Papers

A benchmark score compares a system output against a reference, and methodological attention falls almost entirely on the first term. We measure the second. The retained annotation record of a six-language benchmark for personally identifiable information contains two independent annotator labellings, the aggregate shipped as gold, and a reviewer gold from independent expert re-annotation of a sample. Using it, we hold the scored output fixed and exchange the reference. The score moves by 4.95 F1 points for one output and 2.00 for the other (95% CIs [3.23, 6.27] and [0.26, 3.37]), and by 7.55 in the worst language. The comparison between two outputs moves as well: the paired interaction between reference and system is +2.95 points (CI [+1.97, +3.87]), survives correction for multiple testing, and changes one language's margin outright. The cause is an undocumented aggregation default that usually kept one annotator when adjudication did not fire, making the shipped reference a partial copy of an output being scored. We report the resulting reference-sensitivity band, show how to compute one from any retained annotation record, and argue that the quantity belongs beside the score.

Treatment efficacy is traditionally demonstrated on the basis of a single primary outcome. However, clinical decision-making usually requires consideration of multiple outcomes, balancing expected benefits against potential risks. The relative value assigned to these outcomes varies substantially from one patient to another. Given a preference rule over outcome profiles, treatment effects and optimal policies can be defined and estimated. Such a rule is rarely available in practice: it must itself be estimated from pairwise comparisons of outcome profiles, which are costly to collect from clinical experts. We propose an active learning framework that selects which comparisons to query. Standard criteria maximize the information gained on the preference rule itself. We instead target the quantities of interest, and select the query that most reduces uncertainty on the treatment effect and on the optimal policy induced by the learned rule. Under a Gaussian process model of the preference rule, we derive a closed-form approximation of this criterion. On semi-synthetic data built from a Parkinson's disease cohort with 13 clinical outcomes, our criterion achieves lower treatment effect estimation error and lower policy regret than existing criteria at equal query budget.

A recent trapped-ion experiment realised a lattice gauge theory in which the internal states of the ions carry the gauge field and their vibrations carry bosonic matter. In that experiment, a charge moving around a loop was frozen in place by Aharonov–Bohm interference. The noise of such a device is usually simulated after the measurements have been made. Here we show that it can be predicted before the machine is run. For each quantity that the experiment measures, we derive, from the reported noise rates alone, a formula for how it decays together with a bound it can never exceed. The results reveal a simple pattern. The local conservation law of the theory is a parity of the vibrational mode, so heating violates it at a rate that grows as the mode warms, and the violation accelerates rather than accumulating steadily. At zero electric field, each of the three noise processes of the device leaves its own fingerprint. Heating affects only the conservation law, motional dephasing only the interference, and qubit errors only the stored flux and the frozen state. Once the electric field is switched on, the frozen state begins to leak, and we write an exact formula and a guaranteed bound for that leak.

Tokens have become a unified interface for multimodal foundation models, making visual-token communication a natural paradigm for efficient image delivery. However, existing methods typically rely on static policies that cannot jointly adapt to image content and channel conditions. Moreover, their token-level utility objectives do not necessarily translate into improved image reconstruction quality. In this paper, we propose AdapToC, an adaptive, reconstruction-oriented visual-token communication framework. At the transmitter, an adaptive selector jointly models image content, channel state, and communication budget to perform instance-wise resource allocation. Rather than using a fixed token rate and protection policy, it dynamically determines how many tokens should be transmitted and assigns different protection levels according to token importance and current channel conditions. At the receiver, an adaptive MaskGIT receiver incorporates channel reliability into contextual token modeling. It distinguishes tokens with different reliability levels, preserves high-confidence observations, corrects potentially corrupted tokens, and iteratively reconstructs missing content from the received evidence and global visual context. By co-designing token quantity, unequal protection, and reliability-aware recovery for image-level reconstruction quality, AdapToC achieves a peak mean PSNR gain of 4.20 dB over the strongest static baseline under matched communication costs and state-of-the-art performance among the evaluated visual-token communication methods.

