Papers

Sampling-based quantum advantage raises a basic resource question: how much non-Gaussianity is needed to reproduce the random-matrix statistics often associated with quantum chaos? Passive fermionic linear optics preserves Gaussian structure, and even Haar-random mode mixing fails to anticoncentrate for Slater inputs. We show that overcoming this obstruction requires an extensive input resource. For any pure half-filled input state, the one-body defect $\nu$, defined as the summed occupation variance of the natural orbitals, must scale linearly with system size. For products of bounded-size blocks on $4N$ modes, this condition is also sufficient, with normalized collision moment asymptotic to $2N/\nu$, compared with the Porter-Thomas value 2. For four-mode products, the full Porter-Thomas moment hierarchy is recovered precisely when the defect density tends to its maximum. Assuming average-case hardness, approximate classical sampling remains hard near maximal density, with an error tolerance that increases with the density. Two-copy number fluctuations measure $\nu$ directly, and the same quantity lower-bounds the combined cost of non-Gaussian resource modes and parity-preserving local gates in deterministic exact preparation. Fermionic randomness therefore carries an extensive magic cost, with a quantitative link between sampling statistics, preparation resources, and an experimentally accessible witness.

We characterize compactly supported functions $f$ in Dunkl–BMO spaces as those that can be written as \begin{equation*} f=g+\widetilde{S}_{\mu,\mathcal{P}}, \end{equation*} the sum of some bounded function $g$ and the generalized balayage $\widetilde{S}_{\mu,\mathcal{P}}$ of a Carleson measure on $\mathbb{R}^{N}\times(0,\infty)$ associated with the Dunkl–Poisson semigroup. As a direct application of this representation of Dunkl–BMO functions, we establish a new characterization of the Hardy space in the Dunkl setting via a principal value integral related to $\widetilde{S}_{\mu,\mathcal{P}}$. Moreover, analogous conclusions hold for the Dunkl–heat semigroup as well.

We present a statistical comparison between barred and unbarred narrow-line Seyfert 1 galaxies (NLS1s) to investigate the role of large-scale stellar bars in fueling AGN with low-mass black holes. From a parent sample of 492 NLS1s selected from SDSS and Pan-STARRS1 (PS1), we construct a PS1-resolved matched sample of 101 barred and 101 unbarred NLS1s, matched in redshift, inclination, and image quality. Unbarred NLS1s are modestly but consistently brighter than barred NLS1s in several optical AGN luminosity indicators, including $\lambda L_{\lambda}(5100~A)$, broad H$\alpha$, broad H$\beta$, narrow H$\alpha$, narrow H$\beta$, and [O III]~$\lambda 5007$, with typical offsets of $\sim 0.1$–$0.25$ dex; the broad H$\alpha$ and narrow-line offsets are statistically significant, while the continuum and broad H$\beta$ offsets are marginal. Monte Carlo resampling and a Bayesian model support the same direction of offset. In contrast, the main narrow-line diagnostics, including [O III]/H$\beta$, O3N2, and the [S II]-based electron density, are statistically consistent between the subsamples, although barred NLS1s show a higher N2 ratio. Within the barred subsample, the bar strength parameter $e_{\max}$ shows a mild anti-correlation with the optical continuum and broad Balmer-line luminosities. These results indicate that large-scale stellar bars are not associated with enhanced instantaneous optical AGN luminosity. Instead, barred systems may experience more regulated or time-variable inner gas delivery, building circumnuclear gas reservoirs without necessarily increasing accretion power observed at the epoch traced by optical AGN emission.

We perform an exhaustive study of the parameter space of the chiral magnetic model with a Dzyaloshinskii-Moriya interaction, an in-plane anisotropy term and an out-of-plane Zeeman magnetic field. We map out the phase diagram for the model and find a chiral soliton lattice hosted on a chiral soliton lattice as the ground state in a particular corner of the phase diagram. There is a smooth crossover, as opposed to a phase transition, to the skyrmion crystal lattice phase. Finally, we also discover excited composite soliton states such as an anti-skyrmion coexisting with a bimeron or an anti-bimeron.

