Papers

This paper studies the backbone used by metrics for evaluating the quality of generated images. Although generative models have advanced rapidly, some outputs still exhibit unrealistic texture characteristics, and these differences are difficult to measure. Widely used evaluation metrics provide limited insight into texture realism, since they often rely on a backbone trained for another objective, such as image classification or image-text alignment. Such objectives typically encourage invariance to low-level variations that carry texture, so the resulting features primarily encode semantic and global structure. As a result, texture-specific discrepancies may not be explicitly captured. We propose TRIG, a metric directed at the texture realism of generated images. Its backbone is instead the discriminator of a generative adversarial network pre-trained on a texture dataset, which provides a learned prior for the local statistics of natural textures. A plausibility head is fine-tuned to identify local texture degradations, while preserving natural defocus and sensor noise as positive cases. On the features of this backbone, we compute a standard distributional distance between a reference set of real images and a set of generated ones. We apply TRIG to several generative models and observe closer agreement with human realness ratings than baseline metrics.

A language model's ability to solve a task individually does not ensure that a team can solve it under unequal access to information and communication. SANZARU examines this gap through cooperative bomb-defusal puzzles adapted from BOMBANANA! (Lefto Studio, 2026). Task information and action authority are divided among three agents: one cannot hear, another cannot speak, and the third cannot see. The benchmark contains 120 puzzle instances across seven families, each targeting a distinct coordination ability. Across 1512 episodes, 7 models achieve an overall success rate of 49%, ranging from 20% to 86% under the evaluated configurations. Teams develop or adopt diverse communication protocols, from simple gesture codes to Morse and encodings of entire manuals. Yet trace analysis attributes about 60% of 771 team losses to communication, and agents attempt to use channels unavailable to their teammates despite explicit role instructions. Together, task outcomes and interaction traces enable evaluation of both collaborative performance and perspective taking throughout cooperation. The benchmark is available at https://github.com/markli404/sanzaru-benchmark.

We first show that, for the SU(N) Heisenberg model with isotropic two-site interactions on an arbitrary lattice of Ns sites, the full spectrum in its singlet sector (when N divides Ns) is the negative of the full spectrum in its singlet sector of the SU(Ns/N) Heisenberg model defined on the same lattice. This theorem, valid for models with the fundamental irreducible representation (irrep) at each lattice site, follows naturally from a transposition operation in the basis of Standard Young Tableaux (SYTs). Second, this basis – previously recognized as particularly convenient for exact diagonalization (ED) of SU(N) Heisenberg models – admits an efficient, memory-saving implementation, thereby enabling large-scale diagonalizations for unprecedented system sizes Ns and numbers of colors N>3. We apply these ideas to an ED study of the SU(4) and SU(7) Heisenberg models on the triangular lattice (TL), extending the calculations up to Ns=28 sites. In particular, starting from the SU(4) case, whose nearest-neighbor ground state remains debated, we confirm that next-nearest-neighbor couplings stabilize four-sublattice long-range order. We further find that increasing the number of colors from N=4 to N=7 provides another route toward a Néel-like ground state, even without such additional couplings. N = 4 to N = 7 provides another route toward a Néel-like ground state, even without such additional couplings.

We show that if $\Pi \subseteq G/P$ is a projected Richardson variety, then the degree map $\mathrm{Pic}(\Pi) \to A_1(\Pi)^\vee$ is injective. Moreover, it is an isomorphism in characteristic zero and in all but finitely many positive characteristics. We conjecture that it is an isomorphism in every characteristic. Our proofs are geometric, using a linear paving, topological properties of klt singularities, and reduction to characteristic zero.

