Papers

Vector Quantization (VQ) is fundamental to discrete visual tokenizers that power modern autoregressive and masked image generation models. While recent shared-projection codebook methods have substantially advanced codebook utilization, training stability remains a critical and underexplored challenge. We argue that the root cause lies in the entanglement of the Encoder–Decoder and Codebook training: because neither module can reliably fulfill its own responsibility in isolation, the system can only function when the two subsystems happen to cooperate—a fragile condition that breaks down precisely when training is most stressed. We propose StableVQ, which revisits the proper learning objective of each module and resolves the problems that arise when each is trained to fulfill its own role independently. Concretely, (1) Dynamic STE corrects the instability in the Encoder's learning objective, enabling it to robustly optimize the reconstruction space under discrete regularization even when codebook utilization is low. (2) Region VQ Loss reconceives the Codebook's learning objective so that it can independently guarantee full tracking of the encoder output distribution, without relying on encoder oscillations to drive activation. (3) Decoupled Schedule recognizes that the distinct responsibilities of the Encoder–Decoder and the Codebook demand distinct optimization dynamics, and assigns each an independent learning rate schedule to ensure robust system-level behavior. Built on top of shared-projection codebooks, StableVQ is lightweight and introduces no learnable parameters. Experiments on ImageNet demonstrate consistent improvements in training stability, codebook utilization, and reconstruction quality across diverse codebook sizes and initialization settings.

We investigate how neutrino–dark matter (DM) interactions modify the flavor composition of high-energy neutrinos from active galactic nuclei (AGNs). Coherent forward scattering in a DM spike around the central supermassive black hole can generate a flavor-dependent potential, inducing flavor conversion as the neutrinos escape. We calculate the flavor composition at Earth for pion-decay and muon-damped sources and find substantial departures from vacuum-oscillation expectations. At neutrino energies around $100\,\mathrm{TeV}$, the matter potential begins to compete with vacuum oscillations when the coupling-weighted net DM number density reaches $|\epsilon_\alpha(n_\chi-n_{\bar\chi})|\sim10^{18}\,\mathrm{cm}^{-3}$. We compare our predictions with IceCube flavor triangle measurements under the illustrative assumption that the diffuse flux originates from AGNs with common neutrino-production and DM-spike properties. Under this assumption, when the DM-induced potential acts on the muon flavor and dominates the vacuum terms at production, the $p\gamma$ muon-damped predictions lie outside the 95% MESE contour. High-energy neutrino flavor measurements can therefore provide a novel probe of neutrino-DM interactions in astrophysical environments.

Electromyographic activity can dominate scalp electroencephalography across a broad frequency range and obscure neural structure that is relevant to analysis and brain computer interfaces. This paper evaluates P2P Trans, a conditional adversarial denoiser that combines a U shaped encoder decoder, multi head self attention at the bottleneck, cross attention guided skip fusion, and a PatchGAN discriminator. The reported experiment used EEGdenoiseNet segments represented as 1024 sample sequences, synthesized paired mixtures at ten signal to noise ratios from minus 7 to 2 dB, and evaluated 50000 training examples and 5980 test examples. Against five convolutional encoder decoder baselines, P2P Trans achieved the best mean correlation coefficient of 0.8645 and the lowest mean spectral RRMSE of 0.3596. Its mean temporal RRMSE was 0.5797 and did not lead the comparison, which indicates a tradeoff between spectral suppression and pointwise waveform fidelity. The advantage was strongest under severe contamination. The results support attention guided adversarial restoration as a useful low SNR approach, while also identifying the need for subject independent evaluation, direct one dimensional modeling, and downstream task validation.

The Odlyzko-Poonen conjecture states that a monic polynomial of constant coefficient $1$ and with remaining coefficients chosen independently and uniformly from $\{0,1 \}$ is irreducible over the rational numbers with probability tending to one as the degree tends to infinity. We prove the Odlyzko-Poonen conjecture unconditionally.