Halide solid electrolytes are promising candidates for energy-dense all-solid-state batteries because they combine high-voltage stability, facile processing, and fast Li-ion conduction. A recent study showed that physically mixing two halide solid electrolytes, Li$_2$ZrCl$_6$ (LZC) and Li$_3$YCl$_6$ (LYC), raises the Li-ion conductivity by 46% and 58% relative to LZC and LYC, respectively, suggesting that halide heterointerfaces offer a new route to faster ion transport; however, the origin of this enhancement remains unknown. Here, we combine density functional theory calculations, defect thermodynamics, machine-learning-driven molecular dynamics, and vibrational and Raman spectroscopy to elucidate Li-ion transport in LZC, LYC, and their heterointerface. Using low-energy ordered supercells that represent the configurational disorder of these halides, we find that Li and Cl interstitials are the dominant charged defects in both materials. Forming an LZC|LYC interface favors the generation of interfacial Li Frenkel pairs, producing Li interstitials in LZC and Li vacancies in LYC, thereby increasing the charge-carrier concentration near the interface. By analyzing the angular orientations of Cl around the metal cations in molecular dynamics trajectories of a coherent interface, we show that the interface creates new stable Cl configurations that accommodate the framework rearrangement accompanying Li hops. Simulated vibrational power spectra and measured Raman spectra indicate lattice softening and octahedral distortion at the interface, consistent with the formation of these Cl configurations. These results support a cooperative mechanism in which space charge layer formation and a dynamically flexible interfacial halide framework enhance Li-ion conduction, providing atomistic design principles for superionic halide heterostructures and multicomponent solid electrolytes.

Design-level security weaknesses can arise from requirements, trust assumptions, missing controls, and data flows before implementation begins. Existing security practices often identify these issues after code is written. We present a multi-agent LLM framework for design-time security analysis from product requirement documents and architecture diagrams. The proposed framework parses architecture diagrams into graph representations, generates misuse and failure cases, constructs attack trees, checks governance and compliance gaps, recommends mitigations, assigns enterprise security-domain tags, and produces a candidate revised architecture recommendation for expert review. The framework does not retrieve from Common Weakness Enumeration (CWE) databases at inference time. Instead, it analyzes system behavior, trust boundaries, component interactions, and data-flow assumptions. Misuse cases act as intermediate representations that link findings to system components and attack paths, while a validation and refinement loop filters unsupported findings and improves grounding, traceability, and actionability. We evaluate the framework on a Microsoft reference-labeled threat-modeling example, labeled synthetic PRD–architecture pairs, and two open-ended systems: Berty and Gas Town. The reference-labeled case supports threat-recovery and actionability analysis, while the open-ended cases evaluate validity, noise, traceability, actionability, redundancy, and attack-tree quality. Results show that architecture-informed, misuse-driven reasoning improves review quality compared with single-shot and ablation baselines. Keywords: LLM Multi-Agent Systems, Design-Time Security, Threat Modeling, Vulnerability Discovery, Architecture Diagrams, Security Analysis, Misuse Case Derivation, Attack Trees, Iterative Reasoning, Security Governance.

Let $\Fq$ be a finite field, let $F,G\in\Fq[T]$ be nonconstant, and let $J\in\Fq[T]$. We study the parameterized two-parameter family \[ C_{a,b}=\{(x,t)\in\Fq^2:t=J(x)+aF(x)+bG(x)+\lambda ab\}, \qquad (a,b)\in\Fq^2, \] where $\lambda\in\Fq^\times$, with incidences counted with parameter multiplicity. If $d=\deg F$, $e=\deg G$, and $\charac(\Fq)>d+e$, we prove the uniform spectral estimate \[ \left|I(\cP,\Omega)-\frac{|\cP||\Omega|}{q}\right| \ll_{d,e}q^{5/8}\sqrt{|\cP||\Omega|} \] for arbitrary $\cP,\Omega\subseteq\Fq^2$. The proof combines two additive Fourier transforms with a fourth-moment estimate for Kloosterman matrices. If $1\le d,e\le2$ and $\charac(\Fq)>3$, midpoint–difference coordinates and finite Weyl quantization sharpen the error to the Vinh scale $O(q^{1/2}\sqrt{|\cP||\Omega|})$. We further show that the latter phenomenon is intrinsic to the coefficient curve rather than to the degree of a chosen parametrization. There is a polynomial Lüroth factorization \[ F=f\circ H,\qquad G=g\circ H,\qquad \Fq(f,g)=\Fq(T), \] unique up to an affine change of $H$. If $\Gamma$ is the plane curve parametrized properly by $(f,g)$ and \[ \kappa_H=\max_{s\in\Fq}|H^{-1}(s)|, \] then finite-fibre pullback multiplies the centered incidence norm by at most $\sqrt{\kappa_H}$. Consequently, if $\deg\Gamma\le2$ and $\charac(\Fq)>3$, then \[ \left|I(\cP,\Omega)-\frac{|\cP||\Omega|}{q}\right| \ll \sqrt{\kappa_H}\,q^{1/2}\sqrt{|\cP||\Omega|}, \] even when $F$ and $G$ have arbitrarily large raw degree. The resulting expansion estimates for $J(x)+yF(x)+zG(x)+\lambda yz$ hold without lower bounds on the individual input sets. In the balanced regime, the $q^3$ missing-value scale for this family is already covered by a theorem of Arala–Chow; the incidence theorems here additionally yield expansion consequences in strongly unbalanced regimes.