LLM gateways enforce separate tenant quotas while sharing model deployments and cooldown records that temporarily exclude failing backends. However, a tenant's request failure can update these shared records and restrict other tenants' access to serviceable deployments. We identify two attacks that exploit this gap in LiteLLM. The first uses requests rejected at the key's requests-per-minute (RPM) limit: caller-supplied identifiers for known registered deployments reach failure handling, allowing two rejected requests to redirect another tenant to fallback with zero upstream calls from those requests. The second uses admitted traffic to create cooldown records that persist after backend capacity recovers. To address these failures, we design an origin check that blocks deployment updates from key RPM rejections and tenant-scoped cooldown that preserves the triggering tenant's back-off while retaining shared records for backend faults. Experiments with authenticated proxies and self-hosted vLLM demonstrate that the attacks can force fallback or denial while deployments remain serviceable. Across five paired four-worker runs, tenant scoping reduces victim fallback after recovery from 54/60 to 0/60, while increasing attempts against exhausted shared quotas. These findings show that tenant isolation must cover both request admission and the failure handling that governs shared deployment availability.

We systematically investigate the correlations between nuclear fission properties and the surface energy coefficient $a_{\rm surf}$ extracted from semi-infinite nuclear matter. To this end, we employ the covariant density functional theory based on a point-coupling energy density functional (EDF). Taking $^{240}$Pu and $^{236}$U as representative examples, we employ Gaussian-process emulators to construct the joint posterior distributions of $a_{\rm surf}$ and selected fission observables, constrained by the ground state properties of the two nuclei. The results reveal a strong correlation between $a_{\rm surf}$ and the fission barrier heights. A sensitivity analysis further shows that the height of the outer fission barrier is governed predominantly by the isoscalar-vector derivative coupling constant $\delta_V$ in the point-coupling EDF, whereas that of the inner barrier is by the combined effects of $\delta_V$ and several mutually correlated coupling constants.

Contrastive Reinforcement Learning (CRL) learns representations that estimate goal reachability, yet its policy remains conditioned on raw goals and therefore does not directly exploit the geometry encoded by its critic. We introduce Direction-Conditioned Policies (DCP), a method built around a small modification to CRL: DCP selects previously visited states as waypoints during online training and conditions the policy on their direction and distance in representation space. At deployment, DCP applies the same interface directly to the final goal, requiring neither waypoint selection nor planning. Across nine navigation and manipulation tasks, DCP attains higher final success rates than CRL on seven tasks and spends more time near the goal on seven. Controlled maze experiments further show that DCP captures shortest-path geometry more accurately and that the supplied direction causally influences the actor's behavior. We identify waypoint coverage and ranking as limits to exploration, and show that learned candidate generation improves goal reaching in two controlled mazes.

Classical simulation supports the development and validation of quantum algorithms through full-state inspection, controlled noise models and backpropagation, albeit for small quantum systems. Existing frameworks offer gate-level execution, differentiable pulse-level dynamics or optimised hardware execution. Just another quantum simulator (JAQSI) combines gate- and pulse-level simulation in one differentiable circuit model built upon JAX. Circuits are represented as pure functions of numerical inputs which support vectorised batches and JIT compilation. Within a single circuit, matrix-defined operations, gates synthesised from Hamiltonian time evolution and noise channels can be composed freely. For a fast simulation, gate and channel fusion reduces passes over the state, while adjoint differentiation computes expectation-value gradients with a constant number of statevectors. At pulse level, JAQSI reduces evolution under single-term Hamiltonians to a scalar pulse-area integral and reuses cached execution plans and compiled solvers. In a benchmark we compare JAQSI with PennyLane, Qiskit, Qibo, Qulacs, QuTiP and dynamiqs. At gate level, we observe performance either on par or an order of magnitude faster across statevector, density, noise and gradient simulation than the compared simulators up to 12 qubits. Beyond 18 qubits, JAQSI is on par with PennyLane Lightning in both statevector and gradient simulation. In the statevector and noisy density-matrix pulse benchmarks, it is at least 5 times faster than the other simulators, even with its closed-form solve disabled. Disabling the latter increases its runtime by at most a factor of 1.5. We provide JAQSI as open-source software on GitHub and PyPI.

