Papers

Most existing studies on distributionally robust optimization (DRO) with a decision-dependent ambiguity set focus on the computational and theoretical challenges posed by this class of problems. In this paper, we adopt a combined modeling and computational perspective to understand the trade-offs between modeling fidelity, solution quality, and computational effort, particularly in comparison with DRO models using decision-independent ambiguity sets. Motivated by representative applications in joint pricing-stocking newsvendor problems with price-dependent demand and facility location problems with location-dependent demand, we consider a two-stage stochastic mixed-integer program with (non)convex continuous recourse. Assuming a finite sample space, we model the decision-dependent distributional ambiguity with a polyhedral ambiguity set and reformulate the problem as a nonconvex mixed-integer nonlinear program. To efficiently solve the reformulations, we propose decomposition-based cutting-plane algorithms. Our experiments on benchmark instances indicate that a decision-dependent ambiguity set substantially reduces the postdecision disappointment for the newsvendor and out-of-sample cost for the facility location problems, up to 65% and 7% on average, respectively; thereby mitigating the optimizer's curse relative to a decision-independent DRO. However, this improvement is achieved at the expense of increased computational effort, with the absolute runtime ratio falling between 2 and 25 for medium- to large-sized newsvendor instances and between 2 and 12 for facility location instances.

Extreme magnification by lensing galaxy clusters allows the detection of high-luminosity stars during cluster caustic transient events at cosmological distances. The Dragon Arc at z=0.725 is a frontier target for identifying transient events due to its high frequency of microlensing events, and so far >100 of these events have been detected. The high frequency of events and high cadence of observations allow for the measurement of minimal flux variation between epochs, and therefore the magnification evolution as a source approaches or recedes from a microcaustic can be measured from light curves. In this work, we model the light curves of 10 transient events in the Dragon Arc across eight epochs from two JWST/NIRCam medium-band filters taken over four days. Injected synthetic observations demonstrate that with additional observations, individual transient light curves allow the of apparent degeneracies between stellar characteristics and properties of motion.

Security-relevant Agent2Agent (A2A) executions can cross organizational boundaries, leaving investigators without live access to all participating systems. Offline investigation involves checking preserved records and their cross-record relationships for consistency. This paper presents A2A-ForensicTrace, an offline verification layer that converts runtime observations into typed records, derives protocol-relevant relationships, and commits both under an incident-trace root. An Ed25519-signed receipt binds the root and capture digest to the incident context. Evaluation comprised 240 executions through the official A2A software development kit (SDK), with actions selected by a large language model (LLM). These included 120 condition runs and 120 matched controls. All condition runs returned the expected bounded findings. No control produced an indication, and all roots and receipts verified. Median in-memory latency of the full offline verifier was 1.61 ms for the scenario traces. In the separate scaling experiment, it was 30.85 ms at 1,000 committed leaves. Future work will broaden A2A lifecycle coverage.

A single random Gaussian probe gives an unbiased estimate of the squared Frobenius norm of a layer's quantization error. The estimator is well-behaved because round-to-nearest error is spectrally flat. Across 1,683 tensors from a 35B MoE and a 9B dense model, effective dimensionality is 0.93 to 0.96 times the i.i.d. noise value of the same shape, and on the MoE the median is unchanged from 2-bit to 8-bit. The probe coefficient of variation is predictable from tensor shape. One probe measures per-tensor sensitivity to within 4 to 7%; twenty probes reach 1.3 to 1.4%.RAM applies the propagated form of this estimator to budget-targeted mixed-precision quantization with no calibration data. Gaussian probes carrying the network's own input statistics score every tensor at six bit-widths. A knapsack solver allocates bits under an exact byte budget, with guardrails against catastrophic 2-bit assignments. One probe pass serves any budget. Isolated and propagated scores rank tensors independently on Qwen3.5-35B-A3B (Spearman -0.01), yet the propagated probe rank-correlates 0.81 to 0.83 with the GPTQ layer objective from real activations, while the isolated estimator is uncorrelated with it. That objective is the wrong allocation target: at matched bytes on Qwen3.8-27B, a block-output probe beats a vendor IQ3_M mix and an oracle that allocates from the real-activation objective. On Qwen3-8B the propagated probe ties HAWQ-V2 at matched bytes. Across seven architectures from 8B to 122B, with probe timing up to a 400B model in nine minutes on one workstation, RAM reaches 3.5 to 13.6% lower median WikiText-2 perplexity than size-comparable uniform 4-bit builds on the tested MoE models. (Black Sheep Ai baa.ai)