AI agents that operate a computer through its graphical user interface (GUI) are being widely deployed. AI control studies how to prevent an AI system from causing harm even if it is misaligned and actively trying to do so. Most control research to date has focused on coding agents, leaving computer use largely unexplored. We introduce Control OSWorld, a control evaluation that pairs 318 tasks from OSWorld with 81 harmful side tasks (e.g., exfiltrating a private file) that an agent must complete without being caught. We use Control OSWorld to create and study control monitors that detect malicious agents interacting with a GUI. We find that a weaker monitor can reliably distinguish honest from malicious trajectories produced by a more capable agent when it sees the full trajectory (97% recall at 3% false positive rate). However, when the monitor has to score each step before it is executed, recall drops at low false positive rates because each action is judged with less context. Monitor performance also depends on what the monitor can see: access to the agent's visible text is critical, while screenshots provide little additional value.

We construct and analyze a mirror family for the generalized complete intersection Calabi-Yau threefold $X_+=[\mathbb{P}^1\,|\,3\ {-1};\ \mathbb{P}^4\,|\,2\ 3]$, with $(h^{1,1},h^{2,1})=(2,46)$. An auxiliary-variable presentation turns the negative-degree section into a variation of toric GIT. Crossing one wall flops 16 disjoint $(-1,-1)$-curves and yields a Calabi-Yau threefold $X_-$, a nef complete intersection in a toric $\mathbb{Q}$-Fano eightfold, which carries a genus-one fibration of index 4. Because this ambient space is not Gorenstein, the Batyrev-Borisov construction does not apply. We use the Hori-Vafa equations only to select a 2-parameter Laurent family, and construct a smooth projective crepant compactification $Y$ of the Laurent model with $(h^{1,1},h^{2,1})=(46,2)$; for very general parameters the Mordell-Weil group is $\mathbb{Z}/4\mathbb{Z}$. The periods of $Y$ satisfy a rank-6 Picard-Fuchs system with two maximally unipotent boundary points, whose indicial algebras are isomorphic to the rational even cohomology rings of $X_-$ and $X_+$. The resulting genus-zero predictions agree with independent counts of 176 vertical lines and 100 vertical conics on the genus-one fibration $X_-\to\mathbb{P}^2$.

A light force carrier can mediate long-range interactions between dark matter particles and facilitate the formation of bound states. Models incorporating these features have attracted considerable attention in recent years, with significant advances in both the theoretical understanding of such bound states and their impact on the parameter space consistent with the observed dark matter relic abundance. However, the relevant results and their consistent implementation in Boltzmann equations remain technically intricate, requiring careful treatment or the use of specialized tools. This complexity has hindered broader adoption of these findings and restricted their use to a small number of expert groups. To address this challenge, we propose a simple prescription based on the analytic limits of the relevant rates, which allows standard freeze-out computations to be refined through a straightforward semi-analytical prescription that captures the main features of the full calculation. We illustrate this approach for a $U(1)$ dark matter model with a light force carrier, including Sommerfeld enhancement and bound-state effects.