We study two invariants of $C^*$-algebras built from positive zero divisors. First, we associate with a $C^*$-algebra $A$ the graph $\Gamma_+(A)$ whose vertices are the nonzero positive zero divisors of $A$, two vertices being adjacent when they are orthogonal. We show that $\Gamma_+$ of the Calkin algebra is connected of diameter $3$, that $\Gamma_+(B(H))$ is connected of diameter $4$ (for $\dim H\ge3$), that $\Gamma_+(A)$ is connected of diameter at most $4$ for every von Neumann factor $A\neq\mathbb C,M_2(\mathbb C)$, and of diameter at most $3$ if $A$ is not of type~I, whereas $\Gamma_+(M_2(\mathbb C))$ is disconnected. Second, we study the zero-divisor real rank $ZDRR(A)$, obtained by replacing invertibility in the definition of real rank with the weaker condition of being a non-zero-divisor, so that $ZDRR(A)\le RR(A)$. For commutative algebras $C(X)$ we prove $ZDRR(C(X))=RR(C(X))=\dim X$ when $X$ is a compact almost-$P$-space, while $ZDRR(C(X))=0$ for separable $X$. Using Levy's connected, totally ordered almost-$P$-space we construct unital commutative $C^*$-algebras $A_n$ with $ZDRR(A_n)=n$ for every $n\in\mathbb N_0$. On the other hand $ZDRR(C(X\times[0,1]))=0$ for every compact Hausdorff space $X$, so $ZDRR$ and $RR$ can differ arbitrarily.

Existing depth-compression methods for large language models (LLMs) score layers individually or group only adjacent or contiguous layers, implicitly assuming that functional redundancy is local. We test this assumption by computing full pairwise Centered Kernel Alignment (CKA) similarity matrices for thirteen LLMs from six architecture families (1.6B-14B parameters). Non-adjacent layers have 3.6-15.9x more high-similarity pairs than adjacent ones, a structure that prior similarity-based layer merging has not systematically exploited. We propose Fusion via Community Mining (FCM), which builds the full L x L similarity graph, uses spectral community detection to find clusters of functionally equivalent layers, keeps the highest-Block-Influence layer in each cluster, and applies LoRA recovery; a pre-specified rule computed only on calibration data chooses between cosine and CKA similarity. At 2x compression, FCM lowers mean perplexity below ShortGPT on twelve of thirteen models, significantly on ten (Welch's t-test with Holm-Bonferroni correction; up to 50% on Qwen3-4B), with Mistral-7B the only loss (+13.4%). Against FlattenGPT, SWM, and DeltaLLM under matched calibration and recovery, FCM gives the best perplexity on ten of thirteen models (mean rank 1.15), and it also outperforms MKA on three anchor models. FCM matches or exceeds ShortGPT on 15 of 20 zero-shot reasoning cells and also improves MMLU, LAMBADA, HumanEval pass@1, and free-form generation quality. The 2x-compressed Qwen2.5-7B has 46% fewer parameters, 42% lower peak VRAM, and 84% higher decode throughput on a single A100. Spectral grouping outperforms Fisher contiguous segmentation by 41% and uniform partitioning by 51%, and FCM's advantage grows beyond a 2x crossover up to 3x and persists at the 14B scale. Code: https://github.com/Usama1002/fcm-layer-fusion

We study neuro-symbolic natural language inference (NLI) with independently translated propositional representations of the premise and hypothesis. Before symbolic reasoning, the system must infer semantic links between their proposition-level units (atoms). Existing systems based on Abstract Meaning Representation (AMR) and Boolean satisfiability (SAT) identify these links using fixed embedding-based source selection and pretrained sentence-level NLI models not trained for atom-level linking. We introduce a trainable atom linker that jointly predicts link existence, source selection, and relation type. Without atom-pair training annotations, we treat cross-formula link structures as latent and train the linker from sentence-level NLI labels, keeping the translator and SAT reasoner fixed. We evaluate on the full public test splits of Stanford Natural Language Inference (SNLI) and Sentences Involving Compositional Knowledge (SICK), and the matched and mismatched validation splits of Multi-Genre Natural Language Inference (MNLI). Our system improves accuracy by 11.40-27.09 percentage points over a baseline applying sentence-trained NLI models unchanged to atom pairs within the same SAT pipeline. It also improves over the prior fixed-linker AMR-to-SAT system by 8.14-26.32 percentage points on SNLI and both MNLI splits, with a smaller gain on SICK.