We study the asymptotic and TQFT-type properties of the Kashaev–Luo–Vartanov (KLV) partition function. We show that the partition function depends on the prescribed angle structure only through its peripheral angular holonomies. For any geometric triangulation of a cusped 3-manifold realizing a possibly incomplete hyperbolic structure, we express the exponential decay rate and the 1-loop term of the partition function in terms of, respectively, the volume and the adjoint twisted Reidemeister torsion of the corresponding incomplete hyperbolic structure. Consequently, these asymptotic formulas hold for any angle structure having the same peripheral angular holonomies as the geometric one. We further introduce a Reshetikhin–Turaev-type function associated with certain admissible Neumann–Zagier data, extending the Jones function in Teichmüller TQFT previously studied by Ben Aribi and the author. We show that, after a combinatorial normalization, for any triangulation, the KLV partition function can be expressed as a weighted integral of the squared norm of the Reshetikhin–Turaev-type function, where the weight is determined by the angular holonomies of peripheral curves. In particular, for FAMED triangulations, the Reshetikhin–Turaev-type function agrees with the Jones function, so that the normalized KLV partition function is obtained by integrating the squared norm of the integrand defining the Teichmüller TQFT partition function. This provides a noncompact analogue of the relationship between Turaev–Viro and Reshetikhin–Turaev invariants.

Ground-based millimeter-wave astronomical observations suffer from strong contamination by the emission of inhomogeneous water vapor in the Earth's atmosphere. This emission reduces the observing efficiency and data quality even from a high-altitude, dry location such as the Atacama plateau in Chile. We propose to continuously monitor atmospheric water vapor with a co-pointing dedicated Raman lidar system. We show, with numerical simulations and proof-of-concept observations, how a synergistic use of atmospheric lidar data has the potential to substantially improve the quality of astronomical data sets.

Long-horizon tasks require large language model (LLM) agents to coordinate decisions under constraints that span an entire solution. Monte Carlo Tree Search (MCTS) offers a promising approach to test-time scaling by exploring alternative action trajectories, but model computation and environment interaction make search costly. Efficient search therefore requires effective reuse of trajectory feedback. Standard MCTS maintains prefix-specific statistics, without explicitly accumulating outcomes for decision groups that recur across different paths. To fill this gap, we propose HyperMCTS, a training-free method that augments an ordered MCTS tree with a cross-trajectory hypergraph. Hyperedges represent groups of canonical decisions and accumulate their observed returns within the current task. Our hypergraph-guided HyperUCT selection rule aggregates evidence from overlapping hyperedges into an action prior, allowing outcomes collected under one prefix to inform selection under another while preserving execution histories in the tree. On DeepPlanning, HyperMCTS improves average planning accuracy by 2.3–7.3 percentage points over the strongest baseline for each of three backbone models. It enables Qwen3.6-27B to outperform Claude Opus 4.6 (max) on Shopping Planning, while achieving higher accuracy with fewer LLM calls and output tokens than the evaluated MCTS-based baselines. SealQA experiments further demonstrate improvements in question answering.

We characterize uniform factor-balancedness in Arnoux-Rauzy words, generalizing the work of Espinoza, Popoli, and Stipulanti on ternary alphabets to finite alphabets of any size. In particular, we prove that an Arnoux-Rauzy word $\mathbf{x}$ is uniformly factor-balanced if and only if $\mathbf{x}$ has bounded weak partial quotients.