The sensitivity of radio technosignature searches has improved dramatically over the last five decades; however, as the RFI environment from which these searches are conducted has become increasingly polluted, our advancements in telescope sensitivity have not necessarily been complemented by less ambiguous technosignature searches. In this work, we investigate the resulting loss of opportunity to conduct unambiguous technosignature searches from Earth. We introduce three new concepts, opportunity lost, volume lost, and self-censorship, to quantify the impact of orbiting RFI sources on Earth-based technosignature searches. Using publicly available orbital data between 2008 and 2025, we find an approximately two-fold increase in the spatial occupancy of satellites within representative telescope beams, with the exact magnitude of the loss strongly dependent on telescope pointing. We further demonstrate that the cumulative effect of faint emission from multiple satellites increase the effective system temperature and consequently reduce the volume over which a technosignature of a given intrinsic power can be detected. Using approximately 10,000 archival observations from the Murchison Widefield Array spanning 2014–2024, we find suggestive evidence for increasing RFI occupancy across most of the frequencies observed by the MWA. While other opportunities for terrestrial technosignature searches exist, we argue for the protection and utilisation of uniquely radio-quiet environments such as the lunar farside, which offers an opportunity to regain the ability to perform unambiguous technosignature searches that is being progressively lost on Earth.

Music is universally present in human societies. Ethnomusicologists have long been documenting the diverse expressions of human musicality, and comparative musicology has recently brought several studies of folksong to a more global scale. Such cross-cultural research has not been conducted on lyrics: the language barrier has so far prevented work with multi-lingual data. However, Natural Language Processing (NLP) technologies have reached a stage where this language barrier may no longer be prohibitive. Combining folksong lyrics corpora across five languages, we machine-translate them to a pivot language with a pre-trained neural topic model, and we examine the relationship between content and social function within each language, and across languages for wedding songs. As expected, human evaluation of translation results shows that non-Indo-European languages suffer from overall worse translation quality. Experiments with topic models then indicate that the content of lyrics is at best partially related to the social function of folksongs across all languages. These experiments are just first steps into cross-cultural folk musics lyrics analysis; however, they do indicate that a previously unobserved web of cross-cultural relationships beyond ethnomusicological typologies may be uncovered through the study of what people sing across the world's diverse folk musics.

We present a foundational reinterpretation of quantum dynamics based on the standard von Neumann formalism, positing a structural logical bipartition between a classical observational environment and a quantum observed system. Against universalist frameworks, we argue that theoretical consistency requires distinct propositional logics: Boolean logic governs the environment, while non-Boolean logic applies to the observed system. Within this framework, an ideal classical clock is represented as an open system whose energy spectrum is uniformly discretized. The dynamics follow from the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation under the constraint that the Hamiltonian remains observable. Although the clock's temporal evolution is driven by dissipative coupling to the measurement apparatus, it admits a deterministic solution corresponding to information-preserving cyclic dynamics. This deterministic regime may emerge as a logical attractor, stabilized by the Boolean structure inherent to the measurement interaction. Ultimately, $\hbar$ is derived as a fundamental scaling parameter from the classical clock's action operator, revealing that the quantum of action reflects the discrete logical structure underlying classical temporality. Furthermore, this framework establishes an exact mapping with 't Hooft's cellular automaton formalism, offering an alternative ontological interpretation that not require hidden variables and superdeterministic assumptions. The resulting distinction between quantum dynamics (as potential recontextualization) and classical dynamics (as temporal actualization) provides a novel logical approach to the measurement problem.

