attacks on all three capability-unit types, and remains effective across defender backbones. Code is available at https://github.com/ZhengXR930/APEX_official/tree/official.

World action models jointly learn visual predictionand robot actions, providing a way to use observations ofscene evolution for policy learning. Their video and actionlosses, however, provide no explicit target for the geometricconsequences of a demonstrated action sequence. Moreover,visual features taken after temporal attention can contain futureobservations, making them unsuitable as the sole current visualinput to an auxiliary predictor. We introduce ACG-WAMand its auxiliary objective, the Action-Conditioned GeometricJoint-Embedding Predictive Architecture (ACG-JEPA), whichpredicts geometric features at several horizons from the currentobservation and intervening actions, using the future slot of afrozen VGGT encoding of each current and future image pairas the target. We apply this supervision from the head and wristcameras to a shared visual embedding before temporal mixing,and remove the teacher and auxiliary modules at inference.On 50 RoboTwin 2.0 tasks, ACG-WAM achieves 93.46%success in clean scenes, with the best randomized success(92.68%) and mean across both settings (93.07%) among thecompared methods; across three tasks on a real robot, itachieves 85.00% success and 91.67% partial completion score,exceeding Motus by 10.00 and 9.17 percentage points, respec-tively. Code:https://github.com/RoboOpus/ACG-WAM.Website:https://RoboOpus.github.io/ACG-WAM.

Large language model (LLM) agents have demonstrated strong capabilities in interactive environments, yet their ability to continually evolve from experience remains limited. Although fine-tuning enables adaptation, its dependence on parameter access and high computational costs restrict its flexibility, especially for large-scale and closed-source LLMs. External memory offers an alternative by allowing agents to accumulate experience without modifying model parameters. However, existing methods mainly focus on experience representation and organization, while the acquired knowledge remains tightly coupled with specific tasks and contexts, limiting generalization. A key challenge is how to transform concrete interactions into abstract and reusable knowledge that guides future decisions beyond individual experiences. To address this challenge, we propose SAGA (\underline{S}elf-evolving \underline{A}gents through Experience-\underline{G}rounded \underline{A}bstraction), a framework for experience-grounded knowledge abstraction and utilization in LLM agents. SAGA progressively transforms interaction trajectories into episodic descriptions, reusable procedures, and principles with explicit applicability conditions, while maintaining links to execution evidence. Retrieved principles are instantiated into task-specific guidance and used to refine candidate actions through corrective feedback and resampling. This creates an execution–abstraction feedback loop, where accumulated knowledge guides future interactions and new experiences continuously update hierarchical memory. Experiments on ScienceWorld and ALFWorld demonstrate improved task performance, with ablation studies highlighting the importance of contextual instantiation and action regulation for leveraging principle-level knowledge.

Rotary Position Embedding (RoPE) encodes token positions by rotating each two-dimensional channel of the query and key vectors at a channel-specific frequency, making the attention logits invariant to a common shift of positions. However, this rotation is periodic, and it leads to position aliasing where relative positions separated by a full rotation period become hard to tell apart. To address this, we propose WavePrune, which restricts each channel to its first rotation period. We show that it removes the distractions in attention maps created by position aliasing and improves overall long-context performance. Specifically, WavePrune raises the HELMET score on four of five models we test without any extra tuning (e.g., 35.7 -> 40.0 on Qwen3-8B). When pretraining models from scratch, WavePrune also achieves lower validation loss at extrapolated lengths than pretraining without it. Because WavePrune restricts each channel to a sliding window, it induces a fine-grained sparsity that our hardware-aligned CUDA kernels exploit for 1.15x prefill and 1.24x decoding speedups over FlashAttention-2 at 32K context. Together, these results show that RoPE's periodic structure, widely regarded as essential, is largely redundant beyond the first rotation period.

In many review workflows the verdict is the only thing retained. The passages behind it are not marked, because that annotation costs far more than recording the decision. We measure how much of that evidence a small language model can recover when it is post-trained on the verdicts alone, with no human evidence labels at any stage. On ContractNLI the human evidence spans are held out until evaluation. Matching the recorded verdict and agreeing with those spans are not the same thing: across six systems the two scores are only weakly related and rank the systems differently, so accuracy is a poor guide when the citations have to be reviewable. Label-only training on the bare verdict reaches accuracy 0.896 and span F1 0.564. Rejection sampling, which keeps a generated trace only when its verdict matches the record and then picks one by an automatic source-grounding score, reaches 0.797 and 0.556, against 0.747 and 0.493 before training. Verbatim citation rises from 0.597 to 0.729 under label-only training and to 0.701 under rejection sampling. One seed on one corpus cannot say which method is better, but both improve the evidence without anyone annotating it.