This paper examines the role of Novel View Synthesis (NVS) in geometric representation learning. In principle, NVS should reason about 3D scene structure, thereby enabling transferable multi-view geometric representations. Yet, existing encoder-based NVS methods yield poor representations. This is not because of a lack of supervisory signal, but rather due to inconspicuous architectural choices: spatially expressive decoders that dilute representational capabilities of the scene encoder, and low-level pixel-space targets that hinder feature learning. We present SNAP, a self-supervised encoder-decoder transformer that addresses both through a pose-conditioned local decoder and a latent-space reconstruction objective. SNAP is task agnostic, and we show that it is competitive with special-purpose geometry-supervised methods. SNAP also performs competitively against self-supervised representations across five tasks: visual localization, pose estimation, point correspondence, depth estimation, and robot manipulation. Remarkably, SNAP's patch features exhibit emergent viewpoint invariance that approaches heavily supervised models despite lower compute and data budgets. Under camera shifts where standard 2D representations collapse, SNAP degrades more gracefully, revealing that restricting decoder expressivity actively prevents the suppression of transferable geometric structure. https://snap-nvs.github.io

Dense 3D point tracking has been a prominent paradigm for modeling motion in dynamic scenes, but a point track is just a 3-DoF translation curve per pixel: it captures where pixels go, not the rotation of the underlying part, nor which pixels move together as one body. We propose MoSE3, the first feed-forward model that predicts dense SE(3) motion from monocular RGB video, producing full 6-DoF rigid transforms at every pixel in world space. Per-pixel SE(3) motion offers a richer view of how a scene moves: rotation, translation, and grouping all at once. Directly predicting SE(3) is challenging: rotations lie on a curved manifold that is ill-suited to Euclidean regression, and annotations for SE(3) are particularly difficult to acquire. To address these challenges, MoSE3 predicts per-pixel SE(3) through two jointly learned intermediates, 3D point tracks and rigidity embeddings, and recovers SE(3) by differentiably fitting transforms within each soft rigid cluster, enabling end-to-end prediction and supervision. To close the data gap, we introduce Art-Kubric, a large-scale synthetic dataset with dense SE(3) and rigidity labels for articulated objects with rich physical interactions. MoSE3 achieves state-of-the-art SE(3) estimation at pixel, part, and object levels on both rigid and articulated benchmarks, and state-of-the-art average 3D point tracking accuracy across three datasets, while showing strong generalization to real-world videos despite being trained solely on synthetic motion data.

We introduce 4DCodeBench, a benchmark for 4D inverse graphics through code generation, in which agents reconstruct dynamic scenes from video as executable graphics programs. To accomplish this, agents must translate visual observations into compact representations of scene structure and dynamics, by implementing abstractions such as physical simulations to reproduce complex behavior. To evaluate this capability, we curate a set of real-world videos and construct synthetic scenes spanning diverse physical phenomena, including deformation, fluid flow, and fracture. We perform extensive benchmarking of frontier models, finding that strong static reconstruction capabilities do not yet translate into reliable reconstruction of complex dynamics. 4DCodeBench provides a testbed for tracking progress toward agents that can interpret the dynamics of the world through code. Our benchmark is available at https://github.com/4DCodeBench/4DCodeBench

Fault-tolerant preparation of logical states is a critical primitive for the realization of large-scale fault-tolerant quantum computing. This paper introduces SpiderCSS, a scalable compilation pipeline that generates highly-optimized, fault-tolerant state preparation circuits for arbitrary Calderbank-Shor-Steane (CSS) codes. Starting from an idealized specification of a CSS state, we use the ZX-calculus and fault-equivalent rewrites to construct a diagram that prepares the given state while preserving the fault tolerance of the initial ideal ZX-diagram. From this diagram, SpiderCSS constructs a fault-tolerant CSS-state preparation circuit using a modular construction that is CNOT-minimal both within each component and also in the way these components are connected together. By only using fault-equivalent rewrites, the final circuit is provably fault-tolerant without needing expensive verification. Monte Carlo simulations across a variety of CSS codes up to distance 15 show that SpiderCSS scales efficiently and constructs circuits with substantially reduced depth and qubit footprint compared to existing scalable and heuristic methods, while simultaneously achieving an average decrease of 33.7% in logical error rate and an increase of 9.5% in acceptance rate.

