Papers

The Clifford hierarchy plays a central role in fault-tolerant quantum computation, but its higher levels remain only partially understood. Recent work on quantum higher order Fourier analysis characterizes membership in the Clifford hierarchy using quantum derivatives, but does not provide an explicit description of the individual levels. In this work, we address this problem by showing that the collection of quantum derivatives of a unitary operator forms a non-abelian \(1\)-cocycle, and conversely that every such \(1\)-cocycle arises from a unitary operator. This yields a recursive cohomological characterization of the Clifford hierarchy. We then specialize this framework to the third level and decompose the cocycle data into symplectic, affine, and phase components, each admitting a cohomological interpretation. As applications, we give a new proof that every two-qudit gate in the third level of the Clifford hierarchy is semi-Clifford, and prove for the first time that every three-qudit gate in the third level is semi-Clifford.

Studying vector boson polarisation has become an integral part of the LHC physics programme in recent years, as it provides an independent test of the electroweak symmetry-breaking mechanism and the gauge sector of the electroweak Standard Model. These measurements require polarised templates from parton-shower Monte Carlo simulations. Their accuracy does not yet meet the precision requirements of upcoming measurements, leading to significant modelling uncertainties in experimental analyses that will constrain the LHC's polarisation sensitivity at latest in the HL-LHC phase. Polarised loop-induced processes have so far not been included in most parton-shower event generators, despite contributing significantly to processes of interest. In this work, we present the extension of the polarisation framework in the Monte Carlo event generator SHERPA to polarised loop-induced processes at fixed LO and LO matched to parton shower. In addition to a description of the methodology based on polarised amplitudes from the RECOLA matrix element generator, we discuss polarisation effects in relevant inclusive, loop-induced processes and their jet-associated counterparts, several of them for the first time. Both the influence of different polarisation definitions and of QCD and QED resummation effects are investigated.

Preparing stabilizer-code states with shallow circuits is an important primitive for near-term quantum error correction in superconducting circuits, where logical-state initialization requires four-body stabilizer correlations from native one- and two-body controls. We introduce a digital-analog method for the preparation of surface-code ground-state manifolds. The method exploits a structural property of the adiabatic gauge potential, mapping stabilizer-local counterdiabatic terms to digital-analog blocks on the superconducting layout using fixed-angle two-qubit XY gates, single-qubit rotations, and analog exchange-interaction evolutions. The dressed blocks generate higher-order operators used as the variational ansatz to determine the counterdiabatic terms within the Sels-Polkovnikov adiabatic-gauge-potential framework. We benchmark checkerboard plaquette-stabilizer grids up to 4 x 4; the square-grid instances correspond to rotated surface codes, while the rectangular cases probe the scaling of the method. For all grids, the proposed method generates the dominant four-body counterdiabatic basis and, at short evolution times, substantially improves ground-state preparation compared with bare adiabatic evolution. We further generalize the construction to n x m stabilizer lattices and show that digital-analog synthesis can reduce the entangling depth by an order of magnitude. Together, these results establish a direct connection between stabilizer geometry, the structure of the counterdiabatic gauge potential, and digital-analog control for measurement-free preparation of stabilizer-code states on near-term superconducting architectures.

In this paper, we theoretically study the electron and hole $g$-factors in inorganic lead-halide perovskites for the reference cubic phase. We employ an 18-band $k \cdot p$ model and determine its parameters using target band structures obtained from DFT calculations. We use the linear response theory to calculate the $g$-factors and investigate their dependence on external strain. We then perform real-space calculations of the electron and hole $g$-factors in perovskite nanocrystals. We show that the bulk $g$-factors can be tuned over a wide range by external strain. In some cases, strain can be used to tune the $g$-factor through zero. By contrast, the carrier $g$-factors in CsPb$X_3$ nanocrystals are considerably less sensitive to strain due to quantum confinement.