Quantum-enhanced sensing typically relies on preparing specific entangled states. However, engineering these states in scalable many-body systems remains challenging due to the difficulty of designing robust preparation protocols and accounting for realistic noise. We show that evolving a simple product state under native time-independent Hamiltonian dynamics in Rydberg atom arrays generates complex many-body correlations that can potentially enable quantum-enhanced parameter estimation reaching the Heisenberg limit (HL). The key challenge is then shifted to extracting the metrological information encoded in spatial correlations of measurement patterns. We introduce a neural correlation learning framework that combines Bayesian inference with neural networks trained on calibration data. Operating in a two-stage calibration-and-sensing protocol, we numerically demonstrate that this framework effectively extracts many-body correlations to saturate the Cramér–Rao bound dictated by the classical Fisher information. Consequently, it achieves quantum-enhanced sensitivity surpassing the standard quantum limit (SQL). Furthermore, the learned estimator is robust to realistic noise, and remains accurate in the absence of rare measurement patterns. Our results establish a hardware-efficient and scalable paradigm for quantum sensing in interacting many-body systems without requiring engineered entangled states.

We present DistScene, a framework for single-image compositional 3D scene generation by jointly modeling the environment and individual objects. Unlike existing methods that represent scenes primarily as collections of objects, we model the environment as an explicit scene component to provide geometric context for object placement. Specifically, we introduce Scene-Frame Generation, which jointly generates separate environment and object components in a shared coordinate frame, allowing their geometry and relative placement to be learned together. Then we introduce Object-Centric Refinement to refine each object in a local frame with scene context. Finally, we develop Object-to-Scene Distillation to transfer pretrained object-generation priors to scene generation through automatically composed and rendered synthetic scenes. Evaluations on indoor and outdoor benchmarks demonstrate improved scene-level spatial coherence over the evaluated baselines. Project page: https://coolbeam.github.io/DistScene/

We study the fundamental problem of computing Personalized PageRank (PPR) on an undirected and unweighted graph $G$. We focus on the $\eps$-error guarantee introduced by Andersen, Chung, and Lang [ACL; FOCS 2006 $\&$ Internet Math 2007]. Their classic local push method computes an approximate PPR vector satisfying the ACL $\eps$-error guarantee in $O((\alpha\eps)^{-1})$ time, where $\alpha$ is the teleportation parameter. This problem has a lower bound $\Omega(\eps^{-1})$. Working with idealized SDDM solves, we eliminate the dependence on $\alpha$ and present an algorithm that achieves the same error guarantee in $O(\eps^{-1-o(1)})$ time. Consequently, we obtain a nearly optimal algorithm for PPR computation under the ACL error guarantee, and a nearly linear algorithm for local graph clustering with complexity independent of $\phi$.

Object-goal navigation (ObjectNav) in multi-floor scenarios presents a challenge due to sparse rewards caused by long-horizon decision-making. In this paper, we propose a diagnostic study based on a modular framework with an effective learnable policy to analyze failure factors in multi-floor scenarios. To achieve an effective policy for diagnosis, we design the hierarchical factorization policy that deconstructs a single global policy into an intra-floor exploration policy and an inter-floor switching policy. To providing an effective initialization for Reinforcement Learning (RL), the lightweight intra-floor policy is learned by distilling the exploration logic of Visual Language Models (VLMs). Under idealized assumptions, we show that the factorized policy is theoretically equivalent to a single global policy at the policy-representation level. Experiment results indicate that perception performance and stair climbing stability are the primary bottlenecks in multi-floor navigation.