Code completion is one of the most widely used applications of large language models (LLMs) in software development. Open-weight LLMs are increasingly adopted for locally deployed code completion systems, partly due to privacy concerns. Despite advances in LLM accuracy, the energy cost of inference remains underexplored, particularly under large-context workloads and across programming languages. This study investigates the trade-off between accuracy and energy consumption in LLM-based code completion and how workload characteristics, context size, and model scale influence inference energy usage. We evaluate 25 open-weight LLMs on two workloads: repository-level next-line completion with varying context sizes on RepoBench, and fill-in-the-middle (FIM) code completion across Python, Java, and Rust on McEval. We analyze the influence of input tokens, output tokens, model size, and their interactions on energy consumption using correlation analysis and cluster-robust linear regression. Our findings show that the dominant drivers of energy consumption depend strongly on task structure. In RepoBench, energy consumption is primarily influenced by input context size and its interaction with model scale, whereas in McEval, output generation and its interaction with active parameter count dominate. Output generation is more energy-intensive per token than prompt processing. Across both benchmarks, smaller and heavily quantized models frequently achieve Pareto-optimal trade-offs, often providing accuracy comparable to larger FP16 models while consuming substantially less energy. Increasing model size or context length does not necessarily lead to proportionally better completion quality, while quantization can substantially improve energy efficiency with limited accuracy degradation. These findings support more energy-aware deployment strategies for sustainable AI-assisted software development.

Ejection epochs of parsec-scale jet components in active galactic nuclei (AGN), tracked with Very Long Baseline Interferometry (VLBI), are commonly estimated by extrapolating fitted trajectories back to the VLBI core. However, trajectory uncertainties, non-radial motion, acceleration, and the finite size and position variability of the core can make such estimates uncertain and restrict usable samples. We develop a probabilistic framework for estimating VLBI-component ejection epochs, including accelerated features, and for quantifying how consistently each backward-extrapolated trajectory is associated with an effective VLBI core region. We apply the framework to 1923 jet-component trajectories from the 15 GHz MOJAVE kinematic sample. Ejection epochs are defined as the times of closest approach of the extrapolated trajectories to the core, with trajectory uncertainties propagated through Monte Carlo sampling. The effective core radius is treated as a random variable, whose population-level scale is calibrated from the distribution of closest-approach positions. Each component is then assigned a model-dependent probability that its closest approach lies within this effective core region. The method yields 1589 ejection epochs. The fitted effective core-region scale is $\sigma_{\rm c}=0.16\pm0.02$ mas, corresponding to an average core radius of $0.20\pm0.03$ mas, and gives a population-level upper limit of $\lesssim0.16$ mas on the characteristic 15 GHz core wander perpendicular to the jet. Using the same probability weighting, the full probabilistic sample has $N_{\rm eff}=624$, 2.8 times the legacy MOJAVE value of 222, while the overlapping ejection epochs remain consistent with previous estimates. The framework provides a flexible basis for population studies and cross-correlation analyses of jet structural evolution and AGN variability.

We validate memory-optimal cost functions for transformer kernels derived via the Mathematics of Arrays (MoA). Companion Papers I-IV formally derive kernels for attention forward, backward, fused forward+backward, decode, and the complete block (RMSNorm, gated MLP) as a hardware-independent specification (DNF) transformed to a machine-specific realization (ONF) via gamma, with verification to machine precision against PyTorch. This paper checks those predictions against measured performance on two HPC clusters (Purdue Anvil, NCSA Delta) across CPU and GPU. Three results stand out. (1) We identify and fix a GPU regression: fusing forward+backward, proven to avoid materializing an O(n^2) intermediate, initially ran slower than naive on GPU due to atomic contention. Profiling confirmed 2.00x more atomic instructions; a targeted ONF rewrite reversed it, yielding up to 2.5x speedup. (2) Identical derivations produce markedly different real costs by topology: 535x NUMA-locality penalty on one cluster vs <3x oversubscription on another, showing optimal deployment is a function of the machine's array structure. (3) We report a partially resolved anomaly: identical denotational computations run faster in C than Fortran on CPU but faster in Fortran than C on GPU, narrowed to one dominant kernel and one memory-latency stall mechanism (3.17x time gap matches 3.35x stall gap). We treat hardware-specific optimization as a routine ONF rewrite with fixed, verified DNF, a candidate methodology for scaling AI onto evolving hardware without re-deriving correctness.