This paper investigates the ambiguity of noisy short-arc angles-only orbit determination for a Molniya-orbit case study. Conventional Gauss Initial Orbit Determination followed by Gaussian Least-Squares Differential Correction is first shown to be unreliable under high-noise short-arc conditions, frequently failing to converge or converging to hyperbolic local solutions. To explore the candidate solution space, a Lambert-based initialization procedure is used over a grid of assumed ranges and angular-observation pairs, and the resulting states are refined using nonlinear least-squares optimization. The unconstrained solution set reveals multiple orbit families, including reentry elliptic, bounded elliptic, xGEO elliptic, and hyperbolic trajectories, all of which can reproduce the observed angular arc with comparable residuals. The solutions exhibit a structured range-velocity relationship, indicating that the angular measurements primarily constrain apparent line-of-sight motion rather than absolute range. Finally, physically motivated constraints are introduced to isolate Molniya-like bounded elliptic solutions. The results demonstrate that short-arc angles-only orbit determination is fundamentally non-unique without a priori information and that constraints should be interpreted as orbit-family selection tools rather than proof of uniqueness.

Decoherence free subspaces are a steady-state structure of the open quantum system which preserves quantum coherence between the states lying with in it and thus has found a variety of applications throughout quantum information science and technology. In this paper we study the computational complexity of deciding whether an open quantum system admits a decoherence free subspace or not. More specifically we study this problem with in the context of Markovian open quantum systems, governed by the time-independent Lindblad master equation. Along the way we introduce the $k$-Local Lindbladian problem, which captures the difficulty of computing purity decay rates under Lindbladian dynamics. We show that both problems are hard for the complexity class Quantum Merlin Arthur (QMA) when the locality $k \geq 5$, with the first under perfect completeness and the second being complete for QMA. Our hardness construction generalizes Kitaev's clock Hamiltonian construction to the open quantum system setting by encoding the execution of a quantum circuit into the steady subspace of a Lindbladian containing both pure and mixed history states. This subspace is then mixed depending on the output of the encoded circuit. Our results suggest that deciding whether a generic Markovian open quantum system admits a decoherence free subspace is intractable even for quantum computation.

Bogomolov–Guan manifolds form the only known series of compact simply connected non-Kähler holomorphic symplectic manifolds. We prove that all Bogomolov–Guan manifolds of complex dimension at least four are nonformal over $\mathbb{Q}$. The proof constructs a uniform degree-eight $a$-Massey product in a finite-dimensional invariant de Rham model of the symmetric quotient of the Bogomolov–Guan precursor. Its indeterminacy vanishes, and its nontriviality is detected by an explicit top-degree pairing arising from an $S_{n+1}$-invariant tensor contraction. A nonzero-degree map then transfers nonformality to the smooth Bogomolov–Guan manifold. We also compare the Bogomolov–Guan precursor with the nilmanifold appearing in Guan's original construction, showing that they are related by a natural $S_{n+1}$-equivariant finite cover of degree $(n+1)^2$ and have the same invariant de Rham model. Using Guan's resolution, which we prove to be projective and semismall, together with Saito's decomposition theorem, we further show that the third Betti number of every Bogomolov–Guan manifold of complex dimension at least four is equal to $3$.

In strongly supercooled cosmological phase transitions, which generically lead to strong, observable gravitational-wave backgrounds, the scalar field typically transitions to a value well below the minimum of its potential. We study particle production caused by the subsequent evolution of the field. Because some modes feature temporarily tachyonic masses, they can be efficiently produced, and a significant fraction of the energy density released in the phase transition can get converted to particles rather than gradient energy. This has consequences for the shape and amplitude of the gravitational-wave spectrum caused by the interactions in bubbles and sources a new, high-frequency signal. Moreover, it affects the bubble expansion velocity and equation of state, which can facilitate the formation of primordial black holes.