It is shown that the discriminants of boundary singularities introduced by V.~I.~Arnold naturally arise in integral geometry. They represent the irregularity sets of the volume function. This function maps an affine hyperplane to the volume of the part of a domain in the Euclidean space cut off by this hyperplane. For isolated boundary singularities, the role of the boundary is shown to be related to the hyperplane at infinity in the projective space. Versions of the Milnor fiber bundle adapted to the present problem are defined and studied. Analogs of the local even Petrovsky class are introduced and computed. It is proved that the volume function is locally finite-sheeted only if these classes are trivial. Such components of the complements to the discriminants (quasilacunas) are listed for simple boundary singularities — those having no moduli in the classification. The obtained results establish new obstructions to the algebraic integrability of domains in a Euclidean space.

Teleoperation is becoming increasingly important for collecting high-quality demonstrations to teach robots dexterous manipulation skills. For dexterous manipulation, bare-hand tracking provides a practical way to control robotic hands and demonstrate coordinated finger movements without gloves or exoskeletons. However, this type of teleoperation faces two key feedback limitations: a lack of force feedback and visual feedback of occluded region. The absence of force feedback hinders precise and safe manipulation, as operators must infer contact force visually rather than feel them directly. Occlusion by objects or other robot parts impairs the assessment of hand positions, approach distances, and pre-grasp configurations suited to the object's shape. To address these limitations, we propose a digital-twin-based augmented reality (AR) teleoperation interface that integrates bare-hand tracking, bimanual robotic hands, and virtual representations of the robot and task objects. The interface renders tactile measurements on robot hand meshes as visuo-force feedback. Furthermore, it offers a user-controlled virtual view panel or occlusion-aware transparency rendering to provide occlusion-mitigating visual feedback. We evaluated the interface through user studies involving Task 1 and Task 2, examining how force visualization and visual assistance support demonstration collection in tasks requiring careful force regulation and manipulation under occlusion.

LLM-based text-to-speech (TTS) models can generate emotionally expressive speech, but how reference emotion is routed through the model and realized in decoded speech remains unclear. We introduce two emotion-sensitive metrics for matched neutral and emotional syntheses—a codec trajectory score and a late residual direction score—and use them to score activation-patching interventions. Under controlled matched-reference conditions, this analysis identifies a sparse source-to-readout component-level circuit: 23–27 attention heads and MLPs per emotion, roughly 5% of the components considered, recover or suppress 74–88% of the late emotion-readout shift on held-out cases. The circuit combines a shared component backbone with emotion-specific components; cross-emotion activation swaps reduce the target readout in 47 of 48 cases. In decoded speech, the same intervention produces consistent changes in pitch, energy, and spectral brightness over 24 matched pairs per emotion. A readout-matched residual-direction baseline produces only 17–27% of the intervention's pitch effect, showing that internal readout movement alone does not explain the decoded acoustic changes. These results trace a compact causal route from reference-derived prefix information to emotion-relevant properties of generated speech.

We study recoverable entanglement in a four-qubit cluster-state register whose two detector qubits couple to a scalar field. A local preparation phase leaves the initial reference–register entanglement and detector marginal unchanged, but controls protection under collective noise. At the optimal phase, a fixed decoder recovers a Bell pair after any channel preserving the singlet and triplet sectors. For uniformly accelerated detectors at finite separation, an exact trace-norm formula shows that the same phase is optimal at every time within the secular weak-coupling dynamics. Small separation produces a slow decay, whose rate and phase-dependent amplitude we derive. Matching the local response to an inertial thermal bath gives an analytic optimum time for the entanglement contrast. A detector measurement and conditional phase correction recover a two-qubit teleportation resource. Spatial smearing and an ordered weak-coupling then small-separation limit specify the microscopic scope of the lifetime prediction.

