Papers

We give a Seifert-form criterion for upper bounds on topological shaking numbers and prove that isotropic certificates lift under $(m,1)$-cabling.

We consider a model of collective choice where for each menu there is an agent who is accountable for the choice made. Specifically, we assume that two agents (individuals or selves) allocate choice tasks over different menus using an ownership rule: the owner of the decision over a menu picks what maximizes his own preference and is accountable for it. We characterize three distinct ownership rules under different (nested) choice environments.

As robotic teams tackle increasingly complex tasks in dynamic and unstructured environments, effective coordination requires agents to maintain accurate, aligned representations of their environment, teammates, and mission state. We argue that Mutual Awareness, Shared Situational Awareness, and Team Situational Awareness — three concepts widely invoked in the multi-robot systems literature — are not interchangeable: they form a containment hierarchy in which each type subsumes the previous in scope, and span a distribution spectrum from fully individualized understanding (MA) to fully uniform understanding (SSA), with TSA occupying a mixed position. We establish this through a two-dimensional taxonomy organized along the object of awareness and awareness distribution axes. Treating these terms as synonyms obscures the precise coordination requirements each imposes on a robotic system. A Search and Rescue case study with heterogeneous aerial and ground robots grounds each taxonomy position in concrete coordination requirements. These findings provide a conceptual foundation for principled specification, design, and comparison of collective awareness in multi-robot systems.

We study the reflexivity property of ideals in numerical semigroups. In particular, we characterize irreducible reflexive ideals and determine the Apéry set of a reflexive ideal. Moreover, we study how reflexivity allows us to characterize some classes of numerical semigroups and the interaction of reflexivity with the property of being a trace ideal.

A semantic decision engine such as Jev can return a valid answer and still miss a network deadline, select an infeasible action or leave the service unverified. We systematize 139 paper families by decision interface, execution path and check ownership. Fifty families claim that their engine fits a control loop or time budget, but only four support the claim with matched measurement. Across all 139, four report deadline attainment. The gap concentrates where the decision has no deterministic computation step. Those 72 families make 22 of the claims, none supported, and name a coverage owner in only two. Bounded tests under one event model show that each gap can reverse an admission verdict. A decision that meets a 10 s budget for every isolated request meets it for none once decisions queue ahead of replayed execution times. The same engine passes one coverage check and fails another. We derive a minimum reporting record, design rules and a research agenda for admitting decision engines to control loops.

We present deep, narrowband Gemini North/GMOS images of the Pa 30 nebula that reveal rich small-scale structure in the ejecta filaments. In [S II], the number of detected filaments increases by about an order of magnitude compared to previous studies. The imaging further reveals that the filaments are not smooth radial streaks, but instead are composed of cascades of knots or clumps. The images in [O III] yield the first confirmation that previously detected diffuse [O III] emission in fact originates from the same [S II] filaments. We measure a nebula center consistent with the position of the central star, indicating that the remnant has not received a large transverse kick. The 3$\sigma$ upper limit on the velocity of the stellar kick is $\lesssim$100 km/s. Cross-sectional profiles of the filaments in [S II] and [O III] show a central peak on top of a nebular background, the latter being likely due to diffuse emission or unresolved filaments. The median [S II] width of 0.7” is slightly broader than the 0.50” seeing, providing some evidence of partially resolved filaments and implying a characteristic knot diameter of ${\sim}10^{16}$ cm. The $\approx$1” widths measured in [O III] are consistent with the poorer seeing of the oxygen images. The discovery of this clumpy substructure provides a new observational constraint on models for the origin and evolution of the remarkable filamentary ejecta of Pa 30.

Spontaneous movement analysis in preterm infants relies increasingly on markerless pose estimation (PE) to derive clinically relevant motion biomarkers directly from video recordings. Training accurate infant PE models requires large sets of manually annotated keypoints, and human annotation is inherently prone to error. Noisy keypoints (i.e., keypoints mislocalized with respect to their true anatomical position) are especially problematic in this clinical setting, since they can propagate as artificial artifacts into the reconstructed joint trajectories. Building on the small-loss hypothesis and training-dynamics-based sample selection established in the noisy-label learning literature, we propose a novel framework for detecting noisy keypoint annotations. A hybrid convolutional-attention model is trained to predict the anatomical category of each keypoint from its spatial coordinates and local visual features; the resulting cross-entropy training dynamics are then used to derive per-keypoint descriptors, which are partitioned into clean and noisy subsets via unsupervised clustering. We validate the approach on NeoPose, a newly collected dataset of 65 hospitalized preterm infants, under two realistic noise scenarios (random positional perturbation and left-right swapping) across multiple noise levels. Results show that the proposed approach achieves an F1-score of up to 91.9% in noisy-keypoint detection. The framework further generalizes to the heterogeneous COCO benchmark, where filtering CE-detected noisy keypoints from the training set also yields measurable improvements (up to 7.4 AP points) in downstream pose estimation accuracy at moderate-to-high noise levels.

We prove the heuristically predicted lower bound for the number of rational points of height at most $Q$ lying within $\epsilon/Q$ of a fixed analytic nondegenerate manifold in $\mathbb{R}^n$, provided that $\epsilon \asymp Q^{-\tau}$ for some $\tau \leq 3/(2m+1)$, where $m$ is the codimension of the manifold. Our result establishes the lower bound well beyond the previously conjectured range $\tau \leq 1/m$, and improves upon a recent result of Schindler, Srivastava, and Technau, who established the same lower bound for $\tau \leq 3/(2n-1)$.