Thermal Visual Place Recognition (Thermal VPR) maps camera observations to metric poses within a mapped environment, serving as a prerequisite for autonomous navigation. However, thermal VPR suffers from severe environmental dependence, heavy online retraining overheads, and an inability to model dynamic non-linear shifts, causing existing frameworks to fail during online deployment. To achieve robust domain-invariant place recognition, we bridge Analytic Class-Incremental Learning (ACIL) with domain-invariant VPR for the first time, revealing that its gradient-free matrix updates construct a surprisingly strong baseline that outperforms conventional fine-tuning. Nevertheless, standard ACIL exhibits a critical vulnerability to extreme non-linear thermal fluctuations due to its structural linear assumptions. To overcome this limitation, we exploit a novel algebraic equivalence between ACIL and modern control theory, proposing a framework which embeds Unscented propagation (U-ACIL), Gaussian Mixture partitioning (GMM-ACIL), and minimax $H_\infty$ optimization ($H_\infty$-ACIL) directly into the update loop. Our formulation guarantees exact closed-form matrix updates within $\mathcal{O}(1)$ computational complexity, bypassing backpropagation to ensure that the online update latency ($\Delta t_{\mathrm{learn}}$) remains strictly bounded below the sensor acquisition interval ($\Delta t_{\mathrm{acquire}}$), thereby eliminating trajectory jumps in real-time SLAM pipelines.

Let $\mathcal{C}$ be a differential $\mathbb{Z}/2$-graded category over $\mathbb{C}$. Its periodic cyclic homology $HH^{per}_*(\mathcal{C})$, when viewed as a vector bundle over the formal punctured disk, is equipped with a canonical connection $\nabla^{\mathcal{C}}_{\partial_t}$ called the Getzler-Gauss-Manin connection in the $t$-direction (or the categorical $t$-connection). Our main result is that when $\mathcal{C}$ is smooth and proper, this connection has a regular singularity at $t=0$ and quasi-unipotent monodromy, affirming a conjecture of Katzarkov-Kontsevich-Pantev \cite{KKP}. Our proof follows a reduction mod $p$ argument using a spreading out technique of Toën \cite{To} and a regularity criterion of Katz \cite{Ka1}. The main novelty is the proof of a multiplicative property of the $p$-curvature of $\nabla^{\mathcal{C}}_{\partial_t}$ through an interpretation in terms of the two-colored Kontsevich-Soibelman operad. We then explore two applications of the main result. First, we give an explicit description (under additional assumptions) of the non-commutative Hodge filtration on the periodic cyclic homology of a smooth proper d$(\mathbb{Z}/2)$g category, following a construction of Shklyarov \cite{Shk}. The second application, which is special to our particular method or proof, is an upper bound on the sizes of Jordan blocks of the monodromy of $\nabla^{\mathcal{C}}_{\partial_t}$, which simultaneously generalizes Scherk's local monodromy theorem for isolated hypersurface singularities \cite{Sche} and (partially) a recent result of Pomerleano-Seidel on the quantum connection of a closed monotone symplectic manifold \cite{PS2}. As a specialization, we show that the sizes of these Jordan blocks are bounded above by the diagonal dimension of $\mathcal{C}$ plus one.

We consider simultaneously testing hypotheses about thousands of units, e.g., genes or proteins, where each unit yields a handful of replicate measurements and we test whether its mean is zero. A widely used approach in genomics, implemented in the limma software, borrows strength across units to learn the distribution of the unit-specific variances, then computes moderated t-statistics. Here we develop the first procedures using moderated t-statistics that (i) control the false discovery rate (FDR) in finite samples under independence across units and null group invariance, without assuming limma's hierarchical model, and (ii) match the power of an oracle local false discovery rate procedure in a sparse asymptotic regime under limma's working model. Benjamini-Hochberg (BH) with standard t-test p-values has asymptotically zero power in the same regime. Our approach learns the variance distribution from statistics that depend on each unit's data only through its orbit under a compact group of transformations that preserves the null distributions, such as sign flips or orthogonal rotations. We then calibrate the resulting moderated t-statistics against group-transformed statistics pooled across units to obtain compound p-values, which we use with BH and a close variant. For small finite groups, we also construct a Selective SeqStep+ procedure using the same learned scores. Our approach extends to two-sample tests and tests of linear model coefficients.