Accurate retinal vessel segmentation requires features that capture vascular geometry while preserving information for fine-scale reconstruction. We propose CGDD-Net, a context-guided dynamic detail modeling network that connects adaptive feature extraction to a shared decoder pathway. Context-Guided Scale-Adaptive Deformable Encoding (CSDE) combines fixed-grid convolution with deformable local attention to capture vascular patterns at multiple spatial extents. Spatially Adaptive Multi-Kernel Gating (SAMG) selects receptive-field responses at each location. Dynamic Cross-Scale Detail Fusion (DCDF) aligns the gated intermediate features and compresses them into an eight-channel representation, which is reused at three decoder resolutions together with selected encoder skips. This design consolidates intermediate information before decoding instead of transferring each middle-stage feature through a separate direct skip. On DRIVE, CHASE\_DB1, STARE, and HRF, CGDD-Net achieves AUC values of 0.9824, 0.9938, 0.9895, and 0.9874, with F1 scores of 0.8323, 0.8102, 0.8510, and 0.8157, respectively. The complete model contains 1.96 million trainable parameters. In cumulative ablations, the full model improves F1 over the internal baseline by 2.48, 0.61, and 3.49 percentage points on DRIVE, CHASE\_DB1, and STARE. Twelve directed cross-dataset experiments further characterize transfer without target-domain adaptation. The results support shared intermediate detail delivery as an effective, parameter-compact architecture for retinal vessel segmentation. Code is available at \url{https://github.com/lixincheng-xcl/CGDD-Net}.

Backtests of LLM trading agents often assume that every order fills at the closing price. We ask whether this choice changes only reported returns or also the order of the agents. Five prompted LLM signal policies and seven classical baselines trade the same synthetic price paths under six execution settings, from near-ideal fills to latency, spread, participation, and impact stresses. The main experiment contains $2{,}462$ runs with matched decision frequencies and paired market paths. On the compressed two-asset board, agreement between the near-ideal and default-stress rankings falls to Kendall $\tau_b=0.21$ in the high-volatility regime, compared with $0.82$ in the calm regime. The seed-bootstrap intervals, $[0.00,0.52]$ and $[0.48,0.94]$, are wide and overlap. On a fixed 11-policy board, agreement rises from 0.24 with two assets to 0.85 with ten; the two-asset point estimate differs substantially from the wider settings we tested. Rank changes are related to turnover, and comparisons with buy-and-hold also depend on how that anchor is initialized. The experiment does not compare LLM trading skill. It shows that, on a short horizon, an execution convention can become part of the benchmark's headline. Execution assumptions and rank stability should be reported alongside returns.

Test-time training (TTT) lets a model store information in its weights during inference. When the model learns from its own output, however, each update also changes the model that generates the next training example. Across 128K-token streams, retaining generated-text updates worsens prediction on independent human-written text with three TTT-E2E model configurations (labeled 125M, 760M, and 3B). The same failure occurs when Adam updates Qwen3-4B's existing weights. The same update mechanisms can improve on real text, so writing itself is not the failure. Three matched comparisons trace the causal pathway. Fixed Generation removes over 98% of the damage at 125M and 760M by using a frozen model to generate training chunks. Recorded Replay separates the loss caused by reading degraded text from the additional loss stored by updating on it. A paired one-update comparison then shows the local conflict: an update predicts its source better but new real text worse. This cost grows after Closed Loop adaptation, with a few trajectories accounting for most large failures. Finally, Settlement evaluates the candidate state on independent real text before commitment. It leaves mean endpoint gaps of 0.07 and -0.02 nats at 125M and 760M while retaining real-text adaptation. These results motivate checking prediction on independent evidence before retaining an update.