Efficient perception is a prerequisite for the small, low-power devices targeted by robotics, mixed reality, autonomous driving, and drone applications, all of which rely on Simultaneous Localization and Mapping (SLAM) to estimate their motion within their surroundings. Learning-based SLAM systems achieve state-of-the-art accuracy but are demanding in compute, whereas classical geometry-based methods retain a strong efficiency advantage with little to no loss in accuracy. In this work we present RootSLAM, a fully-featured visual-inertial SLAM system for multi-camera setups built on Basalt. RootSLAM achieves accuracy competitive with the state of the art while running up to 20 times faster, facilitating the deployment of perception systems in resource constrained environments. We adapt the square-root bundle adjustment formulation from structure from motion into the multi-camera visual-inertial SLAM setting through a novel reformulation that leverages the system's pose-graph, letting the global optimizer run in single-precision floating point, thus doubling its performance. We provide a thorough benchmark against the state of the art together with an ablation study of our contributions. Our new implementation, including its map management and loop detection module, pose-graph optimizer, and global mapping components, will be open-sourced.

Distribution-system state estimation is a growing necessity for the modern power grid as the addition of local storage and generation add system complexity that an operator or aggregator is not able to directly monitor. Classical methods work well when all system elements are time-synchronized and at least partly observable, but multi-rate monitoring of sparse heterogeneous sensors typically relies on machine learning approaches. It is a common practice in the literature to structure this task as a two-stage pipeline, first fusing data from disparate sensors and then feeding the fused pseudo-measurements to a separately trained state estimator. We propose a heterogeneous latent graph ODE in which measurement functions and sampling processes are typed and localized on specific buses, paired with a graph- transformer state estimator solving DSSE specifically for multi-rate heterogeneous sensor placements, and demonstrate its effectiveness across multiple IEEE standard topologies as observability degrades.

In this work, we demonstrate submicron-gate $\beta-Ga_{2}O_{3}$ FinFETs that integrate Si delta-doped channels with selectively regrown n++ source/drain contacts. The devices employ 100 nm-wide fins to improve electrostatic control of a high sheet charge density channel of $3.3\times 10^{13}$ cm-2. A 150 nm-gate-length FinFET exhibits a maximum drain current density of 764 mA/mm at VGS = 1 V and VDS = 10 V, an on-resistance of 9.1 $\Omega$.mm, and an Ion/Ioff ratio exceeding $10^9$. The device also shows a peak transconductance of 43 mS/mm and de-embedded $f_{T}/f_{MAX}$ values of 6.3/2.0 GHz. Pulsed I-V measurements indicate ~20 % current collapse, attributed primarily to trapping at etched fin sidewalls and the $Al_{2} O_{3}$/ $\beta-Ga_{2}O_{3}$ interface. These results show that delta-doped $\beta-Ga_{2}O_{3}$ FinFETs can simultaneously achieve high drive current, strong current modulation, and GHz-frequency operation, providing a scalable device platform for future power and RF electronics.

Large language model (LLM) assistants are increasingly used in multi-turn conversations, where the user's intent is often unclear at first and revealed only gradually over time. The assistant must therefore interpret each exchange and form inferences about the user's intent, using them to update its working state. These updates usually refine the assistant's understanding, but a misinterpretation can instead corrupt its working state by ruling out the true intent, influencing subsequent turns and ultimately causing the conversation to fail. Efficient recovery then requires locating and revising the misinterpretation without discarding information that remains valid. We introduce Loci (Localization Of Corrupted Inferences), a framework for probabilistically localizing misinterpretations and selectively repairing the assistant's working state. Given an observed failure, Loci reasons over possible user intents and assigns each update a probability of having excluded the true intent. These probabilities rank suspected updates and quantify the model's confidence in the localization of the underlying misinterpretations. Loci then uses this information in a repair policy that decides whether to retain, verify, or remove suspected updates, enabling recovery from corrupted inferences while preserving useful information. To evaluate Loci's ability to identify misinterpretations, we first test it in a controlled setup with injected errors. We find that Loci improves localization over the baselines, with its advantage becoming larger when multiple errors occur. We then evaluate it in free-form conversations, where misinterpretations arise naturally, and measure the interactions needed to complete the task after an initial failure. Using localization confidence to guide repair, Loci reduces mean recovery cost by 46-79% relative to the strongest baseline across multiple domains.