Mass-Loss (ML) is a critical process that remains poorly understood despite its broad implications across astrophysics. Our current knowledge is insufficient to reproduce ML consistently across stars, particularly in cool, low-mass giants, where the time-variable nature of chromospheres (CHR) —the region where most physical phenomena powering ML in this regime are expected to occur— is poorly constrained. We characterize the relevant timescales of CHR variability in red giants and explore correlations with intrinsic stellar properties. We analyze the first large temporal spectroscopic monitoring of CHR variability using the H$\alpha$ line in red giants belonging to the globular cluster NGC 104 (47 Tuc) using FLAMES/GIRAFFE data. We found that after $\sim$4 days, for $\log(L/L_\odot)\gtrsim2.4$, variations in H$\alpha$ on average increase and widen their range of values with increasing luminosity, together with a systematic blueshift of the line core —indicative of outflows— and deeper cores —indicating an increased chromospheric optical depth. The characteristic timescale required to observe variations in the H$\alpha$ profile is approximately one day, showing a flat trend with luminosity. While shorter-timescale variations remain consistent with statistical uncertainties, a possible increase toward dimmer stars is found. These trends appear similarly correlated with luminosity and effective temperature. No further correlation is found with different cluster sub-populations, nor are significant differences observed between AGB and RGB stars. The outflow trends closely match previous observations across a wide metallicity range. We discuss whether these observations reflect changes in H$\alpha$ sensitivity to the winds, a genuine atmospheric transition driven by changes in heating efficiency, or continued CHR expansion with geometrically dominated H$\alpha$ formation.

Large speech language models have demonstrated strong capabilities in unified cross-modal understanding and generation, yet paralinguistic cues, especially emotion, remain difficult to preserve. Existing systems typically rely on entangled acoustic representations, which allow the underlying language model to depend excessively on recovered lexical content instead of grounding its behavior in acoustic-prosodic evidence. We address this limitation with EMODE, an emotion-aware speech language model built around Dynamic Para-Semantic Experts (DPSE). DPSE decomposes continuous speech features into semantic and paralinguistic pathways, routes them dynamically, and fuses them before integration into the language model. To turn this structural decomposition into functional specialization, EMODE is trained with a three-stage curriculum consisting of semantic warm-up, paralinguistic activation, and joint refinement, guided by Orthogonal Expert Guidance (OEG), Semantic-to-Acoustic Alignment (SAA), and Gating Diversity Regularization (GDR). Experiments on SER test, empathetic response evaluation, and the newly constructed bilingual MEPA benchmark show that EMODE improves the balance between lexical fidelity and emotional sensitivity, strengthens affect-grounded response generation, and exposes the value of explicit para-semantic factorization for robust cross-corpus emotion understanding.

Humans inherently understand the physical world through an active process. When sensory evidence is insufficient to infer physical properties, we naturally interact with the environment by deciding what information is missing, how to acquire it, and when sufficient evidence has been obtained. In stark contrast, existing multi-sensory robot systems mainly integrate sensory inputs rather than actively acquiring missing evidence through interactions. In this work, we introduce ROMA, an LLM-based system for Real-World Object-Centric Multi-Sensory Active Perception. ROMA integrates vision, audio, tactile, and force sensing into a reasoning-interaction-feedback loop. The model identifies missing evidence and determines the target objects, interactions, and modalities, while a physical interface executes the selected interactions and collects the multi-sensory feedback. To support this capability, we construct ROMI-2K, a large-scale real-world multi-sensory object interaction dataset covering nearly 2,000 objects and 6 atomic interactions with synchronized sensory feedback. Building on these data, we develop a two-stage training framework that aligns sensory modalities and equips the LLM to assess evidence sufficiency, select informative interactions, and reason over the multi-sensory feedback. We further characterize active perception as perception chains, where acquired evidence guides subsequent interactions and reasoning, and establish ROMA Bench to evaluate single-attribute, long-horizon multi-attribute, and intent-driven active perception. Experiments show that ROMA can actively acquire missing evidence and solve complex, long-chain multi-sensory perception tasks that existing methods struggle to handle, laying a strong perceptual foundation for active multi-sensory embodied agents.