We prove the existence of infinite time bubble tower solutions for energy critical $k$-equivariant Schrödinger maps $\mathbb{R}^2\to \mathbb{S}^2$ with $k\geq 3$. More precisely, for any integers $k\geq 3$ and $N\geq 1$, we construct a $k$-equivariant solution that is global in one time direction and decomposes asymptotically into a superposition of $N$ bubbles with scales $\lambda_j(t)\sim|t|^{-\beta_j}$, where $\beta_j=\frac{1}{2}\left(\left(\frac{k}{k-2}\right)^{N-j}-1\right)$. Our approach is a backward construction combined with modulation analysis and high order energy estimates. We use Darboux coordinates adapted to the multi bubble profile to express the remainder in a complex scalar form. A key ingredient is the construction of a correction that cancels the leading effect of the nonlinear defect.

Low-light UAV-based RGB-infrared oriented small-vehicle detection is important for nighttime traffic monitoring, emergency response, and urban inspection. Illumination variations, headlight glare, local shadows, and thermal-response degradation cause spatially varying modality reliability, while the small visual extent of vehicles further weakens boundaries, orientation cues, and thermal responses. Accordingly, selecting trustworthy observations based on local modality reliability while further exploiting complementary discriminative information in regions with ambiguous modality preference is key to constructing effective multimodal representations. Based on this insight, we propose ReDiffNet, a reliability-conditioned differential representation network in which modality reliability guides both evidence selection and complementary recovery. Specifically, degradation-aware reliability learning estimates relative spatial reliability, uncertainty-guided differential recovery exploits cross-modal differences to recover complementary cues in ambiguous regions, and reliability-conditioned reconstruction integrates retained and recovered evidence into a unified representation. ReDiffNet achieves 85.3% and 73.9% mAP50 on DroneVehicle and VEDAI, respectively, supporting its effectiveness.

The discretization of continuous frames in Hilbert spaces is well established, while the corresponding problem for Hilbert $C^*$-modules presents additional difficulties arising from the $C^*$-algebra-valued inner product and the structure of compact operators on Hilbert modules. In this paper, we develop an operator-selection framework for the discretization of continuous frames in Hilbert $C^*$-modules over finite-dimensional $C^*$-algebras. Our main result is a trace-controlled selection theorem for positive compact operators acting on countably generated Hilbert $C^*$-modules over finite-dimensional $C^*$-algebras. In particular, we establish a module version of the binary selection principle for positive trace-controlled compact operators. The proof combines finite-rank approximation, the matrix representation of finite-dimensional $C^*$-algebras, and operator estimates adapted to the $C^*$-module setting. We then apply these selection results to the discretization of continuous Hilbert $C^*$-module frames. Under suitable assumptions on the underlying metric measure space, with the coefficient algebra $\mathcal A$ finite-dimensional, and assuming that every closed submodule of $\mathcal H$ is orthogonally complemented. The resulting sampling family is a Hilbert $C^*$-module frame with explicit frame bounds and controlled separation.

While the maximal coding rate reduction (MCR$^2$) objective has become a useful principle for learning compact and discriminative representations, a theoretical understanding of its optimization geometry remains limited, especially regarding why first-order methods often exhibit fast convergence near its local maximizers. In this work, we show that the MCR$^2$ objective satisfies an error-bound property in a neighborhood of its local maximizers. This property guarantees that the distance to the local maximizer set can be bounded above by the gradient norm at any point in the neighborhood, directly implying regularity conditions such as the Polyak–Łojasiewicz inequality and quadratic growth. Leveraging this property, we prove that first-order methods converge linearly to a local maximizer of the MCR$^2$ objective under mild conditions. Numerical experiments validate the predicted local convergence behavior and provide empirical evidence that optimizing the MCR$^2$ objective improves representation geometry while maintaining competitive downstream accuracy.