Progress in machine learning cannot outpace our ability to verify it. With an explosion in papers today, every scientific claim rests initially on trust in the trainer, leading to uneven evaluation, baselines, and forestalling of reliable progress. Traditionally, the burden of verification falls on the reader, who must reproduce expensive training runs. This strategy is impractical due to an explosion in slop contributions, diversity of methods, and the sheer compute required. We put the burden of proof where it belongs, on the trainer, and in the process also cut the overall cost of verification significantly. We introduce Witnesses, a method for certifying training, data usage and evaluation in a neural network training run. Our key insight is that fast behavioral fingerprints with occasional replay challenges are sufficient for auditing neural network training. Our method is applicable at scale with minimal overhead to the trainer, is cheap for the verifier, rejects bad training runs with amplifiable probability, and allows for exact queries of both data inclusion and exclusion. We test our method on language model training runs from 100M to 2B scales, across DDP and FSDP, and demonstrate this minimal overhead. We also introduce a self-regulating leaderboard of "auto-certified" training runs that enables shared baselines and progress. We invite the community to participate in the leaderboard to improve reproducibility in machine learning.

Agent-to-Agent (A2A) communication enables large language model (LLM) agents to exchange tasks, messages, and artifacts across organizations. A valid message alone does not establish that a final workflow claim is supported by a complete, ordered, and case-consistent evidence path. We present A2A-CaseVerify, a deterministic offline verifier that maps preserved A2A runtime objects, business events, and typed support edges to a directed case evidence graph. It commits A2A envelopes, event projections, and support edges, then combines event and edge leaves into a deterministic case Merkle root. The verifier returns SUPPORTED with status OK only when protection and profile-specific reconstruction checks pass. We evaluate one canonical supported healthcare-profile bundle and 13 controlled mutations. We separately test a valid bundle generated with the official Python A2A software development kit (SDK). In these tests, the canonical and SDK-generated bundles are accepted. All 13 mutations are rejected, and each returned reason-code set contains its targeted diagnostic code. A2A-CaseVerify adds offline case-level evidence-support verification to A2A interoperability.

Building on the forest expansion of Alòs, Gatheral and Radoičić and on the explicit Bergomi-Guyon smile expansion derived by Bourgey and Gatheral (2026), we derive fixed-point approximations, in terms of the implied total variance at a small number of magic strikes, for the fair values of power payoff contracts; the variance and gamma contracts arise as the endpoints of this one-parameter family, priced by a single set of formulae. We prove that such approximations exist at every order: at order $n$, $2\lceil n/2\rceil+1$ magic strikes suffice. Numerical tests under the Heston and rough Bergomi models demonstrate good accuracy even for strongly skewed smiles, and the method applies directly to interpolated market smiles without strike inversion. For the volatility contract, we show that the maturity-T smile does not determine the leading correction to the Rolloos-Arslan approximation.