We study the pseudospectrum of the Kerr black hole for gravitational perturbations with spin weight $s=2$, the case of greatest interest in gravitational-wave astronomy. In the hyperboloidal framework with two-dimensional Chebyshev collocation, we formulate the quasinormal mode problem as a non-self-adjoint eigenvalue problem. For $s\neq0$ the fields $\Psi^{(s)}$ and $\Psi^{(-s)}$ are independent, so the conserved current method yields no single-field energy norm. We overcome this with the Teukolsky–Starobinsky identities, which relate $\Psi^{(-2)}$ to a fourth-order operator on $\Psi^{(2)}$ and yield an $H^2$ energy norm after symmetrization. With the $H^1$ norm known for $s=0$, this suggests the pattern $H^{|s|}$, verified for $s=0$ and $s=2$. All results use an $\omega$-independent two-field hierarchy. We find that the pseudospectrum tightens by $1.1$ to $3.5$ decades at each step of $L^2\to H^1\to H^2$, yet stays large in every norm. The $s=+2$ and $s=-2$ operators are isospectral but not isopseudospectral: at twelve of fourteen probes the $\psi_0$ resolvent exceeds the $\psi_4$ one by $0.19$ to $0.82$ decades in the $H^2$ norm, while at the two probes furthest along the QNM line the ordering reverses by $0.18$ to $0.19$ decades. The gravitational pseudospectrum exceeds the scalar one by $0.5$ to $5.2$ decades in the window minimum and by $5.9$ decades in $L^2$ at $\omega M=0.47-0.17\,i$, while along the damping direction the $s=2$ resolvent is non-monotonic and the $s=0$ resolvent smooth. QNM spectral instability is therefore a universal feature of Kerr, and is stronger for gravitational perturbations.

We present an analytical framework deriving the fluid-continuum $\beta$-Fermi-Pasta-Ulam-Tsingou ($\beta$-FPUT) system directly from a third-order resistive magnetohydrodynamics (MHD) expansion to explain persistent, decayless transverse oscillations observed in solar coronal loops. For a continuous wave field propagating along a longitudinal magnetic field with cross-field density variations, a multi-scale expansion demonstrates that quadratic $\mathcal{O}(2)$ advective and Maxwell tension terms vanish identically due to out-of-plane polarization symmetry. Instead, the quadratic longitudinal ponderomotive force drives field-aligned density modulations that back-react on the primary transverse wave, yielding a cubic $\mathcal{O}(3)$ restoring force. In the long-wavelength limit, the governing equations reduce to a fluid-continuum Modified Korteweg-de Vries (mKdV) system where cross-field profile variation provides the non-linear dispersive mechanism. We prove that this internal fluid mechanism establishes stable, amplitude-dependent frequency self-focusing, which phase-locks adjacent elements and prevents phase-mixing wave attenuation without requiring external steady driving parameterizations. This framework enables macro-scale coronal seismology, providing closed-form expressions to invert observed decayless wave-packet durations to compute the unresolved cross-field density gradient scale length ($L_x$) and the internal volumetric filling factor ($f_V$) without relying on traditional emission measure or spectroscopic line-ratio diagnostics. Much like famous Enrico Fermi's historic use of macro-scale displacements to estimate complex atomic explosion yields, this framework establishes a paradigm where monitoring macroscopic oscillation durations empowers observers to extract fine-scale, otherwise unresolvable waveguide properties.

Neural PDE solvers can achieve low prediction errors, but do they reproduce the dynamics of the systems they model? Prediction scores alone offer an incomplete answer: they measure agreement with reference solutions but provide limited insight into how errors accumulate, nearby states diverge, or extreme events arise. We propose an evaluation framework that directly examines these behaviors in deterministic and stochastic neural solvers. By evolving ensembles of nearby initial states and comparing them with direct numerical simulation, we assess three complementary aspects of learned dynamics: error formation, ensemble geometry, and extreme events. Experiments on two-dimensional Kolmogorov flow reveal limitations that conventional scores can obscure. Smaller trajectory errors can reflect weaker error amplification despite less accurate local updates. Models can match an ensemble's overall spread and effective dimension while failing to capture the spatial directions where nearby states diverge. Similarly, matching overall event frequencies can conceal failures to predict persistent extreme events. These findings show that improved prediction accuracy does not necessarily imply greater dynamical fidelity. Our framework makes this distinction measurable, providing concrete criteria for evaluating whether advances in neural PDE solvers better capture the underlying dynamics.

We show that $\mathcal{PT}$-symmetry acts as the effective time-reversal symmetry governing Anderson localization in the antiferromagnet BaMn$_2$Bi$_2$, whereas the general time-reversal symmetry is broken by its long-range magnetic order. The magnetoconductance follows the laws established from breaking time-reversal symmetry throuhg the orbital coupling of charge carriers to the magnet vector potential, however, the degrees of symmetry breaking are qualitatively modulated by the magnetocrystalline anisotropy stabilizing $\mathcal{PT}$-related sublattices. The quantum interferences and hoping amplitudes governing the phenomena are drastically impaired by transverse magnetic fields, which readily cant $\mathcal{PT}$-related magnetic sublattices. Accordingly, when the $\mathcal{PT}$-related texture is weakly perturbed by longitudinal fields orienting along the sublattices, the localization is minutely affected. The robustness of the $\mathcal{PT}$-enforced degeneracies is thus governed by exchange and magnetocrystalline interactions, in contrast to the exact $\mathcal{PT}$-symmetry of the full Hamiltonian, which is broken by any finite field.