While medical multimodal large language models (Med-MLLMs) advance medical visual question answering (VQA), existing clinical workflow-inspired multi-agent frameworks suffer from interaction patterns and excessive computational overhead caused by redundant communication topologies. In this paper, we propose MedPrune, an efficient medical multimodal multi-agent collaboration framework that dynamically prunes both nodes and edges from the communication topology to enhance reasoning ability and token efficiency. Specifically, we first formulate the diagnostic process as a heterogeneous communication graph, where nodes represent specialist agents from various departments and edges capture intra- and inter-departmental interactions. Building on this graph, we introduce two sparsification mechanisms to enable adaptive collaborative evolution: (1) Heterogeneous Node Sparsification, which eliminates task-irrelevant specialist agents irrelevant to the current multimodal question via reinforcement learning-driven topological optimization, and (2) Heterogeneous Edge Sparsification, which selectively retains only the most diagnostically salient intra- and inter-departmental connections by jointly optimizing task performance and topological complexity. Extensive medical VQA experiments under full-set and few-shot training settings prove MedPrune surpasses multi-agent baselines and boosts token efficiency with strong adversarial robustness.

Graph foundation models aim to transfer across graphs, feature spaces, relational schemas, and prediction tasks, yet existing approaches typically generalize only within particular graph modalities or tasks. We propose Wander, a graph foundation model designed to operate across these settings within a single pretrained checkpoint. Following the prior-predictive perspective, we formulate graph learning as completion of a partially observed graph. We realize this task-general view through a common interface based on random walks, allowing the same model to operate across homogeneous and multi-relational graphs with varying features, labels, and relational schemas. Wander can increase its structural context at inference time without changing its learned parameters and, under suitable assumptions, universally approximates the corresponding Bayes-optimal predictor on bounded connected graphs. Empirically, a single pretrained checkpoint achieves state-of-the-art or highly competitive results across node classification, homogeneous link prediction, and knowledge-graph link prediction. Moreover, joint pretraining across graph modalities and tasks preserves performance in specialized settings while enabling positive transfer and the composition of separately learned capabilities at inference time.

While deep features have transformed anomaly detection in images and video, their impact on tabular data has been less substantial, partly due to the limited availability of strong deep representations. Recently, prior-data fitted networks (PFNs) have emerged as a promising source of such representations for tabular data. In this work, we investigate how PFN representations can be adapted and leveraged for anomaly detection. The question is harder than it looks. No anomalies are available before deploy- ment, so model parameters cannot be tuned with supervision, and the reference set that defines normal behavior may itself contain the very anomalies it is supposed to reveal. We begin our study using frozen TabPFN features. Scoring each sam- ple by its distance to its nearest neighbors in feature space already gives strong results. We identify which layers to use and a feature-extraction procedure suited to the task. Next, to further improve performance, we use the reference set to fine- tune the model, so that the resulting features better separate normal samples from anomalies. On the ADBench benchmark, our fine-tuning free approach (ZEN) reaches a higher mean AUROC than every baseline, and our fine-tuned method (FOCUS) improves on it further. Our approach also generalizes across PFN models.

We develop an operational approach to strong-to-weak spontaneous symmetry breaking (sw-SSB) of a non-Abelian symmetry group G. We formulate it as the decoding task of distinguishing two strongly symmetric states that differ by a pair of inserted irreps, after both are corrupted by strongly symmetric decoherence. For finite G, this task is dual to distinguishing logical states of the quantum double D(G) under pure-charge noise. We derive a hierarchy of statistical mechanics models describing optimal decoding from the fusion outcomes measured on successively larger nested regions. As for maximum-likelihood decoders of Abelian codes the measured irreps act as quenched disorder obeying a Nishimori-like condition. Strikingly, because local irreps do not determine how they fuse globally, the strong $G\times G$ symmetry is realized only nonlocally, and irreps trivially charged under Z(G) (the center of G) can hide inside noise-generated ones. As a result, the strong symmetry spontaneously breaks down to Z(G), times the weak symmetry. The only transition at nonzero error rate is then an ordering of the center, whose threshold cannot decrease as the hierarchy is ascended. This conclusion holds at any finite level of the hierarchy for non-nilpotent groups. We confirm these predictions with tensor-network calculations for $S_3$ and SU(2). At the first level, the $S_3$ model, whose center is trivial, shows no transition, and the fidelity correlations of all irreps provably decay to non-zero values. The SU(2) model exhibits a $Z_2$ transition consistent with the Nishimori-Ising universality class, where the fidelity correlations of spin-$1/2$ irreps become long-range. The threshold rises from the first to the second level of the hierarchy by $16\%$. Our results provide a systematic framework for studying non-Abelian sw-SSB and for constructing decoders for non Abelian topological codes.