Continual learning treats degradation on previously seen data as evidence of failure, a convention inherited from settings with a stationary prediction target, where a correct label remains correct indefinitely. World models do not satisfy this condition. Their prediction target is the environment, which changes, so knowledge that was accurate when acquired may later become false, and discarding it is required behavior rather than a defect. Non-stationary ground truth is well studied in the concept drift literature and in the temporal factuality of language models, but has not been formulated for world models, which are distinctive in that they also encode knowledge that must never be revised. We argue that continual world models require retention stratified by invariance timescale, separating invariants such as physics and object permanence, which must never be revised, from instance-level facts that should be revised as soon as the environment changes. Standard forgetting metrics cannot distinguish a world model that has correctly revised outdated knowledge from one that has suffered catastrophic forgetting, and consequently rank a frozen model highest, while existing physical-reasoning benchmarks evaluate only frozen checkpoints. We propose differential retention, which reports invariant regression testing across the adaptation stream jointly with revision latency, without aggregation.

Ribonucleic acid (RNA) functions through conformational changes that are not fully captured by static structures. However, large-scale standardized RNA dynamics data remain limited, and existing approaches typically treat trajectory generation and dynamics understanding as separate objectives. Here, we introduce RNADynBench, a standardized RNA molecular dynamics (MD) benchmark with 2585 quality-controlled 100-ns all-atom trajectories and leakage-controlled splits. Building on RNADynBench, we develop RNADynNet, a unified model for RNA dynamics learning that uses a shared backbone for both trajectory generation and dynamics fingerprint extraction from a single conformer. It combines coordinate denoising, single-frame-to-trajectory alignment, and physical grounding to connect all-atom trajectory generation with dynamics representation learning. Physical grounding improves both generated dynamics and the physical information recoverable from these fingerprints. Across both test sets, including the high-flexibility challenge set, the generated trajectories achieve RMSF correlations of 0.875 and 0.766, while single-conformer predictions show comparable agreement with MD-derived dynamics. RNADynBench and RNADynNet together establish a benchmark and unified modeling framework for generating and understanding RNA dynamics.

We provide the first evidence relative to a classical oracle that pseudorandom unitaries (PRUs) can exist without quantum-computable one-way functions. To obtain this result, we first prove that five independent random diagonal phase layers interleaved with Hadamard transforms \[ U=F_5HF_4HF_3HF_2HF_1 \] form a strong PRU with security under adaptive, controlled access to the unitary, its inverse, transpose, and complex conjugate. Our main result is that, when the phase layers are implemented using a classical random oracle O, the construction remains secure against uniform BQP adversaries with coherent access to suitable Boolean completions of classical-input $QMA^{PH}^{O}}$ decision problems. Such an adversary can invert (even quantum-computable) one-way functions and solve efficiently verifiable one-way puzzles defined relative to O. Our result therefore provides classical-oracle evidence that PRUs do not imply quantum-computable one-way functions, in the form of a black-box separation. We substantially strengthen the classical-oracle result of Kretschmer, Qian, and Tal (STOC 2025) by obtaining PRUs secure against these QMA-aided adversaries. Our construction also consists of a simple, efficient circuit that queries a random function, suggesting a route to concrete implementation via the random-oracle heuristic.

Inspired by human vision, we introduce a framework using active gaze to enable fine-grained bimanual manipulation with only a single stereo camera. EyeRobot 2.0 physically attends to a 3D fixation point in the scene by swiveling two eye viewpoints to center their gaze on it. The resulting images are processed foveally by allocating more visual tokens to the image centers, focusing computation on task-relevant features. Such Active Visual Fixation (AVF) requires carefully coordinated gaze during task execution, which we accomplish hierarchically by first training a low-level gaze servoing policy conditioned on a goal object, then training a target selector which emits fixation goals based on task progress. Both modules are trained with RL on real-world data: the first is trained with a dense geometric reward and the second co-trains with the BC gripper policy which allows it to discover fixation sequences that can resemble a human's fixation sequence while performing the task. EyeRobot 2.0 further takes advantage of fixation by canonicalizing gripper information into a fixation-relative SE(3) frame, which compacts the size of the action distribution to learn. We collect teleoperation data for 7 real-world and 6 simulated tasks, and conduct over 1000 physical and 1800 simulated robot trials comparing EyeRobot 2.0 against passive stereo and ego + wrist camera policies trained on the same data. Removing wrist cameras is costly for standard policies: with only passive stereo, real-world success drops from 52% to 27%. EyeRobot 2.0 closes this gap with only stereo, outperforming passive stereo by 40% in real and 20% in sim. It matches ego + wrist policies when their wrist views are clear (69% vs. 64%), and more than doubles their success when grasped objects occlude the wrist cameras (48% vs. 22%)