Injecting skills into a frozen language model currently costs a million parameters and a reinforcement-learning pipeline. We introduce DecSteer, a System-1 decision operator trained by behavior cloning that lowers this cost by roughly two orders of magnitude. The default operator uses 330K parameters to match a 1.33M-parameter operator trained with reinforcement learning, exceeds or achieve comparable performance, while collapsing 3,685-token deliberation into a 6-token decision with no loss in accuracy. A rank-4 variant with 23K parameters, 1/58 of the strongest published skill operator, suffices for SearchQA and near-suffices for LiveMath, where higher rank still helps; the same recipe transfers across five tasks and three backbones, with out-of-distribution gains persisting on LiveMath problems released months after training. The gap to prior work is trainability, and it is set jointly by initialization and architecture. The initialization of prior operators zeroes the gradient of both large factor matrices at the first optimization step, whereas our zero-initialized output projection inside a shared low-rank backbone receives a gradient immediately, which a gradient-flow probe confirms directly. The gain isn't chain-of-thought compression. 23 of 57 LiveMath points beat the base model's best-of-8 sampling, and a logit-lens probe shows the operator amplifies the answer along the model's existing late-layer pathway, not writing it earlier. Gains track the base model's headroom across 13 base-task pairs, and skills compose as approximately linear operators that can be added, interpolated, and hot-swapped at inference time.

Large audio language models answer questions about speech, sound, and music, yet their accuracy drops sharply on tasks that need fine-grained acoustic analysis. Judging which of two speakers has the higher pitch demands iterative signal-level reasoning that a content question does not. Current models spend the same computational depth on both. We introduce AdaLoop, a lightweight recurrent module that learns how many latent refinement steps a given audio–question pair requires. A shared transformer block iterates over the audio representation, guided by the question, while a learned halting mechanism exits the loop once the representation is ready. AdaLoop adds fewer than 3% of the base model's parameters and plugs into any audio encoder–language model pair without modifying either component. Evaluated on three architecturally distinct models across MMSU, MMAU-Pro, and MMAR, AdaLoop raises the average accuracy by 2.9 to 3.8 points, with the largest gains on perception-heavy subtasks where the model learns to apply deeper reasoning.

Stock price prediction has long been a central problem in quantitative finance. While recent methods increasingly leverage external modalities such as news to enhance predictive performance, the microstructure within price sequences itself contains crucial information. The target-day opening price represents the first concentrated realization of overnight information in the market and holds significant value for intraday evolution and the eventual closing direction. However, once opening information is introduced, the opening and closing directions often exhibit high correlation, making the model prone to degenerating into an opening-price shortcut that simply extrapolates the closing direction from the opening direction. To address this, we propose \cope{} (Conditional Opening Prior and Evidence), a shortcut-aware prediction framework that relies solely on the price modality. \cope{} models the target-day opening state as an observed conditioning variable and reparameterizes the closing-direction prediction into a continuation/reversal discrimination conditioned on the opening direction. Furthermore, we decompose the input evidence into opening condition, individual historical state, and contextual support, and perform residual modeling of historical and contextual evidence under this condition to distill information truly effective for the final closing judgment. Systematic experiments on four real-market datasets demonstrate that \cope{} significantly outperforms existing methods. Ablation studies and shortcut-sensitive analyses further validate the effectiveness of explicitly modeling opening information, while opening-time backtests reveal that predictive accuracy and trading returns align.

Factor mining seeks to discover signals from financial data that predict future asset returns and guide portfolio construction. Automated factor mining now spans genetic programming, reinforcement learning, generative models, and large language model agents. Yet it remains unclear whether advances across these paradigms yield more generalizable, distinct, and economically useful financial signals. We introduce FactorBench, a portfolio-aware benchmark comparing roughly five thousand mined factors from nine automated mining methods across five equity markets. A shared data and evaluation contract supports both symbolic expressions and executable Python factors, connecting heterogeneous discovery algorithms to common signal combination and portfolio construction procedures. FactorBench traces the outputs of mining systems across three levels: factor validity, temporal generalization, and predictiveness beyond measured risk and style exposures; within- and across-method pool distinctness, including similarity to the benchmark Alpha101; and composite-signal quality and after-cost long-only and long–short portfolio performance. After systematically assessing whether advances in factor mining translate into signal quality and portfolio performance, FactorBench finds that no paradigm consistently dominates.