Let p be an odd prime, let q_0 := p^s with s >= 1, and put q := p q_0^2. We study the smooth projective curve R_{p,s} with function field F_q(x,y,z), y^q - y = x^{q_0}(x^q - x), z^q - z = x^{2q_0}(x^q - x). The two-equation layer is already present in the ray-class and big-action literature; for p = 3 it gives the classical Ree curve. In analogy with the generalized Suzuki curve, we call R_{p,s} the generalized Ree curve associated with p and s. For p > 3 our principal geometric result determines the full geometric automorphism group: Aut_{F_q}(R_{p,s}) is isomorphic to the semidirect product of U and F_q^*, with |U| = q^3. The natural p-group U gives a big action; we determine the complete ramification filtration of the elementary abelian cover R_{p,s} -> P^1_x and prove that (R_{p,s}, P_infinity) is Castle. In characteristic 3 the same subgroup is only the stabilizer of P_infinity in the full Ree group, so the automorphism structure exhibits a sharp characteristic-three dichotomy. On the arithmetic side, writing Y_{p,s} : y^q - y = x^{q_0}(x^q - x), Z_{p,s} : z^q - z = x^{2q_0}(x^q - x), we prove the F_q-isogeny Jac(R_{p,s}) ~ Jac(Y_{p,s}) x Jac(Z_{p,s})^q. The first factor is supersingular and all three curves have p-rank zero. For p > 3 the first Newton slope of Z_{p,s} satisfies 1/(pq_0 + 2) <= lambda_min(Z_{p,s}) <= 1/3, so Z_{p,s} and R_{p,s} are not supersingular. For fixed p > 3 and s -> infinity, the order of the full automorphism group is asymptotic to 2^(8/5) p^(-4/5) q^(8/5).

Visual designers get inspiration from references to expand their design space. They decompose what makes a reference evocative into conceptual and visual elements, ranging from explicit attributes such as objects and colors, to less readily articulated concepts and visual motifs. They then create different visual forms to explore how the selected elements could be combined differently. Novices often struggle with these moves, instead focusing on surface features or producing limited visual variation, thus becoming fixated on the reference. Existing tools support editable visual attributes and high-level themes, but provide limited control over how conceptual interpretations relate to expressive visual motifs or how their combinations can be systematically re-expressed. We present ReVision, an AI-based tool that decomposes visual and textual references into editable conceptual interpretations and visual motifs, enables their recombination across conceptual and visual spaces, and renders each direction as divergent visual-form variations, supporting more divergent exploration during the creation process.

LLM agents increasingly rely on user approval to authorize security-sensitive actions at runtime. Such approvals are granted within a specific task and execution context. In long-lived agents, authorization decisions may need to persist across tasks or sessions. We find that this continuity can outlive the context that originally justified the approval, creating residual authority reusable without renewed consent. We expose this failure mode through a longitudinal attack that starts from a target security-sensitive action, identifies the authority required to execute it, induces benign interactions that legitimately obtain that authority, and later replays the residual authority during adversarial execution. Across controlled and live settings, we demonstrate that residual-authority replay arises in practice and substantially increases the success of prompt-injection and context-rebinding attacks. We evaluate 508 AgentDojo attack cases across six LLM families using production-derived authorization semantics. With residual authority, attack success rate (ASR) increases by up to 35.1 percentage points compared with a fresh authorization state. In live context-rebinding attacks on 55 Terminal-Bench cases across three real-world production coding agents, residual-authority replay increases ASR by 24.9 percentage points on average. These findings expose a fundamental mismatch between persistent authorization and the contextual nature of user consent in long-lived LLM agents.

Membership inference (MI) asks whether a specific record appeared in a model's training set and is increasingly used as evidence for data provenance and copyright auditing. These applications require determining whether the exact queried record was used for training, rather than merely whether the model was exposed to similar content. Making this distinction is challenging because web-scale datasets naturally contain near-duplicates, including syndicated articles, mirrored pages, and lightly modified images. We show that this creates a fundamental confound for standard MI. A clean-reference audit typically calibrates membership against a null in which neither the queried record nor its near-duplicate family is present. In deployment, however, the queried record may be absent while a non-identical family member was used for training. We introduce a four-world audit that independently varies exact-record inclusion and family presence to separate these cases. Natural near-duplicate families cause severe false attribution. On CC-News, a clean-reference LiRA auditor labels 99.70% of family-present exact non-members as members at 1.00% false-positive rate. This failure persists across alternative scores, model architectures, and executed deduplication and retraining. Controlled interventions further reveal that the effect depends on the learning objective. In classification, faithful families largely substitute for the exact record, reducing exact-given-family inference to near chance. In autoregressive language modeling, the exact sequence retains a detectable residual, while family presence still confounds clean-reference decisions. These results show that positive model-only membership evidence may establish family-level exposure without establishing exact-record provenance.