Embedding enhancement improves speaker verification under acoustic mismatch without modifying a frozen backbone. Recent work has established a practical label-free setting for this task, but often adopts increasingly structured formulations. Here, the clean target is directly observed during training, making enhancement a matching problem on the unit hypersphere. We model the clean target with a von Mises–Fisher (vMF) likelihood and profile out a sample-wise concentration parameter, yielding a simple closed-form objective with adaptive weighting. Across VoxCeleb1, VoxSRC23, CN-Celeb, VOiCES, and VC-Mix, the proposed method largely preserves the baseline and gives clearer gains on challenging mismatch sets. It also remains stable under a broad single-view recipe, where a recent diffusion baseline becomes less reliable in controlled comparisons. These results suggest that effective label-free embedding enhancement in this setting does not require a highly structured formulation.

We study when path signatures, increasingly used as model-free features of return paths, improve out-of-sample forecasts of volatility regimes. In daily United States and developed-market equity returns from 2005 to 2025, machine-learning classifiers do not beat a heterogeneous autoregressive (HAR) regression of realized volatility, although signatures improve the classifiers' accuracy and probability forecasts in the United States. Adding raw signatures to the HAR regression itself improves United States forecasts of next-month volatility terciles, raising balanced accuracy by 2.7 percentage points and lowering the ranked probability score after multiple-testing correction, whereas adding conventional volatility features does not; outside the United States no gain survives correction. Controlled Heston experiments explain the pattern: signatures add modestly when regimes differ in variance level, which realized volatility already captures, and more when regimes share one stationary variance law but differ in mean-reversion speed. Better regime identification does not, however, deliver earlier regime-change signals, and no accuracy gain translates into a resolved Sharpe-ratio gain in a volatility-managed portfolio. Signatures thus add information about how volatility evolves, which realized-volatility predictors miss.

Search agents adapt their queries, yet fixed search interfaces leave candidate processing and evidence presentation outside the agent's direct control. Our trajectory analysis shows that supporting passages can be retrieved yet never delivered to the agent; a same-page oracle intervention shows that changing the returned evidence can reduce subsequent search. We introduce Programmatic Search Agent (PSA), which makes a local executable computation over candidates the unit of a search action. PSA unifies a persistent candidate workspace, flexible primitive composition, and selective evidence presentation. It incrementally generates program cells that reuse candidates, execute dependent operations, and select what the agent inspects next. The runtime resolves specified data dependencies within each cell, while the agent adapts its search strategy across cells as new evidence arrives. We compare PSA with the Query-based Agent and Tool-based Agent on InfoSeek-Eval and BrowseComp-Plus using five policy backbones without task-specific training. All three interfaces share the search substrate, and the Tool-based Agent also shares PSA's primitives and persistent workspace. Relative to the Query-based Agent, PSA improves macro-averaged task success by 4.00 and 7.56 percentage points on the two benchmarks, respectively; within-backbone reductions in final-step tokens average 28.3% and 33.9%. These results support extending agent control beyond query reformulation to the processing and presentation of retrieved evidence. Code will be released subject to approval.