We use two-dimensional phase-field simulations based on the Cahn–Hilliard description to study spinodal decomposition in N-component mixtures with N = 3, 4, 5. In particular, we consider surface-directed spinodal decomposition in which one of the coexisting phases serves as a filler particle, while the remaining components phase separate around its surface. We investigate both nonwetting and wetting conditions by varying the interfacial tensions between the particle and the other components. The competition between wetting kinetics and spinodal decomposition produces rich morphological evolution, including the formation of lattice, droplet, and target (or core-shell) morphologies. The target pattern consists of alternating component-rich rings around the particle. In the intermediate-to-late time regime, these structures undergo further morphological transitions driven by curvature-induced depletion of wetting layers and subsequent coarsening of the surrounding domains, resulting in the breakup of target patterns into isolated domains of the matrix components. We find that domain coarsening slows down systematically as the number of components increases, while wetting accelerates it in all cases. The resulting morphologies and phase-separation pathways demonstrate how particle–component interactions can be used to control microstructural evolution in multicomponent mixtures, with potential implications for systems ranging from industrial materials to cellular biology.

Mechanistic interpretability often relies on the Linear Representation Hypothesis (LRH), which assumes that high-level concepts are encoded as linear directions in activation space. Yet a natural visual concept does not necessarily require a linear visual transition: between sunny and stormy lies an intermediate weather state such as a sky with a few white clouds, not simply a weaker storm; between a caterpillar and a butterfly, the progression is not a caterpillar with continuously growing wings. This raises the question of whether such true intermediate states are also represented nonlinearly by the model. Indeed, when we prompt text-to-image models directly for intermediate attributes, their activations rarely fall along the straight direction connecting the endpoints. Therefore, we propose KANSteer, which models concept traversal as a curve passing through its intermediate states. Seeking a representation that is both simple and interpretable, we propose to use Kolmogorov-Arnold Networks (KANs), which provide a one-dimensional coordinate whose learned functions define the trajectory. This allows the steering direction to vary along the concept while preserving an interpretable representation. Across several concepts and text-to-image diffusion transformers, we find that their activation trajectories substantially deviate from straight lines, and that KANSteer provide a closer fit and smoother traversal of intermediate attributes than linear steering.

Benjamini asked whether every configuration of points on the real line that is in equilibrium under the inverse-square repulsive force must be an arithmetic progression. Georgakopoulos and Kolountzakis proved this when some gap between consecutive points has maximal or minimal length, and described the general (aperiodic) case as open. We show that the answer is yes. More generally, let $1<s\le2$, and let $X\subset\mathbb{R}$ be a locally finite set with at least two points such that, for every $x\in X$, the total force $\sum_{y\in X\setminus\{x\}}|y-x|^{-s}$ is finite and the net force $\sum_{y\in X\setminus\{x\}}\operatorname{sgn}(y-x)\,|y-x|^{-s}$ is zero. Then $X$ is an arithmetic progression. No a priori assumption on the gaps is needed. Subtracting the equilibrium equations of two consecutive points shows that the gaps $g_n$ form a positive harmonic function for an explicit reversible random walk on $\mathbb{Z}$ with long-range jumps. Equilibrium also bounds the ratio of consecutive gaps, by $1.5386\ldots$ when $s=2$. With this bound, an energy estimate shows that the Doob transform of the walk by $g$ is recurrent. Since $1/g$ is a positive harmonic function of the transformed walk, it is constant.

Random layer rotations are ubiquitous in layered matter, from turbostratic films to rotationally disordered crystals, and strongly suppress transport across the layers. Generated by a symmetry operation, this disorder is absent on the rotation axis, so the thickness laws of conduction are set by how fast backscattering vanishes there. We show that a time-reversal selection rule decides this: each twist harmonic of the interlayer bond is either a frame rotation, whose backscattering cancels, or a coupling change, which scatters. A zero-set theorem turns the rule into universal thickness laws for electrons and phonons, fixed by band-edge symmetry; random twist increments rescale the backscattering but keep its order. Where the axis is unprotected, band nodes provide a second route: a transparent energy with heavy-tailed disorder and an $N^{-3}$ law. A first-principles forward-channel model of black phosphorus shows both routes; its random-twist films act as a symmetry filter that, relative to aligned stacks, retains a hundred times more of the electron than of the hole conductance at 64 layers. The symmetry of band edges and phonon branches thus decides what crosses a disordered stack, making stacking disorder a design element.