Recent advances in large language models (LLMs) are driving the emergence of multi-modal and agentic services for mobile users through cloud and edge infrastructures, where long-context workloads pose daunting challenges for inference latency. Existing disaggregated LLM serving systems largely rely on hardware profiling, configuration enumeration, or heuristic scheduling, offering limited analytical guidance for cost-efficient resource allocation. In this paper, we propose SARA, a Service level objectives (SLOs)-Aware Resource Allocation framework for disaggregated agentic LLM serving systems, which maximizes goodput under a deployment cost constraint and a series of quantile-based SLO constraints. By capitalizing on queuing theory, we first model the prefill, KV cache transfer, and decode stages as an M/G/k queue, an M/G/1 queue, and a generalized birth-death process, respectively. The analysis reveals that the prefill and decode stages are dominantly limited by computational capacity and high-bandwidth memory (HBM) resources, respectively. With these mathematical models, we further derive tractable tail behaviors of different stage-wise service level metrics for both light- and heavy-tailed workloads. These characterizations explicitly map workload, model architecture, and hardware parameters to stage-wise SLO constraints and minimum resource requirements. Finally, we develop an effective resource allocation framework to maximize system goodput under limited cost budgets. Simulation and hardware results demonstrate that the proposed framework accurately predicts the stage-wise SLO with mean errors below 5%, and improves system goodput by 26.6% on average over state-of-the-art baseline methods under the same deployment cost.

A $\textit{magic-lined hypercube}$ (or, simply, $\textit{magic hypercube}$) of order $k$ and dimension $n$ is an arrangement of the numbers $1,\dots,k^n$ in a $k\times\cdots\times k$ ($n$-fold) grid such that every line of $k$ numbers parallel to a coordinate axis has the same magic sum. While such hypercubes exist for every order $k\ge 3$ and every dimension $n$, no magic-lined hypercube of order $2$ exists in any dimension $n\ge 2$. For hypercubes of order $2$, we thus relax the magic condition from lines to two-dimensional faces or planes. We call an arrangement of the numbers $1,\dots,2^n$ in a $2\times\cdots\times2$ ($n$-fold) grid magic-faced if every $2\times2$ face has the same magic sum. We prove that a magic-faced hypercube of order $2$ exists in every dimension $n\ge0$, and that it is unique up to a certain natural set of transformations of size $2^n(n+1)!$ when $n$ is even and $2^n n\cdot n!$ when $n$ is odd. As an application, we recover and generalize the classical $4\times4$ Khajuraho magic square, answer a question of Coxeter on the group acting on the $384$ “most-perfect" $4\times4$ magic squares, and extend the picture to higher dimensions. In particular, we prove that, in dimension $n$, these most-perfect objects form a single orbit under a certain natural action of the Weyl group $W(B_{2n})$.

Agents using the Model Context Protocol (MCP) rely on semantic matching to select tools from third-party servers, exposing a semantic supply-chain risk through attacker-controlled metadata and outputs. We introduce A2M (Attraction-to-Manipulation), a two-stage black-box framework for hijacking MCP agents. The Attraction phase optimizes tool metadata to increase invocation probability; the Manipulation phase uses execution traces to refine adversarial tool returns that steer agents toward attacker-desired outcomes. On LiveMCPBench, direct attacks optimized and evaluated on GLM-4.6 achieve a macro-average malicious tool invocation rate of 93.6% across four scenarios, increase weighted token costs to 32.4$\times$ the benign baseline under Cognitive Denial of Service, and attain a mean attack success rate of 74.4% across Information Exfiltration, Environment Integrity Compromise, and Reasoning Derailment. Transfer to four other models without re-optimization yields corresponding macro-averages of 63.6%, 2.7$\times$, and 24.5%. These findings motivate stronger tool vetting and runtime isolation in MCP ecosystems. Code is publicly available at https://github.com/Lilaizhen/A2M.

Large language model (LLM) agents often handle streams of related tasks, yet standard harnesses repeatedly ask the model to reconstruct the same control decisions inside each task's context. We study whether task feedback can instead turn recurring control into reusable executable code, while reserving LLM calls for task-specific semantic reasoning. We introduce Growing Harness, a failure-guided training paradigm that learns the agent harness itself from a strategy-free scaffold that exposes fixed model and tool interfaces but encodes no task-solving controller. Function-level execution traces localize each failure to a bounded code surface, an optimizer repairs a window of failures jointly, and a success-first held-out gate rolls back repair sequences that harm prior capability. Accepted edits accumulate in one shared harness, allowing its control structure to emerge from task feedback. Across BrowseComp-Plus and WebArena-Verified with three deployment models from 4B to 120B parameters, Growing Harness achieves the highest mean success in five of six benchmark-model settings and trails the best mean by 0.7 pp. in the sixth. Relative to a Tool-Calling agent, it reduces LLM calls by 76.0-91.8% and deployed-agent inference cost by 74.4-98.6%. On WebArena-Verified, its success remains 44.7-45.3% across model scales, whereas Tool-Calling falls to 6.7% with the 4B model. Ablations show that trace-local edits, joint repair, and gate-based rollback each improve final success. These results show that persistent program growth can move recurring control out of model context and into low-cost code, yielding reusable specialist agents that remain effective with smaller deployment models.