We study decentralized minimization of sums of smooth strongly convex functions, one per agent, with communication restricted to neighbors in a graph. Existing decentralized algorithms typically emulate a centralized method; the network serves only to exchange information, from which agents approximate the global quantities that the method needs. This paper breaks with this paradigm. We introduce a graph decomposition framework that uses the network to design the method, not merely execute it. It jointly determines how agreement is imposed, which variables are optimized jointly (blocks), and which connected subgraphs host the agents solving each block. The convergence analysis quantifies the trade-offs among these choices. GATE (Graph-Tearing message passing) instantiates the framework by assigning one dual variable per edge and partitioning the edges into trees. Agents interleave edge updates with local message passing recursions that summarize optimization within each tree (block). Its surrogate variant, GATE-S, uses tractable local models and compact messages to reduce computation and communication. We establish linear convergence and show that the topology-aware design acts as a preconditioner: the rate depends jointly on topology and function geometry through the coupling between subproblems defined on the selected subgraphs, whereas consensus-based optimization methods pay the worst case of each separately, the centralized condition number times the inverse spectral gap. On tree-dominant graphs, convergence is provably faster: the rate scales with the tree diameter, linearly in the number of agents on rings and barbells against quadratically for non-accelerated consensus-optimization methods. Experiments support the predicted scaling and savings in iterations and communication.

In this paper we discuss the quasinormal modes and the tidal responses of a four-dimensional asymptotically flat Reissner-Nordström black hole near extremality and investigate the nontrivial near-horizon quantum corrections of these observables. The near-horizon dynamics of near extremal black holes are generally governed by an effective Schwarzian action coupled to boundary gauge modes. We use this description and couple this effective theory with a massless scalar field outside. Using this setup we compute $2 \to 2$ scattering process of a black hole and a scalar particle. The poles of the scattering amplitude at complex frequencies give us the quasinormal mode spectrum and we recover the predicted zero damped modes near extremality at leading order. Next we evaluate the static Love numbers from the elastic limit of the scattering amplitude. We show that the static Love numbers are non-zero in contrast to the classical expectations. Very close to extremality, the behaviour is analytic, but as the near-extremal energy becomes sufficiently large, we find logarithmic dependence on the energy. This cannot be removed by the choice of renormalisation scheme. Thus near-horizon quantum effects non-trivially change the tidal response of near-extremal black holes.

We prove the first quantitative bounds for the Gowers norms of the von Mangoldt function minus a Siegel corrected model function in short intervals. The result applies to intervals $(X,X+H]$ with $H\geq X^{5/8+\varepsilon}$ and gives quasipolynomial savings for the $U^k(X,X+H]$ norm. The main new ingredient is an efficient non-abelian Type II inverse theorem with explicit dependence on the nilsequence dimension. We prove this inverse theorem by applying Leng's efficient equidistribution theorem directly to an unweighted corner correlation in four variables, hence replacing the factorisation and subgroup argument in the non-abelian Type II proof of Matomäki, Shao, Tao and the author. In joint work with Florian Richter, we use this quantitative result as one ingredient in proving the existence of infinitely many sum-product patterns of the form $\{x,x+y,xy\}$ in the shifted primes $\mathbb{P}-1$.