Within the Hatta-Yang holographic graviton-dilaton amplitude for near-threshold $J/\psi$ photoproduction, we identify exact dilaton-null spin-projection channels in the Gottfried–Jackson basis. The $m=0$ and $m=-\lambda_\gamma$ amplitudes receive no dilaton contribution; for photon polarization normal to the reaction plane the $m=0$ channel further isolates $A_g(t)+B_g(t)$ and requires nucleon spin transfer. Standard beam-polarization spin-density-matrix elements then furnish a TT-sensitive combination and a second bilinear containing linear dilaton-TT interference. Comparison with modern GlueX and CLAS12 cross sections shows substantial sensitivity to the shape of the original holographic parameterization. The polarization observables therefore provide direct probes of the tensor structure of the production amplitude.

By homogenizing high-contrast periodic metric graphs, we create continuous media that admit bound states produced by local defects at energies embedded in the continuous spectrum. This is achieved by fitting two copies of a lattice graph simultaneously into space and coupling them by connecting edges. The homogenization of an ODE on a graph to a PDE in space is achieved by representing the associated operators in a common functional space through interpolation by Fourier analysis. The two coupled graphs result in an effective medium with internal degrees of freedom that allow a decomposition into two orthogonal spaces of hybrid states. Critical high contrast retains microscopic resonances in the effective medium and allows a spectral band of one hybrid state space to overlap a spectral gap of the other. This serves as the mechanism for creating bound states at frequencies embedded in the continuous spectrum of the effective medium. These bound states in the continuum persist for $\varepsilon$-scale metric graphs due to $O(\varepsilon)$ operator-norm estimates for reduced resolvents on the defect region.

Generative models often suffer from mode collapse and limited sample diversity. While prior works attempt to mitigate this by jointly generating a batch of samples and repelling their trajectories, these heuristics do not explicitly maximize the diversity of the resulting endpoints. We introduce JIVE, a training-free framework that enhances generative diversity by injecting velocity perturbations aligned with the leading right singular subspace of the generator's endpoint Jacobian. By leveraging this local geometric structure, JIVE provably maximizes endpoint diversity while preserving sample quality. To maintain practical efficiency, we compute these perturbation directions via matrix-free iterations rooted in classical numerical linear algebra, requiring only a small computational overhead. Across different benchmarks, JIVE boosts both pixel and feature-level diversity in few-step and one-step generation.

SlopBench asks which models produce the stiff, repetitive prose readers call AI slop, a question detectors leave open once they have classified a text as machine-written. We evaluated eighteen models on 112 hand-written tasks in email, social posts, essays, and workplace chat, sampling each model on each task up to ten times, for 19,928 outputs in all. SlopBench scores four surface behaviors a reader can check by hand: length against the word band each task specifies, opener repetition across a model's own samples of one task, and paragraph rhythm and fixed lexical constructions against pre-ChatGPT human corpora. Under one fixed weighting, Kimi K2.6 scores lowest at 21.1 and Mistral Large highest at 40.6. Across 500 random reweightings Kimi has the lowest score in 58 percent of draws and Mistral the highest in 97 percent. No draw preserves the full order of the eighteen, and a scenario bootstrap leaves exactly one of those ranks unambiguous. We ran three further checks on that middle order: a crowd arena, an AI detector, and lexical diversity. None of them confirmed the order. We therefore report the four behaviors separately and treat the composite as one weighting among many, and we release the prompts, outputs, reference statistics, and scoring code.