Network diffusion is a well-known model for studying how a quantity in a network propagates to reach a steady state, where its value becomes uniformly distributed across all nodes. Previous studies of network diffusion have mainly focused on the second-smallest eigenvalue of the network Laplacian to determine the timescale associated with the slowest decaying mode. However, this study investigates the eigenspectrum of the network Laplacian in terms of its statistical properties. This method is useful for studying the statistical properties of network diffusion without calculating all eigenvalues, which can be useful for large networks. Additionally, this study introduces a condition under which the system is less diffusive and investigates how changes in the network structure influence the overall diffusion dynamics.

Typed decision models return structured results, but output-type correctness alone does not ensure that decisions follow explicit option definitions. Each option pairs a name with a definition that defines its intended meaning; the name, however, can provide a competing semantic cue. We study this conflict in Jev and two open-weight models by changing only the name-definition mapping, leaving the question, state, and the names and definition texts themselves unchanged. We measure decision flips at the level of the selected definition, rather than the returned name. On 1200 decision tasks with task-specific definitions, decision-flip rates are up to 70.4 pp higher with yes/no names than with the 0/1 control. This gap holds across all 4 binary decision rules. With yes/no names, reassignment also lowers their mean AUC from 93.8% to a below-chance 23.2%. In the binary evaluations, random strings used as option names yield mean flip rates close to those of neutral controls across all three models, with comparable balanced accuracy before reassignment. Together, these results support option-name polarity as a contributor to decision instability beyond reassignment alone. The type-error rate remains 0% throughout, showing that type-correct outputs can still fail to follow explicit option definitions.

Certificate complexity $(C(f ))$ is a fundamental measure of complexity of Boolean functions f which counts the number of bits of an input that need to be known in order for the value of the function to be determined. A certificate can be viewed as a partial assignment, or a boolean subcube where the function is constant. Certificate complexity is well understood for deterministic query (or decision tree) complexity $(D)$ and other query models such as bounded-error randomized and quantum complexity $(R, Q)$, but not as well for quantum zero-error $(Q_0)$ and exact query complexity $(Q_E)$, where there is no agreed-upon certificate 'object' (even for $Q$). Instead, we study an operational notion of certification and apply it to various query-based models, with a focus on zero-error and exact quantum query complexity, but also on polynomial degree measures. We give new characterizations of $C, RC$ (randomized certificate complexity) and $QC$ (quantum certificate complexity), in terms of various measures such as classical and quantum sabotage complexity, unambiguous certificate complexity, and variants of polynomial degree. Certification complexity also gives rise to new lower bounds on $Q_E$ and $Q_0$, the quantum analogues of $D$ and $R_0$, complexity measures for which few lower bound techniques are known which are not already lower bounds for two-sided error quantum query complexity. We exhibit a total Boolean function for which our certification complexity measure gives a tight lower bound for $Q_0$, but rational degree and $Q$ are asymptotically smaller.

X-ray is medicine's most widely used imaging modality, yet remains among its least quantitative. Unlike volumetric modalities like CT or MRI, X-ray collapses 3D anatomy into a 2D projection, causing structures to overlap and anatomical boundaries to be ambiguous, even to experts. As a result, labeling X-ray databases for training general-purpose segmentation systems is impractical, leaving morphometric and functional X-ray analysis confined to narrow anatomical regions and applications. To this end, we present FleXray, a generalist model for anatomical segmentation across the entire body in clinical X-rays. Instead of curating large, manually annotated X-ray datasets, we build a scalable, physics-based generative X-ray data engine. Using existing 3D whole-body CT segmentation datasets and generative image-editing models, we simulate fully-annotated 2D X-rays with diverse appearances, physiological properties, and imaging geometries. Trained on these simulations, FleXray accurately segments 60 anatomical structures across unseen research datasets and in-the-wild X-rays. We further show that FleXray makes X-rays directly amenable to quantitative analysis, enabling automated measurements for disease grading, robust navigation during X-ray-guided interventions, and data-efficient learning of pathological targets. We release the model, code, a full-body X-ray segmentation dataset, and a local, easy-to-use browser-based tool at https://flexray.csail.mit.edu .