Learning population dynamics from unpaired temporal marginals is an ill-posed inverse problem that requires structural assumptions on the underlying dynamics. We introduce $\textit{Discrete Action Matching}$ (DAM), a finite-state counterpart of Action Matching based on discrete Wasserstein geometry. For a prescribed marginal path and transport geometry, we derive an action-minimization objective for its canonical minimum-kinetic-energy current. Our key observation is that the density dependence of the discrete action reduces to neighboring density ratios. Along an empirical interpolation of the snapshots, DAM first estimates these ratios and then learns an action potential. The learned fields also define a graph-supported Markov sampler. Experiments on controlled synthetic dynamics and real mouse gastrulation data evaluate marginal reconstruction and interpolation. Additional experiments approximate numerical surface-transport paths from paired samples.

On-policy self-distillation (OPSD) provides denser token-level supervision and better computational efficiency than Reinforcement Learning with Verifiable Rewards (RLVR). However, this denser supervision may introduce substantial noise and training instability. Existing improvements often rely on high-variance per-token statistics and introduce extra hyperparameters and trade-offs. Based on the advantage formulation in RLVR, we analyze the OPSD objective from the same perspective, incorporating outcome correctness signals. We find that vanilla OPSD imposes insufficient penalties and excessive rewards on incorrect trajectories because it applies a fixed divergence objective regardless of outcome correctness. Furthermore, the reliability of teacher supervision is associated with both trajectory outcome and the cumulative average teacher entropy along the rollout. Based on these observations, we propose Outcome-Guided On-Policy Self-Distillation (OG-OPSD), which dynamically adapts both the divergence objective and distillation position according to binary outcome rewards and the cumulative average teacher entropy. Extensive experiments show that OG-OPSD consistently improves the performance of vanilla OPSD and multiple strong baselines in mathematical reasoning, multimodal reasoning, and out-of-distribution tasks across Qwen3 models at 1.7B, 4B, and 8B scales, as well as Qwen3-VL-2B.

Prior work suggests that sentiment can often be captured by approximately linear directions in LLM activation spaces, but a single direction may not fully capture sentiment representations. In natural communication, sentiment is shaped not only by polarity but also by usage factors, such as tone and audience adaptation. We test whether these factors systematically modulate sentiment representations beyond a shared sentiment direction. We construct a controlled paired dataset that holds event content fixed while varying sentiment polarity and usage factors, and analyze Llama, Mistral, and Gemma. We identify a shared sentiment direction, remove it, and test the residual structure through erasure and generation-time tone steering. Across models, the shared direction is robust (median cosine 0.953-0.975), yet removing it leaves 0.833-0.909 of the original positive-negative representation-difference norm. The residuals contain compact, reproducible usage-conditioned structure. Targeted erasure weakens held-out usage metrics more than random and label-shuffled controls. On Llama, outputs steered along residualized tone components are preferred in 92.8% of blind target-tone comparisons while preserving the requested sentiment polarity in 98.7% of evaluated outputs.

A backbite on a Hamiltonian path of a graph $G$ adds an edge of $G$ from an endpoint $u$ of the path to a vertex $v$ and deletes an edge of the path at $v$ so that the result is again a Hamiltonian path. We study the connectivity of the reconfiguration graph $R(G)$, whose vertices are the Hamiltonian paths of $G$, with two adjacent when a single backbite carries one to the other. We prove that $R(G)$ is connected whenever $G$ contains the square of a Hamiltonian path as a spanning subgraph, and that any two Hamiltonian paths can be reconfigured using $O(n^2)$ backbites. Combining the theorem with known results on spanning squared paths gives connectivity for every graph with $\delta(G)\ge\lceil\frac{2n-1}3\rceil$, for the circulants $\mathrm{Circ}(n;S)$ with $a,2a\in S$ for some $a$ coprime to $n$, and, with high probability, for the random graph $G(n,p)$ with $p\ge c/\sqrt n$, for a sufficiently large constant $c$. In the other direction, graphs with arbitrarily high connectivity may have disconnected reconfiguration graphs. For every $n\ge8$ and every $1\le m\le\lfloor n/2\rfloor-3$ we construct a graph on $n$ vertices with $\kappa=\lambda=\delta=m$ whose reconfiguration graph is disconnected, with at least $(n-2m-4)!$ components. We conjecture that $\delta(G)\ge n/2$ suffices for connectivity.