We consider the behavior of deterministic, full-batch, bias-corrected Adam in separable linear classification with softmax parametrization under log-loss. In this setting, under a wide range of conditions Adam is known to approach max-norm-margin optimality when its stability constant $\epsilon$ is zero, while with a positive $\epsilon$, it is known to approach Euclidean-margin optimality. Our main contribution is the quantitative description of Adam's behavior for small fixed positive $\epsilon$. We give sufficient conditions under which an Adam-trained classifier nearly maximizes the max-norm margin before the updates become gradient-like. We also show that the classifier reaches a fixed target Euclidean margin only much later. Specifically, we show that for polynomially decreasing stepsizes with exponent \(a\), where \(1/3<a<1\), the updates become approximately proportional to the negative gradient after $\Theta(\log(1/\epsilon)^{1/(1-a)})$ iterations. At that time, the classifier still nearly maximizes the max-norm margin. Reaching a fixed target Euclidean margin above that of every max-norm-optimal classifier, but below the optimum, is shown to require $\epsilon^{-\Theta(1)/(1-a)}$ iterations. Under inverse-linear stepsize decay (\(a=1\)), the update transition takes polynomially many iterations, whereas reaching the target margin takes exponentially many. Experiments support these predictions. The later change in the classifier can improve or worsen generalization after training error reaches zero, connecting the analysis to grokking and its reverse.

User conversations with large language models (LLMs) often contain highly sensitive personal information that can be exploited by LLM providers to create detailed user dossiers, enable targeted advertising, and train more powerful models. To protect user privacy, anonymizing LLM proxies have emerged as a practical solution that separates user identity from their prompts, yet this approach still leaves the prompt content visible to LLM providers. We study the impact of this gap by conducting the first empirical investigation into the risk of prompt authorship re-identification. Towards this end, we create PromptAnonBench, a novel benchmark for evaluating prompt anonymity, consisting of over 175,000 cleaned, authentic multi-turn user prompts from various real-world datasets (SWE-Chat and WildChat). Using the embeddings of historical user conversations, an attacker can correctly detect and re-identify at least one anonymized conversation for 50–75% of SWE-Chat users and up to 10% of WildChat users at a 10% false acceptance rate for out-of-set users, even with text-based defenses applied. Our findings unveil the risk of relying only on anonymity for private LLM inference and the gap in existing text privacy defenses.

A graph $G$ is det-extremal if $|\operatorname{det} A|=\operatorname{per} A$ for its adjacency matrix $A$. Det-extremal cubic bipartite graphs arise in the study of Pólya's permanent problem, and McCuaig characterized the $3$-connected ones as vertex-sums of copies of the Heawood graph. The total domatic number of a graph is the largest number of pairwise disjoint total dominating sets. Characterization of the cubic graphs with total domatic number $1$ has been a long-standing open problem. In this paper, we prove that a connected cubic graph is det-extremal if and only if its total domatic number is $1$. We further show that McCuaig's characterization extends to all $3$-connected cubic graphs, and that every connected det-extremal cubic graph has girth $3$, $5$ or $6$. We also prove that a connected det-extremal cubic non-bipartite graph has at least $28$ vertices, and that this bound is best possible. Through this correspondence, these results carry over to cubic graphs with total domatic number $1$. In addition, in the language of configurations, our results imply that every triangle-free $3$-configuration has a blocking set.

Learning properties of neural networks has recently attracted growing interest, with existing approaches operating either directly on network parameters or through probe-based representations of network behavior. While probing methods have shown strong empirical performance, their theoretical foundations remain limited. In this work, we study when finite probe-based representations are sufficient for learning neural functionals. We establish general identification and universality results for probing, and show that using intermediate hidden representations can provide significantly more informative representations than relying only on final outputs. Motivated by these results, we introduce HIDDENPROBE, a simple architecture for learning from hidden probe responses. Across a range of neural functional benchmarks, including both MLPs and Transformers, HIDDENPROBE consistently improves over existing probing methods and achieves state-of-the-art performance. Our code is publicly available on GitHub.