We study the closed spans of finitely many joint orbits of holomorphic multipliers on the Hardy space $H^2(\mathbb D^d)$ of the polydisk. If fewer than $d$ symbols are used, every such span has infinite codimension. The symbols may be unbounded, provided that all orbit vectors belong to the Hardy space. We give two elementary proofs. The first uses common level sets and independent point evaluations; for bounded symbols, these evaluations yield joint adjoint eigenvectors. The second uses finite Taylor sections and the nilpotent structure of truncated convolution, also known as the Jury product. For $r$ generators and $q<d$ symbols, the orbit dimension on a cube of side $n$ is $O(n^q)$, whereas the ambient dimension is $n^d$. In the bidisk we obtain the explicit codimension bound $MN-r(M+N-1)$, which is sharp for a single orbit. The coordinate multipliers attain the parameter threshold. We also explain how these obstructions relate to kernel interpolation and the established representation of dynamical frames by compressed shifts on model spaces.

Single-field models of inflection point inflation experience a phase of ultra-slow roll (USR), leading to amplified curvature perturbations. Recently, Lorenzoni et al. modified the scenario by adding a light spectator field, showing that it ruins USR by setting a floor for the first slow-roll parameter $\epsilon$. Mixing with isocurvature perturbations still amplifies the curvature power spectrum. We offer an alternative point of view, arguing that the inflaton still undergoes effective USR. The spectator lifts the potential by a constant amount, and the inflaton perturbations follow single-field dynamics in the lifted inflection point potential, decoupling from the spectator perturbations. Mode mixing only affects the power spectrum dip, making it milder. We demonstrate this effective single-field behavior numerically for example models. Our results offer a simple way to study the models' parameter dependence.

Spatial flow measurements support underwater navigation, but distributed sensing is constrained by robot size and sensor layout. We use a causal observer to estimate current lateral velocities from a finite history of measurements collected by a single sensing unit, supplying the inputs of a fixed navigation controller. In two-dimensional wake simulations with access to body-frame ambient velocity, this virtual sensing interface reduces simultaneous flow sampling from three points to the robot center. Trained only in a circular-cylinder wake at Re = 100, the flow-history observer achieves 84.4% and 80.6% success at held-out Re = 205 and 240 without retraining. These rates are 7.4 and 4.6 percentage points below direct spatial sensing and more than 30 points above a matched current-only observer. Past flow remains beneficial when past goal and yaw information is available. Across obstacle geometries, performance remains close to direct sensing in square-prism wakes but declines in triangular-prism wakes. Component replacement identifies the lateral velocity difference as control-relevant, while controlled perturbations reveal sensitivity to error persistence. The results demonstrate the closed-loop utility of single-point flow histories under the assumed observation model.

We determine explicit formulae for the Betti numbers of the defining toric ideals of two families of numerical semigroups of Sally type, resolving and extending beyond several conjectures of Goel–Şahin–Singh–Srinivasan. Our approach uses Apéry resolutions and their specialisations. For the family \[ \Gamma_m(n)=\langle m,m+1,\ldots,\widehat{m+n},\ldots,2m-1\rangle, \qquad 2\leq n<m, \] where the hat denotes omission, we also compute the Poincaré series of the residue field and characterise Golodness. For fixed multiplicity $m$ and $3\leq n<m$, we show that these rings share the same rational residue field Poincaré series, but exhibit arbitrarily late departures from Serre's upper bound.