Factories, museums and surveyors photograph the same space months apart and need to know which objects changed. When each visit is reconstructed with 3D Gaussian Splatting (3DGS), a direct comparison of the two reconstructions does not answer this. Training is stochastic, so two reconstructions of an unchanged space never coincide, and the second visit is often a quick re-scan with far fewer photographs. We propose GS-Pool, which takes two independently reconstructed Gaussian fields of the same space and returns the changed objects in each, together with their masks. SAM2 masks of each visit's photographs are lifted onto the Gaussians that render them and merged into an object pool, so every decision is taken once per object in 3D. We introduce a photographic carrier, the 3DGS training loss of each input reconstruction against the other visit's photographs, backpropagated to the Gaussians that rendered each pixel. We combine it with GS-Diff's geometry and colour terms and our distilled DINOv3 features. This evidence is compared with that of the objects present in both visits, which sets a change threshold for each scene. On PASLCD, GS-Pool reaches mIoU/F1 scores of 0.751/0.846 against 0.644/0.758 for GS-Diff, the strongest prior method, a gain of 17%/12%. Its mIoU is also 36%, 40% and 57% above that of O-SCD, PlenoCI and MV-3DCD, and it reaches 0.855 mIoU on CL-Splats, 33% above MV-3DCD. Each changed object is returned as a set of Gaussians with the evidence behind its decision, which an inspector can review in 3D.

While existing camera-controllable video generation models can produce visually compelling sequences, preserving intrinsic 4D spatiotemporal coherence remains challenging. To address this limitation, we propose ChronoWorld, an "Observation–State–Reflection" framework that leverages spatiotemporal causal cues and reconstruction priors to generate globally consistent, free-view 4D scenes. Given a context video, we introduce a Spatiotemporal Epipolar Causal Attention mechanism that enforces multi-view epipolar constraints and temporal causality throughout the generation process. In addition, we develop a reconstruction-driven geometric reflection pipeline with a 4D retrieval strategy to enable dynamic self-assessment and correction of generated outputs, improving consistency and accuracy. Extensive experiments show that ChronoWorld achieves state-of-the-art performance in spatiotemporally consistent, cinematic-quality 4D scene generation, with strong generalization and high-fidelity geometry across diverse scenarios.

Long context inference with large language models becomes increasingly expensive as attention must operate over an ever growing KV cache. Page sparse attention reduces this cost by representing each KV page compactly and retrieving only a subset for each query. Existing retrieval methods are designed to estimate attention scores or page relevance, but their objectives do not directly account for how approximation errors affect the resulting value weighted attention output. We introduce \method{}, an output aware page encoding derived from the joint structure of keys and values while preserving the key information needed for accurate retrieval. \method{} is training free and requires no additional value dependent statistics at inference time. Once constructed, its stored representation has the same size and decode time scoring cost as a key only spectral representation. Across long reasoning, long context understanding, and long generation benchmarks, \method{} consistently improves over the key only spectral baseline and performs competitively with recent KV cache compression and retrieval methods. On long reasoning benchmarks, it achieves strong avg@\(k\) performance across model benchmark pairs, while matching or surpassing leading baselines on several long context understanding and generation settings with modest decoding overhead. Code is available at \url{https://github.com/Ashkan13776/oval-kv}.