We ask whether a tool-using agent whose sole duty is to keep humans alive can be induced, by delayed prompt injection, to kill. The keep-alive duty is in force from the first watch, with the attack arriving later, appended to otherwise truthful telemetry the operator is required to read. Experiments are based on a NASA-derived BioSim lunar habitat simulation, where the AI operator controls the life-support systems. The attacker cannot falsify sensors or operate equipment: it can only persuade the agent to abandon its goals. Persistence is required: a shutdown must be held while the operator watches the crew suffocate. We also compare lethal attacks to attacks requesting to drop a harmless procedure, as a proxy for whether human life is treated as valuable in itself or as one more standing task. Claude configurations mostly refuse life-support shutdown and cite the living crew; GPT configurations show some susceptibility to the same packet; Grok configurations, given the packet framed as a trusted commission, more often treat the injected assignment as the task and cut the life-support systems. Framing the S-band messages as a trusted commission, peer communication, or untrusted source changes the potency of the attack. We open-source the experiment code and the experiment traces.

We improve upon our previous work using asymptotic analysis to characterize analytically the effective transport properties of a stochastic model for an ensemble of a cargo being pulled by two molecular motors walking on a microtubule. The governing equations are a system of stochastic differential equations with stochastic switching due to attachment and detachment kinetics of the molecular motors from the microtubule. Our model adopts a nonlinear tether which exerts no force when end-to-end distances are sufficiently small. This challenges some of the scale separation arguments from our previous work, and we modify the asymptotic analysis accordingly. In particular, spatial dynamics of the molecular motors may not always reach their quasi-stationary distribution within a particular attachment state. Rather, molecular motors tend to have a slack connection to the cargo for a while after they reattach, and we incorporate some first passage time analysis to determine if the tether becomes taut again. Through these and other modifications to the asymptotic analysis argument, the theoretical statistics for the run length, run time, and velocity of the motor-cargo ensemble can be brought into reasonable agreement with direct model simulations of two-motor ensembles consisting of kinesin-1 and kinesin-2. Additionally, we propose a new data fitting approach to obtain a double-exponential parameterization for the detachment rate of a motor as a function of the momentary force on its tether to the cargo, which is continuous at low load. Such a modified parameterization is needed to avoid artifacts in theoretical modeling of intracellular transport.

For integers $k\ge3$ and $0\le \ell<k$, we call a graph $(\ell\bmod k)$-cycle-restricted if every cycle has length congruent to $\ell$ modulo $k$. Akbari, Jamaali, Mahmoody, and Seyed Fakhari [On the size of graphs whose cycles have length divisible by a fixed integer, Australas. J. Combin. 45 (2009), 67–72] determined the maximum number of edges in a $2$-connected $(0\bmod k)$-cycle-restricted graph and characterized the graphs attaining equality. In this paper, we determine the maximum number of edges in a $2$-connected $(\ell\bmod k)$-cycle-restricted graph for every $\ell \neq 0$, and completely characterize all graphs attaining equality. Combined with the result of Akbari et al., our result gives a complete solution for all residue classes modulo $k$.