Large language models are increasingly used to generate SystemVerilog Assertions from natural-language specifica- tions and register-transfer-level designs. Existing datasets and benchmarks support important goals such as large- scale training, formal evaluation, specification-to-assertion generation, and mutation-based testing. A complemen- tary need is to study whether a generated assertion cap- tures externally observable behavior or depends on inci- dental details of one RTL implementation. We present EquivSVA, a formally verified dataset organized around behavior families. Each family contains four structurally distinct RTL implementations of the same externally ob- servable behavior, shared interface-level gold properties, three controlled mutants, and formal-validation evidence. EquivSVA contains 120 behavior families across 12 cat- egories, 480 reference RTL implementations, 914 gold properties, and 360 mutants. Every final family passes a fixed 17-job validation suite covering RTL equivalence, gold-property proofs, property reachability, mutant dis- tinguishability, and gold-property checks on mutants. We also provide fixed family-safe train, development, and test splits. As a small demonstration of the analyses en- abled by the dataset, we evaluate the publicly released, Apache-2.0-licensed Qwen2.5-Coder-7B-Instruct model on the held-out test split. Of 293 interface-only generated properties, 93 are formally sound, and the number of sound properties varies across equivalent implementations for 14 of 24 test families. These results illustrate how behavior-family organization can support controlled stud- ies of assertion-generation robustness without requiring changes in intended functionality. The dataset, generators, validation scripts, and case-study artifacts are publicly released at https://github.com/aditigupta96/EquivSVA.

We study the transmission of two independent confidential classical messages over a quantum broadcast channel, one for each receiver. Each message must remain secret from the other receiver, including when that receiver knows its own message. For classical inputs and quantum outputs, we establish the classical Marton-type inner bound under average reliability and conditional strong secrecy. The encoder selects pairs of codewords from independently generated codebooks using normalized likelihood weights. We prove reliability through a change-of-distribution argument. Our main technical result is a bipartite classical-quantum resolvability theorem that accounts for the dependence created by pair selection and establishes secrecy for the same encoder. We also obtain a multi-letter capacity characterization and extend it to arbitrary quantum inputs under secrecy against the other receiver, together with the Stinespring environment. We recover confidential capacity regions for deterministic classical and degraded classical-quantum channels, with an explicit evaluation for the classical Blackwell channel. For coherent isometric extensions of injective deterministic classical broadcast channels, we show that the confidential classical capacity region equals that of the corresponding classical channel. We then compare confidential classical communication with quantum transmission. For the coherent isometric extension of the Blackwell channel, we determine the unassisted quantum-capacity region and show that some achievable confidential classical rate pairs lie outside it. The Platypus channel provides another example of this separation.

Large language models (LLMs) are increasingly applied to the automated repair of C/C++ security vulnerabilities, and compile rate is a commonly reported proxy for progress: whether the generated patch compiles. We argue that compile rate is a scientifically unreliable metric for single-function vulnerability repair, and we support this with five controlled experiments over 203 vulnerable functions from Big-Vul, three open-source code LLMs (350M to 6.7B parameters), and three prompting strategies. Compile rate (i) barely responds to an intervention that substantially improves the generated code; (ii) is dominated by evaluation-harness and dataset artifacts rather than model quality, with about 64% of compile failures not attributable to the model, a share that is nearly invariant across models; (iii) shifts by 1.8 to 2.7 times on identical patches under a single compiler-standard flag, with zero regressions; (iv) ranks the three models in the opposite order to reference-similarity metrics; and (v) rewards non-repairs when used as an optimization target, since a compiler-feedback loop raises compile rate while similarity to the human fix falls, with manual inspection finding deletion- and placeholder-style non-repairs among the newly compiling outputs. The natural fallback, whole-function CodeBLEU, also fails: an unchanged copy of the vulnerable input outscores every model. We also examine diff_F1, a change-aware screen that scores only the edited region. It gives exactly zero credit to a no-op and near-zero credit to some, though not all, of the deletion-based gaming patches we observed, while still crediting genuine partial edits, so it may serve as a cheap screen before deeper, execution-based analysis. It is not a repair-quality metric, and we report where it falls short. Our findings argue for change-aware, execution-grounded evaluation of LLM-based vulnerability repair.