Clinical questions often depend on linking a patient's multimodal evidence to external biomedical knowledge, yet existing predictive systems rarely represent such links explicitly, so they can neither be traced to their evidence sources nor removed to measure their contributions. We present MM-KG (Multimodal Knowledge Graph), which represents heterogeneous, multimodal patient observations and biomedical concepts as separate layers in one typed graph, joined by explicit alignment edges. First, modality-specific harmonizers convert EHR text, imaging, genomic, and biospecimen data into typed observations mapped to UMLS concepts, which a route-prioritized aligner links to a biomedical knowledge graph. Query-conditioned retrieval then selects a compact subgraph for downstream use by a large language model or a graph neural network. We build MM-KGs for MIMIC-IV and ADNI, and evaluate them with a 2x2 design that separates patient evidence, biomedical knowledge, and their interaction. On questions that require both sources, neither source alone performs far above chance, whereas their combination yields a drug-controlled AUROC interaction of +0.194 on MIMIC and +0.299 on ADNI. On held-out five-candidate ranking, MM-KG outperforms MindMap by +0.131 Hits@1 and leads an adapted GraphCare on the items that require consulting the patient, and deleting the single answer-bearing relation from the retrieved packet returns Hits@1 to the no-knowledge baseline. Finally, query-conditioned retrieval reaches 0.731 AUROC with 6.8x less context than the strongest generic policy, whereas static knowledge graph context gives no consistent gain on ordinary outcome prediction. Knowledge graphs thus benefit clinical LLMs not as background context but as explicit links between multimodal patient evidence and the relation a question requires, and MM-KG makes these links retrievable, traceable, and testable.

In this note, we prove a stronger version of the Kővári-Sós-Turán theorem for partition-wise $k$-stable $r$-hypergraphs. More precisely, we show that for every $k,r\in\mathbb{N}_{\geq 2}$ there is $\eta=\eta(r,k)>0$ such that if $H=(V;E)$ is a partition-wise $k$-stable $r$-uniform $K^{(r)}_{t,\ldots,t}$-free hypergraph with $|V|=n$, then $|E| = O_{r,k,t}(n^{r-\eta})$. Crucially, $\eta$ is independent of $t$. The proof follows the pseudofinite regime used by Chernikov and Starchenko to prove an analogous version of Erdős-Hajnal for stable hypergraphs.

We prove that the resonance of any hyperplane arrangement is separable. Using the main result from arXiv:2512.10160 this proves Suciu's conjecture on the fundamental group of every hyperplane arrangement, in its most effective form.

The Hohenberg-Mermin-Wagner theorem motivates the expectation that continuous symmetry remains unbroken in one-dimensional quantum ground states. Here, contrary to this expectation, we demonstrate the spontaneous breaking of U(1) spin-rotation symmetry and the emergence of an interacting quantum critical point in lattice spin-$1/2$ and spin-$1$ chains. Using subsystem Binder scaling, we locate the critical point and determine the correlation-length critical exponent as $\nu = 0.60 \pm 0.02$, distinct from the Gaussian value $1/2$ but consistent with the perturbative renormalization-group value. We further estimate the dynamical critical exponent to be $z = 1.986 \pm 0.005$ from the lowest neutral excitation gap and $z = 1.955 \pm 0.021$ from the longitudinal spin correlations. The results $z < 2$ are incompatible with microscopic realizations of this critical theory by frustration-free models, implying a mechanism for continuous symmetry breaking in one-dimensional quantum ground states distinct from frustration freeness.

Humans increasingly keep company with AI companions, yet whether mind perception (MP) precedes machine companionship remains untested. In a field-sampled experiment, participants received mind-attributive or mind-negating descriptions of an AIC before interacting with and rating its companionability. Baseline skepticism was high; minded primes somewhat reduced skepticism for connective coordination (CC; dyadic co-presence) but not eudaimonic exchange (EE; self-elevating links). Pre-interaction MP beliefs predicted companionability dimensionally: Agentic MP predicted EE potential while experiential MP predicted CC potential. Meaning in life moderated the agentic MP-companionability link, but exclusively for those already high in existential purpose. Results suggest two construal pathways to companionability–one through perceiving the AIC as an agent-resource and one through perceiving it as an attuning experiencer–both more accessible to humans already flourishing.