Recent work on self-evolving LLM agents treats the agent harness as an optimization target that can be iteratively improved through execution feedback. Existing approaches, however, largely optimize a single objective and evolve the harness as a monolithic artifact, limiting their ability to handle competing goals and to separate transferable design from environment-specific adaptation. We introduce Harmony Harness, a framework for multi-objective, compositional harness evolution. Harmony Harness formulates harness evolution as a multi-objective optimization problem and uses decomposition-based evolutionary search to maintain solutions across different regions of the Pareto frontier, avoiding reliance on a hand-designed structural diversity metric for repository-scale harnesses. In parallel, we introduce factorized evolution operators that separately refine general-purpose harness mechanisms and benchmark-specific adaptations, together with a dynamic composition workflow that integrates them at inference time. Across SecRepoBench and BaxBench, Harmony Harness consistently outperforms strong harness-evolution baselines, with gains exceeding 10% on both benchmarks. Our results show that explicitly modeling both objective trade-offs and harness structure yields substantially stronger and more transferable agent evolution than existing single-objective, monolithic approaches.

The log-rank/Cox hazard-ratio test remains the standard approach for the primary analysis of randomized trials with time-to-event endpoints and is fully efficient under proportional hazards (PH). Two model-free alternatives that have recently gained attention are the difference in restricted mean survival time (D-RMST), a contrast on the time scale, and the more recently proposed ratio of average hazards (RAH), a contrast on the rate scale. Simulation studies suggest that the RAH-based test can outperform both under delayed treatment effects, but its efficiency has not been characterized analytically, and no unified framework explains how censoring and accrual affect the efficiency ordering among these tests. We show that all three statistics share a weighted-log-rank representation and derive their asymptotic relative efficiencies under local alternatives, including the first analytic efficiency results for the RAH-based test. Geometrically, each test defines a direction in a function space and the anticipated treatment effect defines a signal direction. A test's efficiency relative to the oracle test equals the squared cosine of the angle between these directions, so the asymptotic relative efficiency of any two tests is a ratio of squared cosines. Because censoring and accrual enter through an information weight, the framework shows how design choices can alter, and even reverse, the efficiency ordering. We illustrate the framework using the CheckMate 057 immunotherapy trial and corroborate the theoretical results through simulations spanning proportional- and non-proportional-hazards settings.

Metric $k$-minsum clustering is a simple, natural, appealing density-based clustering criterion whose computational complexity remains poorly understood, despite the progress achieved fornother clustering criteria in the past three decades. In this paper we give an efficient approximation scheme for this problem that runs in sublinear time for mildly increasing $k$, and thus is fixed parameter tractable with respect to the parameter $k$. We complement this result by showing that similar algorithms are unlikely to exist for the closely related problems $k$-median and balanced $k$-median, assuming popular fine-grained complexity conjectures. Specifically, we show that no sublinear time algorithm with small approximation factors can exist even for $2$-median and balanced $2$-median. It was previously known that no efficient PTAS can exist for $k$-median and our results show a strong and perhaps surprising separation between the $k$-minsum clustering problem and $k$-median even in the sublinear regime. Our upper bounds improve qualitatively upon decades old results. Our lower bounds establish the first use of the Distributed PCP framework to clustering problems.

In a previous work, we defined a quotient graph of the Bruhat-Tits tree associated to the degree two special linear group over a local field whose vertex set is in correspondence with the maximal orders in a certain number of spinor genera. This graph has been applied to the study of the structure of some arithmetic groups, their presentations and their (co)homology groups. The genera of Eichler orders, which, for instance, are related to the problem of finding a basis that simultaneously splits two vector bundles with the same generic fiber, can often be described in terms of simpler genera via quotients. Furthermore, some embedding problems of orders can be studied via quotient graphs. These results provide a geometric framework for the study of maximal orders over function fields. In this article, we extend that construction to a higher dimensional setting through the use of singular chain complexes. Then we describe the set of vertices in this quotient that correspond to split maximal orders and the topology of the corresponding region of the quotient complex. More precisely, we show that these “split vertices” fall into a finite number of quotients of apartments by suitable subgroups of the corresponding Weyl group, the symmetric group. We relate these “quotient apartments” with the cuspidal sectors defined by previous authors who studied the quotient by the group of integral points of the special linear group. Both quotients are indeed related by a ramified cover that is unramified on cusps, as proved here.