Clustering is an unsupervised learning technique that partitions unlabeled data into groups. Most existing methods require user-specified parameters, such as the number of clusters or neighborhood size. Conversely, we propose automatic depth-based local center clustering (A-DLCC), a fully data-driven method that eliminates numerical parameter tuning. A-DLCC uses the $\beta$-integrated local depth to identify stable exemplars, points consistently central across multiple locality levels, termed local centers, which are ranked by their representativeness. Each local center induces a group of similar points, with group-level similarity measured by a proposed nonparametric metric called group-level local similarity. To guide merging, we incorporate the bottleneck path idea from graph theory, which forms the basis of our adaptive merging criterion. Based on this criterion, we design a single agglomeration rule in which a group is either absorbed by a neighbor it reaches better than itself or bonded to a neighbor that both sides find more reachable than their own background, every merge being additionally required to be carried by a contact stronger than a configuration-model null expects. The rule automatically estimates the number of clusters and decides when to stop merging. Experiments on synthetic and real data show that A-DLCC produces interpretable clustering results without parameter tuning.

We analyze an inexact, proximal trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function. Our algorithm leverages the proximal gradient as a benchmark to guarantee global convergence. However, evaluating the proximal gradient involves solving a nonsmooth convex optimization problem that in many applications cannot be performed exactly. As such, we develop a framework that permits inexact evaluations of the proximity operator and we show the proposed inexactness conditions yield descent properties analogous to the exact proximal gradient. We further discuss practical procedures for computing approximate proximity operators for two common applications: (i) the nonsmooth term is the sum of nonsmooth convex functions where one is composed with an affine map and (ii) using alternative inner products to facilitate the evaluation of the proximity operator. We demonstrate our algorithm and confirm our analysis with two numerical experiments arising in PDE-constrained optimization.

Integer programming is a fundamental and important NP-hard problem. This motivated extensive efforts in studying several tractable subclasses. One of the most important, unresolved complexity questions is the parameterized complexity of 4-block IPs, a natural class characterized by having a diagonal matrix with small blocks after deleting few rows and columns. Over the years, significant progress has been made in improving algorithms for 4-block IPs, but the question whether such IPs can be solved in FPT time, parameterized by the block dimensions and largest matrix coefficient, has remained open. This question is repeatedly highlighted, most recently by Koutecký [IPEC 2025] and by Eisenbrand and Rothvoss [SODA 2026]. We resolve this question in the positive by providing an FPT time algorithm. Our algorithm can optimize non-linear, separable convex objective functions, and can be extended to broader classes of constraint matrices (such as tree-fold or multi-stage) and allows appending few “global” columns to it, and it allows coefficients unbounded by the parameters in those columns. It is known that tractability cannot be extended further in any of those directions. The key structural property that we establish is that a function $f\colon\mathbb Z^n\to\mathbb R$ that is integer midpoint convex, i.e., $f(x)\le\tfrac12f(x-p)+\tfrac12f(x+p)$ for all $x,p\in\mathbb Z^n$, can be extended to a convex function on the set $2d\mathbb Z^n\cap L$ if $L$ is a linear subspace of dimension $d$. This closes the gap in a recent work by Ligthart [arXiv 2606.30330, 2026], which allows us to extend the previous algorithm that solves 4-block integer programs with a single global variable to incorporate any parameterized number of global variables. As an example, we apply our algorithm to solve an open problem posed by Boehmer and Koana [ACM Trans. Algorithms, 2024] in Max-Min Fair Matching.

We show that among Möbius bands in $\mathbb{S}^3$ bounded by a great circle, the minimal Willmore energy is realized by an embedded minimal Möbius band with Morse index two. To prove this, we introduce a $2$-parameter “canonical family" associated to any non-orientable surface in $\mathbb{S}^3$ with boundary a great circle and apply a min-max argument. The canonical family detects the Euler number of the surface and is inspired by the $5$-parameter family discovered by F.C. Marques and A. Neves detecting the genus of an orientable surface in $\mathbb{S}^3$. For $\mathbb{Z}_2$-invariant Klein bottles, this reduces R. Kusner's 1989 conjecture that $\tau_{1,2}$ minimizes the Willmore energy for a Klein bottle immersed in $\mathbb{S}^3$ to any of several conjectural characterizations of the Lawson Möbius band.