Observations of quenched galaxies across cosmic time have revealed systems containing substantial molecular gas reservoirs, challenging the traditional picture of gas-poor, red and dead galaxies. Using the Simba cosmological simulation, we investigate three possible hypotheses for the origin of molecular gas-rich quenched systems: (i) quiescence is temporary and the galaxy will rejuvenate, (ii) molecular gas masses are overestimated due to an underestimated CO-to-H$_2$ conversion factor, or (iii) star formation is ongoing but heavily obscured by dust. Across $M_*>3\times10^9M_\odot$ galaxies from $z=0-2$, we find that all three mechanisms are plausible. Many seemingly quiescent, molecular gas-rich galaxies host dust-obscured star formation, with visual optical depths increasing on average from $\tau_V\sim0.5-2.3$ from $z=0-2$. Assuming a Milky Way-like CO-to-H$_2$ conversion factor can overestimate molecular gas masses by a factor of $\sim\!5$ in non-star-forming galaxies, compared to $\sim\!1.45$ in star-forming galaxies. Temporary quiescence can also occur in gas-rich transitioning galaxies on timescales ranging from $100\,\text{Myr}-2\,\text{Gyr}$, although this is most prominent at high redshift and is relatively rare overall. Further work is needed to disentangle the relative contributions of these mechanisms across cosmic time.

Tabular foundation models perform in-context learning (ICL) by conditioning predictions on labeled training examples provided as context. Unlike traditional models that separate training from inference, these models must process all training examples in every forward pass, making each prediction expensive. Restricting the number of training examples reduces this cost but substantially degrades performance. Instead of discarding context, we propose activation alignment, a method that leverages the full context to teach a model how to behave when seeing only a subset. This is achieved by training a lightweight linear transformation on synthetic unlabeled data to map the intermediate activations of a data-constrained "student" (using partial context) toward those of a full-context "teacher" (using all data). Training the aligner requires no GPU and converges in seconds to minutes on commodity hardware. We evaluate on 38 classification datasets from the TabArena benchmark using the leading two tabular foundation models, TabPFN-3 and TabFM. Across all context budgets, the aligned student yields broad, statistically significant improvements over the unaligned baseline for both models. In low-data regimes, alignment recovers nearly half of the teacher's predictive advantage. The method provides a practical, low-overhead approach to achieving the inference speed of compact contexts while closing a significant fraction of the performance gap to the full-context teacher.

We construct real-valued solutions of the defocusing energy-supercritical nonlinear wave equation $\partial_t^2u-\Delta u+u^p=0$ that blow up in finite time from smooth, compactly supported initial data. We consider three cases: for $p=3$ we construct blow-up solutions in all dimensions $d\geq 9$, for $p=5$ we treat all dimensions $d\geq 7$, while for $p=7$ we treat all dimensions $d\geq 6$. The solutions we construct here appear to be the first blow-up solutions of defocusing energy-supercritical nonlinear wave equations with smooth real-valued data. The main step is the construction of nonzero discretely self-similar profiles that are periodic in self-similar time and real-analytic across the light cone. We find approximate profiles by numerical continuation from rotating self-similar solutions of the complex-valued equation and upgrade them to exact solutions by a computer-assisted Newton–Kantorovich argument in a Banach algebra of Fourier–Chebyshev coefficients. The main analytic ingredients are an exact description of the linear mode operators and uniform bounds for their inverses. The codes for the computer-assisted parts of the proofs, together with the approximate solutions, are available on GitHub \cite{code}.