In 1949, De Bruijn and Erdős considered infinite stick-breaking sequences. In this work, we consider finite sequences and prove that an infinite sequence that is due to De Bruijn, Erdős, and Toulmin is in some sense unique.

Adapting step-distilled text-to-image (T2I) models through post-training incurs additional computational costs and affects native few-step generation behavior. This motivates a complementary route beyond style-specific adaptation: drawing on the visual knowledge already encoded in step-distilled T2I models to elicit stylistic capabilities through language. Pursuing this direction requires textual guidance that captures how visual attributes jointly define a style and remain applicable as the depicted content changes. To explore this approach, we introduce StyleForge, a fully automatic, training-free framework that expresses reference styles as reusable rendering instructions. By integrating overall rendering characteristics with local color and lighting behavior, StyleForge organizes visual evidence from reference images into a coherent specification of how the target style should be expressed. The specification is then compiled into textual guidance that can be reused across content prompts, enabling frozen step-distilled T2I models to render different subjects and scenes in the reference style while retaining native few-step generation. Extensive experiments show relative gains of up to 29.47% in generation quality scores over the strongest baseline, while Pareto analysis indicates that improved stylization is accompanied by strong adherence to the requested content. Code is available at https://github.com/sunshy-1/StyleForge.

Secure device-to-device (D2D) caching requires users to generate delivery signals from their own caches and to recover their requested files without learning the other files. We construct schemes that meet both requirements when communication is limited to nearby users. The network consists of $K$ users on a cycle, a library of $N$ independent files, and a reception radius $r$. Delivery uses one round of noiseless orthogonal local broadcasts, with no server transmission. Each user's cache has capacity $M$ file units. An outer secret-sharing code assigns file shares to senders, and a secure local caching scheme at each sender delivers the requested shares. The cache budget includes the sender's library representation, random state, and delivery keys. We prove that each receiver's cache and all audible broadcasts jointly reveal no information about nonrequested files, despite the dependence between the outer shares. The converse counts transmissions crossing a contiguous user block and uses secrecy to remove one user's observation from the entropy bound. Let $h=2r$ and $K\ge h+1$. The private coded caching (PCC) instantiation attains the minimum peak sum load $K/h$ for every $M\ge Nh$ when $N>1$. For $N\ge K$, its memory-sharing envelope is within a factor $15$ of the optimum throughout $M\in[N/h+2,Nh]$. We also apply lifting without secrecy constraints, achieving the optimal load on $M\in[hN/(h+1),N]$ and a factor-$9/2$ guarantee on $M\in[N/(h+1),N]$ when $N\ge K$.

This paper develops a mesh-free numerical method for the one-phase Mullins-Sekerka flow, in which the interface bounding a set moves as the Wasserstein gradient flow of its perimeter. One difficulty in computing this flow is that two pieces of the interface with opposite normals form a hidden boundary when components merge. Our approach represents the interface by an oriented point cloud, which we treat as an oriented varifold. We introduce a quantity that measures how much nearby normals cancel each other and use it to detect the hidden boundary. Based on this quantity, we construct a perimeter estimator, prove that its expected error decays at an algebraic rate in the number of points, also in the presence of a hidden boundary, and use it in a minimizing movement scheme for the flow in two dimensions. Numerical experiments show that the scheme computes mergers of components through the hidden boundary, while the perimeter term in the scheme decreases at every step and the area is nearly conserved. As hidden boundaries also appear in other perimeter-driven interface problems, we expect our oriented representation to be applicable to them as well.