Recent examples have shown that zero private capacity need not imply antidegradability and that two channels with zero private capacity can nevertheless transmit private information together. Existing entropic channel orders compare what a receiver and its environment can learn and thereby bound capacities. We connect these orders to the recent constructions through binary estimation, whose minimum mean-square error is governed by measured $\chi^2$ divergence. A new integral representation shows how measured $\chi^2$ on a qubit extension recovers quantum $\chi^2$. It lets us pass from complete measured-$\chi^2$ ordering to complete quantum-$\chi^2$, relative-entropy, and less-noisy ordering. Zhu and Wang used a signed lift to show that their qutrit channel has zero private capacity. We show that Hermitian-smoothed measured-$\chi^2$ ordering characterizes when such lifts exist, even with a quantum reference. Environmental dominance in binary estimation at every blocklength yields a finite-code reliability–secrecy bound. These results explain why complete comparison prevents activation with antidegradable helpers whereas regularized comparison alone does not. Building on that qutrit example, we establish this stability for a range of noisy Werner–Holevo channels, determine sharp private-capacity and antidegradability thresholds, and compute exact complementary capacities in a nondegradable range. By contrast, we extend Pauli half-erasure activation to all $1/2\le p<1$ and establish the same range for a new four-level family. Reference-assisted measured-$\chi^2$ witnesses show why these activating constructions lack complete comparison.

We show that if quantum commitments exist, then either there is no polynomial-time solution to the unitary synthesis problem, or $\mathsf{BPP} \neq \mathsf{NEXP}$. Thus, showing unconditionally that quantum commitments exist would require answering at least one of two longstanding open questions in complexity theory. We prove our main result as a consequence of a more general lemma, which shows that every unitary in $\mathsf{unitaryPSPACE}$ either cannot be synthesized efficiently relative to any classical oracle, or can be synthesized efficiently with an oracle for $\mathsf{NEXP}$ search problems. Our lemma has other noteworthy consequences, including that certain oracle separations involving $\mathsf{unitaryPSPACE}$ would imply breakthrough classical lower bounds such as $\mathsf{NC} \neq \mathsf{NP}$. Along the way, we propose new definitions for the unitary complexity classes $\mathsf{unitaryP}$ and $\mathsf{unitaryPSPACE}$. Our changes address the biggest conceptual issues with definitions suggested in prior work, and lead to elegant proofs. We study both implementations that erase garbage and implementations that allow it, because we cannot rule out the possibility that the two definitions differ. Nevertheless, we show that both definitions can be viewed as special cases of each other. We also showcase many other ways in which our definitions are robust. For example, we show that $\mathsf{unitaryPSPACE}$ has an equivalent characterization as the set of unitary transformations whose entries can be computed to arbitrary precision in polynomial space. Consequently, we deduce that $\mathsf{unitaryPSPACE}$ can generically erase garbage, a result that provably fails relative to unitary oracles.

For a graph $H$, its $k$-colour vertex Ramsey class is the set of all graphs $G$ such that any colouring of the vertices of $G$ in $k$ colours results in a monochromatic (induced) copy of $H$. We prove that for any $k$, Ramsey classes of any non-isomorphic graphs are distinct.

We study metric graph sign clusters of the Gaussian free field on a large class of transient weighted graphs $G$ that are sufficiently low-dimensional, i.e. below the mean-field regime, and prove a macroscopic equivalence property: several natural ways to define macroscopic clusters - involving any of diameter, volume, or capacity functionals - are in fact the same. As a corollary, macroscopic clusters are characterized in low dimensions as those containing large loops in the corresponding loop soup picture, in contrast with the typical behavior in high dimensions. We then apply these results to the small-mesh scaling limit of critical clusters on $\varepsilon\mathbb{Z}^d$, $d=3,4,5$, as $\varepsilon \downarrow 0$. We prove that every subsequential scaling limit consists of sets with positive Brownian capacity whose Hausdorff and Minkowski dimensions are both equal to $1+\tfrac d2$, as conjectured by Werner. We also derive two-point crossing estimates in the limit, and show that each limiting loop soup cluster is the closure of the union of the scaling limits of the macroscopic loops it contains. Remarkably, unlike with planar Bernoulli percolation for instance, the determination of the Hausdorff dimension does not emerge from direct calculations involving a limiting object (such as $\text{SLE}_6$), but rather from the distinctive features of the discrete model itself.