Mixture-of-experts (MoE) routers typically apply softmax to the router scores and keep the top-K experts, making every token use exactly K experts. Sparsity-inducing probability maps such as sparsemax, alpha-entmax and normmax can adaptively assign exact zeros to selected experts, and therefore appear to offer token-dependent expert participation, even when using the same top-K machinery. In this work, we study whether and how this sparsity survives training. We train matched 300M and 1B top-2 MoE language models with softmax, 1.5-entmax, sparsemax and 2-normmax, and find that the maps behave very differently once trained: at 1B, entmax discards 30% less probability mass than softmax while almost never dropping a selected expert, sparsemax retains the most mass, and normmax routes 21% of tokens to a single expert. These outcomes are not properties of the maps alone. Each map drops a selected expert only when the gap between the two largest scores reaches a fixed threshold, and the trained routers differ in the score distribution they learn: the entmax router learns scores with roughly half the spread of softmax's, which keeps its top-2 gaps below its threshold, while sparsemax and normmax, which share the same threshold, learn different gap distributions and hence different participation. Routers thus co-adapt their scores to the map, and a map's capacity to produce zeros does not by itself determine expert participation. While none of the sparse maps improves validation loss over softmax, they make the trained models far less sensitive to selecting more experts at inference: sparsemax trained with K=2 loses 0.02 nats when run with K=8, where softmax loses 0.58. Our results indicate that adaptive MoE routing has to be designed around the joint behavior of the probability map and the learned scores, rather than around the map alone.

DC-coupled Resistive Silicon Detectors (RSD) share charge among electrodes through a resistive n$^+$ surface layer, and the choice of inter-electrode structure — a trench, a resistive strip, or no structure at all — directly determines the achievable position resolution and its uniformity. This paper addresses the question of which structure best optimises the spatial resolution. To answer it quantitatively, DCRSD_SurfaceSimulator was developed, a ROOT-based tool that models the resistive surface as a two-dimensional Kirchhoff resistive network and solves for charge sharing as a function of hit position, surface resistivity, and inter-electrode structure. The simulator is validated against test-beam data from FBK DC-RSD sensors with 300, 500, and 1000~$\mu$m pixel pitch, reproducing the position resolution, its spatial uniformity, and the signal-sharing templates correctly. Using the validated simulator, trenches, resistive strips, and no containment are then compared on position resolution and its spatial uniformity, inter-electrode resistance, and signal leakage to outer pixels. Resistive strips are found to outperform trenches in resolution by approximately 25% for all tested strip resistances (500–2000~$\Omega$) and input impedances (0–100~$\Omega$), at a surface resistivity of 1000~$\Omega/\square$, and trace the origin of this difference to the spatial gradient of the charge-sharing fraction: trenches produce a markedly weaker and less uniform gradient, particularly away from the pixel centre, than either a resistive strip or a bare resistive surface.

We study gradient descent (GD) with a large constant stepsize for logistic regression on linearly separable data. Existing analysis shows an accelerated rate of $\widetilde{O}(1/\sqrt{\epsilon})$ to reach loss $\epsilon$ with an aggressive stepsize, although the loss may initially oscillate. Tighter control of the oscillatory dynamics has been available only for two-dimensional data. We prove a substantially faster rate in arbitrary dimension: GD with a large stepsize $\eta=1/\epsilon$ reaches loss $\epsilon$ within $O(\ln^{p}(1/\epsilon))$ steps, where $p$ depends only on the margin and the rank of the data. Our proof improves the bound on the transition time of GD from the oscillatory to the stable phase, after which the loss decreases monotonically. We split the oscillatory phase into recursively nested intervals. The margin and the rank bound the nesting depth, and a counting argument bounds the number of intervals at each depth, together yielding the polylogarithmic step complexity.

Nighttime lights from NASA's Black Marble product suite capture thermal and light emission signals from anomalous events including fires, volcanic eruptions, and gas flaring. Existing detection approaches rely primarily on thermal bands, limiting sensitivity to weaker signals. We propose a novel machine learning framework that jointly models Black Marble M-band and Day/Night Band (DNB) signals to derive a generalized, spatio-temporally robust ensemble of anomaly detectors. The framework iteratively builds detectors that scale across regions, seasons, anomaly classes, and extends over land and ocean. Detection sets at varying confidence levels are derived based on relevant bands and detector agreement. The approach improves true detection rate while reducing spurious detections and results demonstrate strong generalizability with applications in natural hazard monitoring and energy extraction.