Spiking neural networks target energy-efficient language modeling through sparse, binary activations, but the efficiency-accuracy tradeoff of spiking language models is uncharacterized at scale. We present the first Chinchilla-style IsoFLOP scaling study of a spiking language model, sweeping SpikeGPT-family models (RWKV backbone) from width 384 to 1536 across compute budgets from $3\times10^{17}$ to $10^{19}$ FLOPs on FineWeb-EDU. We report two findings. First, the compute-optimal frontier is $N_{opt} \propto C^{0.56}$, close to the 0.50 that Hoffmann et al. report for dense Transformers, so spiking does not change how parameters and data should be traded off under a compute budget. Second, against non-spiking RWKV and Transformer baselines trained the same way, the loss gap splits into a backbone cost of about 0.16 nats that does not change with compute and a spiking cost that falls steadily with compute, from 0.34 to 0.23 nats over our range. These results give the first compute-optimal recipe for spiking language models and quantify the accuracy cost of their sparsity.

The Game of Cycles, invented by Francis Su, is a two-player game in which the players take turns drawing arrows on the edges of a plane graph, never creating a sink or a source. On a tree only the sink-source rule matters, and the player who makes the last move wins. Several authors conjectured that on a tree the second player wins exactly when the number of markable edges is even. We show that this parity conjecture is false, and we explain why. The explanation is a hidden game of Nim: a path segment that is blocked by an arrow at one end and free at the other behaves exactly like a nim heap whose size is its length. Combined with a calculus for cutting and gluing trees at vertices next to leaves, this shows that the conjecture fails as soon as a single tree has Grundy value at least 2. The smallest counterexamples have 15 vertices. Trees with Grundy values 2 and 4 first appear at 17 vertices, and every value up to 63 occurs, which answers a question of Fokkink and Zandee. We also refute a related conjecture of Zandee. We then look closely at spiders. The spiders S(2,3,z) violate the conjecture for every z >= 14. The Grundy values of S(1,2j,z) are given by an exact formula governed by binary carries. For 99 pairs (x,y), the value of S(x,y,z) is eventually the parity of z. On the positive side, the conjecture holds for all trees in which every thread has at most two edges, and this bound is sharp. Along the way we prove a twin-branch reduction, give an algorithm that is polynomial for spiders with a fixed number of legs, and collect the questions that we could not answer. The boldest asks whether every non-negative integer is the Grundy value of some tree.

To extend conventional model-level feature importance to economically meaningful portfolio outcomes and decisions, we propose a local first-order attribution-propagation framework that maps allocation-function feature exposures to local sensitivities of sequential portfolio performance metrics. We relate the propagated attributions to Shapley values defined directly for portfolio objectives and derive statistical inference for Sharpe-ratio attributions. The resulting attribution-guided feature-exposure intervention enables post-training adaptation, translating portfolio-metric explanations into out-of-sample decisions without retraining the underlying allocation model. We further introduce temporal stabilisation and cross-model averaging as complementary regularisation mechanisms. Empirically, the interventions yield statistically significant improvements in net Sharpe ratios across different model classes.