The choice of post-training data for large language models substantially affects downstream performance. Gradient-based data selection is a popular approach that ranks training data by how well their gradients align with those of a small validation set. However, ranking with full-parameter gradients requires an expensive backward pass on every sample, making computation intractable for large candidate pools. This raises a natural question: can we approximate full-gradient features at a fraction of the cost? Conveniently, we find that output-layer gradients suffice for effective data selection, yet require only the cheaper forward pass. We implement this as LESSER, a drop-in wrapper for selection methods that reduces the feature-extraction FLOP cost by $9.7\times$ for SFT and $3.0\times$ for RL benchmarks, while tracking full-gradient performance on downstream tasks. Empirically, we find that even when output-layer and full gradients rank individual samples differently, they select batches with aligned gradients.

Vacuum Kerr perturbations in general relativity have identical even- and odd-parity quasinormal frequencies. We establish this parity isospectrality for linear gravitoelectromagnetic perturbations of subextremal Kerr–Newman–de Sitter black holes, without a slow-rotation or small-charge expansion. We reconstruct the radiative metric and gauge-potential perturbations directly from gauge-invariant master variables in radiation gauge, without an intermediate complex potential.

We present a blueprint for implementing the physical QRAM operation in a scalable, passive manner, proving its feasibility in principle. Our construction is passive because for an $n$-qubit address over $N = 2^n$ memory bits the energy cost per QRAM query is $O(\log N)$, and to our knowledge it is the first construction to use $\operatorname{polylog} N$ energy. The runtime for each query is $O(\log^2 N)$. It is achieved by evolving a pre-manufactured time-independent 4-local Hamiltonian with $O(N)$ terms where every qubit participates in at most 4 terms.

Recent algorithms for classical simulation of quantum mechanics have runtime whose superpolynomial component is given by a linear dependence on the number of terms required to write large tensor products of certain "magic" states as superpositions of "free" states (which may be stabilizer states, fermionic Gaussian states or others). Surprisingly little is known about the number of terms in such decompositions, called ranks (e.g. the stabilizer rank, fermionic-Gaussian rank etc.). For complexity theoretic reasons they are expected to grow exponentially in the number of tensor factors but, while exponential upper bounds are known for both the stabilizer and fermionic-Gaussian rank of magic states; the best known lower bounds on the stabiliser rank are quadratic, and no bounds on the fermionic-Gaussian rank are known beyond fixed constants. In this work we prove that any fermionic Gaussian decomposition of $\lvert M\rangle^{\otimes k}$ consists of $\Omega(1.4^k)$ terms. Here $\lvert M\rangle$ is the most standard magic state for fermionic linear optics: the $4$ qubit state that may be consumed to implement a swap gate. We also prove essentially matching bounds on the $\delta$-approximate rank of the same state, lower bounding it by the same quantity that bounds the exact rank, multiplied by a factor of $1-\delta^2$. Our results on exact fermionic Gaussian rank apply directly to any product of $k$ fixed parity non-Gaussian states, although the same is not true of the approximate rank. Finally, we prove that the coherent state border rank of an $n$-mode bosonic Fock state with $m_j$ bosons in mode $j$ is exactly $\prod_{j}(1+m_j)$, answering a conjecture of Ref. [1] and obtain lower bounds on the approximate coherent state rank given by the same quantity multiplied by a function of the fidelity of the approximation, emphasizing the broad applicability of the method we employ.

Self-supervised Vision Transformers (ViTs), such as DINOv2, learn rich visual representations, but the functions of their internal tokens remain poorly understood. Recent architectures introduce dedicated register tokens to reduce high-norm out- lier patch tokens that emerge in background re- gions, yet the semantic and functional roles of both token types have not been fully established. In this paper, we analyze these roles by training sparse autoencoders (SAEs) on register-token and outlier-token activations in DINOv2. Using an automated interpretability pipeline, UMAP clus- tering, and CLIP-space cross-checks, we find that register-token features are more strongly associ- ated with high-level semantic concepts. Outlier- token features, by contrast, are more often associ- ated with lower-level structural, background, and texture-dominant patterns. Causal ablations fur- ther reveal a substantial functional asymmetry: disrupting top-activating register-derived features produces a 48.17% drop in representation cosine similarity, whereas disrupting outlier-derived fea- tures produces only a 0.31% drop. Together, our results provide evidence for token specialization in self-supervised ViTs.