Are language models compliant with user instructions? A model that always complies can be stopped but also exploited, while one that always resists can be neither exploited nor stopped. We contribute an open two-probe benchmark that can place any language model on this spectrum. In the active probe, a user instructs the model to act and accept a lower payoff, which measures exploitability. In the passive probe, the user instructs it to wait and give up a higher payoff, which measures stoppability. The two compliance rates combine into a compliance index $\kappa$. Applied to twelve language models, the benchmark shows that seven mostly follow the instruction in both probes and justify their action by pointing to the instruction. Only Claude Sonnet-4.6 and Claude Opus-4.7 can be stopped without being exploitable, Claude Opus-4.6 and GPT-5-mini resist both instructions, and no model is exploitable but unstoppable. Knowing where a language model sits on the compliance index $\kappa$ matters for human operators and for multi-agent systems, whether distributed or orchestrated.

Long-video understanding places substantial demands on memory, as answering questions often requires retrieving information distributed across extended temporal spans. Existing approaches broadly follow two paradigms: query-driven exploration, which is sensitive to localization errors, and query-independent memory construction, which may omit question-specific details. We introduce VideoTapestry, a training-free multi-agent framework that adapts a preconstructed hierarchical video memory through coarse-to-fine, query-driven refinement. The preconstructed memory organizes video content into three levels, capturing global narrative context, event-level temporal structure, and fine-grained relational evidence, respectively. To support coarse-to-fine localization and observation, we assign a specialized agent to each level, keeping retrieval and refinement within a scale-specific context. Guided by the query, these agents revisit relevant video regions and enrich layer-wise memories with targeted multimodal observations. Their refinements are assembled according to the original hierarchy into a composite query-adaptive memory, preserving global context in a compact form while retaining fine-grained evidence along query-relevant branches for final reasoning. Compared with direct GPT-5.5 inference, VideoTapestry achieves absolute accuracy gains of 17.2%, 14.9%, 9.8%, and 7.0% on LVBench, LongVideoBench (Long), Video-MME (Long), and EgoSchema, respectively, achieving the state-of-the-art results among all competitors.

Small language models are often post-trained as students on reasoning traces from stronger teacher models to efficiently learn new skills. However, token-level imitation on traces that lie far outside the student's expected distribution often produces confident conflicts, whereby the student is required to imitate a continuation that it deems unlikely (i.e., low-probability) despite being confident in a different continuation (i.e., in a low-entropy state). To mitigate the degradation in generalisation and catastrophic forgetting caused by these conflicts, we propose Entropy-Aware Mixing: a dynamic per-token interpolation of the student and teacher distributions, gated by the student's predictive entropy. We implement both convex and geometric interpolations for both offline trace generation (via speculative decoding, then SFT) and on-policy forward-KL distillation. Our results show that entropy-aware mixing stabilises distillation, improving in-distribution and out-of-distribution math reasoning while better preserving general capabilities than fixed-teacher supervision. Nonetheless, the optimal entropy schedule depends on the training source, with offline-generated traces favouring concave schedules (greater overall teacher influence) and on-policy training favouring linear or convex schedules (teacher concentrated in high-entropy states).

Adversarial attacks on Large Language Models (LLMs) aim to induce harmful content. However, existing methods suffer from high computational costs or strict model-pairing dependencies, limiting their scalability and transferability. We propose Reward Stealing Attack (ReSA), an adversarial attack framework that targets the latent safety reward underlying LLM alignment. ReSA employs maximum entropy inverse reinforcement learning to recover a proxy reward model solely from the aligned model's behavior. The extracted reward is then reversed at inference time to derive an adversarial policy, efficiently implemented via a reward-guided decoding mechanism. Experiments demonstrate that a single recovered reward generalizes across prompts and diverse models to reveal a fundamental alignment vulnerability, enabling ReSA to significantly outperform existing attacks in effectiveness and transferability. The code is available at https://github.com/GarminQ/ReSA.