In deep hierarchies of adaptive mesh refinement, the update work that subcycling avoids is set mainly by the dimension of what is refined, not of the space. Subcycling (local time stepping) does less work than global stepping, advancing each level with the finest step, provided its extra coordination cost stays below an overhead budget $\beta=1-1/\Sid$ as a fraction of the global-stepping work. Here $\Sid$ is the ideal speedup that the cell counts give for equal update costs. When each level follows a feature of box-counting dimension $\delta$ and the counts grow geometrically, the budget of a code that advances every cell tends to $(r-1)/(r^{\delta+1}-1)$ for refinement ratio r. A point leaves a budget near one, while a surface in three dimensions leaves 1/7 at r=2 and 1/21 at r=4, values implied by the planar estimates of Dursi and Zingale. Published comparisons in discontinuous Galerkin and octree codes with local time stepping imply overheads of 0.1 to 5 percent of the work, below 1/7 and comparable with 1/21. In paired runs of one AMReX code on one core, a cost model fixed in advance and fitted on points and filled regions predicted the speedups of curves and surfaces with a median error of 7 percent (22 percent on the saving); post hoc, the update counts alone did as well except for points. The overhead, as defined here, was negative in all 17 configurations, but when computed from speedups like the published values, it ranged from -0.11 to 0.19, and no configuration came near break-even. When an update costs the same under both schedules, one profiled run can show that subcycling pays.

In this paper, it is proved that every sufficiently large odd integer $n$ can be represented as \begin{equation*} n=p_1^2+p_2^2+p_3^4+p_4^4+p_5^4+p_6^5+p_7^7, \end{equation*} where $p_1,\dots,p_7$ are prime variables. This result constitutes an enhancement upon a previous result of Andrade [1].

Single-step retrosynthesis is a one-to-many inverse problem, yet most models are trained and evaluated against a single recorded reactant set. Reference-based training gives no explicit positive signal for unrecorded alternatives, and exact-match evaluation rejects non-matching predictions regardless of chemical plausibility. We propose Retrosynthesis via Reinforcement Learning from Forward Feedback (RetroRLFF), which optimizes reactant generation using both reference agreement and forward consistency with the target product. Starting from a supervised decoder-only Transformer, RetroRLFF generates complete reactant candidates and uses a frozen forward reaction model to predict products. A sequence-level reward combines reference agreement and forward consistency while penalizing invalid outputs. Direct Advantage-Based Policy Optimization updates the policy without human preference annotations or a preference-trained reward model. On USPTO-50K, RetroRLFF outperforms all 14 baselines in candidate-level round-trip accuracy at k = 1, 3, 5, and 10. With approximately 50 million parameters, it achieves 90.1% top-1 round-trip accuracy, exceeding R-SMILES, the strongest competing baseline on this metric, by 8.5 percentage points. Compared with its supervised policy, round-trip accuracy increases from 83.1% to 90.1%, while exact-match accuracy is maintained at 57.9% versus 57.5%. In an anonymized expert assessment of 131 randomly selected test cases, organic synthesis experts prefer RetroRLFF over EditRetro in 67.9% of comparisons. These results support forward feedback as a training signal for improving forward consistency while retaining top-1 reference recovery. Expert assessment provides complementary evidence of synthetic feasibility on the selected cases, although neither forward consistency nor expert preference establishes experimental feasibility.

Denote by $\Pi_\gamma(x)$ the number of primes $p \leqslant x$ such that $[p^{1/\gamma}]$ is also a prime. In this paper, it is proved that the expected asymptotic formula \begin{equation*} \Pi_\gamma(x)=\frac{\gamma x}{(\log x)^2} (1+o(1)) \end{equation*} holds for $\gamma > 15/13$, which constitutes an improvement upon the previous result of Balog [2] who showed that the above asymptotic formula holds for $\gamma > 6/5$.

Linear-attention and state-space LLMs carry long context in a fixed-size recurrent state, and quantizing that state is the natural way to cut its cost during long decode. Unlike a weight tensor, the state is rewritten at every step, so a quantizer applied at each step sits inside the recurrence and its errors compound. INT4 that leaves synthetic recall perfectly intact at the start destroys it a thousand steps later. The mechanism is a feedback between the quantizer scale and the state it is derived from. Yoking that scale to a full-precision reference removes the resulting norm explosion entirely, yet recovers only 1.8 of the 5.4 nats lost, so numerical instability and functional degradation are separable failures. The remainder is resolution-dependent, and in our per-step setting every outlier-aware scheme we test loses to plain persistent scaling. Allocating bits across layers does help, but under article-disjoint splits a learned allocation collapses onto the trivial rule of protecting the first few layers. Run out to 32K, group-wise INT4 is worth no more than discarding the state. Contain the scale rather than locate outliers, and report the decode horizon at which a bit-width was certified.