Many economic applications establish stability of Markov dynamics using the monotone mixing condition (MMC) of Hopenhayn and Prescott (1992). Working in the same setting as that paper, we introduce a weak monotone mixing condition (WMMC), phrased in terms of the reversal of rank between populations, and show that it is strictly weaker than the MMC and both necessary and sufficient for global stability under the Kolmogorov metric. We apply these results to a small open economy version of the Aiyagari model, showing how the WMMC can be used to establish global stability in a setting where the MMC fails. In addition, we show that, when the state space is one-dimensional, the MMC and WMMC coincide, implying that the original MMC is necessary as well as sufficient in this setting.

We introduce NSV-Shift, a contrastive benchmark for evaluating whether speech-to-speech models can understand non-speech vocalizations (NSVs) and adapt their responses accordingly. Each pair contains two conversations with identical lexical content that differ only in the NSV embedded in the final turn. Our pilot contains 22 human-verified pairs (44 audio conditions) and evaluates five models on NSV perception, emotion understanding, and response adaptation. Results show that models generally perform better at detecting NSVs than at interpreting their fine-grained emotional meaning or producing appropriately differentiated responses. The data construction pipeline, dataset, and evaluation pipeline are publicly available at https://github.com/ChenzwNina/nsv-construction.

Training efficiency has become the central driver of recent progress in foundation models. To overcome the massive computational and data requirements of large-scale training, researchers increasingly adopt strategies such as selective data sampling, efficient pre-training, and simplified reinforcement learning pipelines. While these strategies drastically reduce overhead, they prompt a critical, yet neglected question: Is efficiency achieved at the expense of model robustness and security? To our knowledge, we present the first systematic cross-domain investigation of the efficiency-vulnerability trade-off. Across vision and language models, we show that efficiency-oriented training increases susceptibility to adversarial and privacy attacks. We characterize this vulnerability by analyzing the models' internal geometry and functional representations, demonstrating that the evaluated efficient variants consistently exhibit sharper loss geometry together with systematic changes in representational structure. We further extend our analysis to "zero RL training", finding that models trained using simplified RL recipes exhibit substantially greater susceptibility to catastrophic forgetting and more pronounced overconfidence than those trained through conventional alignment pipelines. Our findings suggest that training efficiency is rarely a "free lunch"; rather, the mechanisms that minimize computation can inadvertently compromise safety. We conclude by calling for a paradigm shift toward multi-objective training that jointly optimizes for performance, cost, and security.

Plug-and-Play (PnP) algorithms are a class of iterative methods for inverse imaging. Within an optimization algorithm, they combine a flexible fidelity term, encoding the forward operator, and a pretrained image denoiser, in order to deal with more severe corruptions such as blurring or downsampling when reconstructing an image. This work studies provably convergent PnP methods for mixed-noise forward processes by using the infimal convolution as a fidelity term, providing a statistical interpretation as a joint maximum a-posteriori estimator over both noises, and preserving the Bayesian MAP interpretation of PnP methods. Independently, we extend the PnP formulation to multiple prior terms using the Davis–Yin three-operator splitting. This extension can be combined with either standard fidelities or the proposed mixed-noise infimal-convolution fidelities. We verify that these generalized PnP methods are convergent under standard Kurdyka–Lojasiewicz conditions. Numerical experiments on Laplace-Gaussian and Poisson–Gaussian noise demonstrate stable convergence of single-prior and multiple-prior PnP methods, and divergence under fidelity mismatch. Furthermore, PnP with infimal convolution fidelities are able to scale to noise up to 38% standard deviation, with multiple priors reaching different stationary points that qualitatively preserve more textural properties.