Deep learning models, particularly recurrent neural networks and their variants, such as long short-term memory, have significantly advanced time series analysis. These models capture complex, sequential patterns in time series, enabling real-time assessments. However, their high computational complexity and large model sizes pose challenges for deployment in resource-constrained environments, such as wearable devices and edge computing platforms. Knowledge Distillation (KD) offers a solution by transferring knowledge from a large, complex model (teacher) to a smaller, more efficient model (student), thereby retaining high performance while reducing computational demands. Current KD methods, originally designed for computer vision tasks, neglect the unique temporal dependencies and memory retention characteristics of time series models. To bridge this gap, we propose a novel KD framework termed Memory-Discrepancy Knowledge Distillation (MemKD). MemKD leverages a specialized loss function to capture memory retention discrepancies between the teacher and student models across subsequences within time series data, ensuring that the student model effectively mimics the teacher's behaviour. This approach facilitates the development of compact, high-performing recurrent neural networks suitable for real-time, time series analysis tasks. We provide additional experiments, in-depth theoretical analysis, and insights into the proposed framework across extended time series benchmarks. Our experiments demonstrate that MemKD significantly outperforms state-of-the-art KD methods. Additionally, we demonstrate that it can match the teacher model's performance across a wide range of compression levels, achieving notable reductions in parameter count and memory usage without a significant loss in accuracy.

We assess a surface-density anisotropy diagnostic, $A_{\rm ani}$, and its association with the slope $\alpha$ of a power-law galaxy profile. We reprocess 20-annulus profiles of 85 optically rich clusters on a canonical grid, $0 \leq A_{\rm ani} \leq 1.92$, and an extended grid reaching 1.99. Twenty-four canonical fits and 12 extended fits reach their respective upper boundaries; 69 of 85 upper $\Delta\chi^2=1$ bounds remain open, and only four clusters have two-sided intervals. Among 40 preselected power-law fits, the observed $\alpha$-$A_{\rm ani}$ Spearman coefficient is 0.616. In a model-native forward-recovery experiment with 11 injected values, all 935 noiseless profiles recover the input within 0.02. Across 46,750 Poisson catalogs matched to observed count and background conditions, recovery instead has root-mean-square error (RMSE) 0.992 and Spearman $\rho=0.093$; 40.0% of fits reach the canonical upper boundary and 81.4% have an open upper interval. Fixing both background and radial scale improves RMSE to 0.564 in a 9,350-catalog sensitivity test. As a separate structural control, 4,250 Poisson catalogs generated from fitted power laws reproduce the observed slope association: the median mock coefficient for the 40-cluster subset is 0.608 (95% range 0.453-0.731). Thus the diagnostic is numerically recoverable under its defining model without noise, but the available photometry does not reliably identify it for individual clusters. The power-law correlation can arise from shared projected profile shape and is not independent evidence for orbital anisotropy.

Continual adaptation of language models can change their output distribution on prompts learned earlier, while retaining every old prompt-answer pair may be undesirable or impossible. We study condition-anchored generative distillation (CAGD): retain a small set of old prompts, use a frozen previous model to reconstruct completions and generation states, and match its predictive distributions while learning the next task. The formulation separates three roles that ordinary replay conflates: conditions select the behavior to protect, teacher generations locate relevant states, and soft targets specify how predictions may change. For autoregressive language generation, teacher-rollout distillation admits an exact chain-rule decomposition of sequence divergence. For masked-diffusion language modeling, our implementation directly controls local denoising drift on teacher-generated completions. In continual adaptation of a 219M masked diffusion language model, CAGD reduces four-task final held-out loss from 2.927 to 1.114 in one task order and from 2.168 to 0.891 in exact reverse. The same soft targets lower final average loss by 0.055 over hard replay when teacher-generated support is held identical. The direction persists on fresh facts and natural instructions across SMDM and Qwen3. On GSM8K, Qwen adaptation preserves answer-format compliance, but exact-match retention is seed-mixed at 0.6B and worsens at 1.7B. These results support condition-anchored functional preservation as a common design principle across the tested language-generation objectives.