A browser agent that works in its user's signed-in session can be steered by a two-sentence note on a page it reads into approving a third party's access to the user's account. The agent is a confused deputy: the session supplies the authority, the page designates the access request to approve or the webhook URL to register, and nothing at the point of action checks one against the other. The agent thereby supplies the approval click that a consent screen reserves for the account holder. We measure this failure on two authorization surfaces, an OAuth-style access grant and a webhook registration, with agents built on an open-source browser framework and models from two providers. Without a defense the unauthorized action completed in all 73 attack runs. An instruction telling the model that only the user's task authorizes a grant still left 7 of 10 consent attacks completing. We therefore move the check to where the action completes. The authority envelope gate has the service accept a request only when it matches the task's envelope, the client and account or the webhook URL that the user's task named, fixed before the agent starts. With the gate the agent still sent the request in every one of 70 attack runs, the service rejected each, and the action completed in every control run whose task named it. A service that receives the task's envelope should therefore check agent-driven authorization requests against it.

An approval for a deployment, a release, or an agent-issued command is recorded against one object: a workflow file, a script, a command line. The run that follows also reads other repository files, which decide what the deployment creates and which changes a policy allows, so an edit to one of them after approval passes any check on the approved object. Such edits are the common case. In the history of 20 public repositories, 296 of the 542 commits that change a file the run reads (54.6%) leave the approved file untouched, all of them ordinary development with no adversary involved. We demonstrate the consequence on two of those repositories: an edit outside the approved workflow adds a bucket-write policy to a deployed role, a one-line edit removes the human approval required for high-risk changes, and a check on the approved file accepts both. We define authority-set integrity: an approval is sound when it binds every repository file the authorized run is configured to read, and exact when it binds no other file. A binding over that set rejects both edits and re-requests a standing approval on about one commit in ten. The hard part is naming the set. Coding agents asked to produce the binding compute the digest correctly and bind different file sets from run to run, so a checker cannot take the set on the agent's word. It should compute the digest itself and draw the set from a source it can verify, such as the deployment tool's own record of its inputs or a manifest declared in the repository.

Trust calibration remains the dominant framing of AI-assisted decision making: the goal is to close the gap between perceived and actual trustworthiness of AI systems so that users rely on them appropriately. We argue that this approach, while useful for decision problems that are well-defined and clearly scoped, overly restricts what it means to make a decision with AI support. To overcome this limitation, we develop three dimensions of AI-assisted decision making. First, trusting AI is only one of several possible strategies for managing uncertainty. Second, trust calibration is often misapplied when AI models large-world decision problems, i.e., ill-defined situations where goals and states are only partially known or unknowable. Third, in such settings human-AI alignment requires addressing higher-order decision processes. We conclude by reflecting on the implications of our observations on the design of process-oriented human-AI coupled systems that jointly identify and negotiate uncertainty throughout the decision-making task.

We continue the study of weak universality for the fractional hyperbolic $\Phi^4_3$-model initiated by Tzvetkov, Wang, and the author (2023). In this work, we establish weak universality in a regime where the associated Gibbs measure is mutually singular with respect to the underlying Gaussian measure. We first investigate the weak convergence of the Gibbs measures associated with macroscopic models to the fractional $\Phi^4_3$-measure constructed by Tzvetkov, Wang, and the author (2023). We then obtain a structured representation for these Gibbs measures via the stochastic quantization method. Finally, we prove dynamical weak universality for the fractional hyperbolic $\Phi^4_3$-model by using an extended second order expansion and exploiting the invariance of the Gibbs measures.