Data imbalance is pervasive in machine learning, from rare words and anomalies to underrepresented patterns in heterogeneous or cross-tabulated data. We study idealized optimizers geometries in continuous time to model small-step training in deep learning. We assume that the source of imbalance is unobserved: the optimizer has only access to the aggregate training loss ignoring the exact contributions of the majority and minority groups. In this setting, we characterize a region where majority losses are optimized regardless of the admissible minority structure. We derive explicit equations of this zone and bounds on the time needed to leave it. These bounds exhibit a milder dependence on minority amplitude for sign, spectral, and Newton descent than for Euclidean gradient descent. Experiments with AdamW and Muon suggest similar advantages over SGD across language, tabular, and image tasks.

Federated Learning (FL) enables collaborative training of models across institutions without centralizing sensitive data, making it well-suited for privacy-concerned applications, such as medical imaging. To protect FL model updates during secure aggregation, additive masking is commonly employed. However, its underlying classical key establishment is only computationally secure. On the other hand, physics-based Information-Theoretically Secure (ITS) key exchange introduces practical constraints: finite key generation rates and time-limited storage severely limit throughput and sustained training of uncompressed models. In this work, we address this bottleneck by developing an FL framework that integrates frozen backbones, knowledge distillation, and quantization. These techniques reduce communication payload and, consequently, key material consumption. Moving beyond simulation, we benchmark this framework on a real physics-based key distribution testbed involving a chest X-ray classification application. Our results show that key usage can be reduced by $\sim$35$\times$ while maintaining predictive accuracy. This prevents buffer depletion and key expiration, enabling sustainable FL training under physical key generation constraints.

Motivated by Gal's conjecture, Ferroni and Higashitani conjectured that the $h^*$-polynomial of any Gorenstein lattice polytope admitting a quadratic triangulation is $\gamma$-positive. Together with conjectures predicting quadratic properties of toric ideals of smooth lattice polytopes, this suggests that smooth Gorenstein lattice polytopes should have $\gamma$-positive $h^*$-polynomials. In this paper, we prove that the Ehrhart polynomial of the polar dual of every pseudo-symmetric simplicial reflexive polytope is magic positive. For pseudo-symmetric smooth Fano polytopes, we prove the stronger statement that all magic coefficients are strictly positive. Consequently, for every pseudo-symmetric simplicial reflexive polytope, its polar dual is Ehrhart positive and has a real-rooted and $\gamma$-positive $h^*$-polynomial. We also prove that the Ehrhart polynomial of the polar dual of the symmetric edge polytope of every cycle is magic positive. This gives an affirmative answer to a question of Konoike, who had previously proved partial positivity results for this family.

Let $\mathcal H$ be the space of support functions of centrally symmetric, strictly convex, compact planar bodies whose boundary is a $C^1$ curve, endowed with the $C^1$ topology. We prove that for a residual subset of $\mathcal H$ the outer billiard maps about the associated bodies admit unbounded orbits escaping to infinity. In particular, this residual set includes support functions arbitrarily $C^1$-close to those of disks or ellipses. This provides an affirmative answer, in the strictly convex $C^1$ setting, to a famous question of Moser and Neumann concerning the existence of unbounded outer-billiard orbits. The key ingredient is a rigidity theorem: if $h\in\mathcal H$ has a purely singular radius-of-curvature measure, then every continuous invariant tangent graph consists entirely of periodic points. We then show that for a generic table in $\mathcal H$ these periodic invariant graphs are absent, allowing us to construct escaping orbits via Mather's diffusing mechanism in a Birkhoff region of instability.

We derive a quantum master equation in Lindblad form for the open quantum Rabi model in the perturbative deep strong coupling regime, where the spectrum is close to degenerate and harmonic. The Lindblad form is obtained by combining secular and singular-coupling approximations, working in a Schrieffer-Wolff transformed frame. We benchmark our equation against a Bloch-Redfield one, analyzing the time-evolution and steady state properties of several observables and find excellent agreement. Analytical results are obtained in limiting cases.

Motivated by the peculiar features of the trans-Neptunian object (TNO) Máni and the discovery of ring systems around Centaurs and trans-Neptunian bodies, we investigate the stability of particles around a small irregular body hosting a deep equatorial crater. This study is the third contribution in a sequence devoted to the dynamics around non-spherically symmetric bodies. Using Máni as a reference model, whose crater depth exceeds 10% of its radius, we map the system stability through complementary methods: Poincaré surfaces of section (PSS), survival maps, and the finite-time Lyapunov exponent (FTLE). In the nominal case, the $1\!:\!1$, $2\!:\!1$, $3\!:\!1$, and $4\!:\!1$ spin-orbit resonances (SORs) are consistently identified by all techniques. The prominent $3\!:\!1$ SOR exhibits a bifurcated structure at high eccentricities, matching structural transitions observed at lower Jacobi constant values in the PSSs. Increasing the rotation rate ($\lambda$) and crater mass ratio ($\mu$) enlarges resonance widths and promotes overlap, making the $2\!:\!1$ and $4\!:\!1$ SORs progressively dominant. Lower rotation rates allow stable trajectories to persist at higher eccentricities, whereas the $1\!:\!1$ SOR is highly sensitive to stronger perturbations and disappears in the most extreme cases. In contrast to mass-anomaly models, which can clear the region interior to the $2\!:\!1$ SOR, the crater configuration considered here preserves stable regions in this vicinity, suggesting alternative scenarios for the formation and maintenance of debris structures around irregular minor bodies.

Training-free model merging aims to combine multiple fine-tuned models into a single model without further optimization on labeled data. Yet, in transformers, independently merging individual layers can affect a shared attention computation because the query-key and value-output operators depend on composed matrices, overlooking the functional structure. Moreover, when merging earlier components, downstream components receive different activations than they do in the original model, thus, the merged and original execution paths no longer match. In this paper, we introduce Sequential Local Operator Alignment, a training-free method that merges transformers along the execution path of the partially merged model. Our method uses calibration data to estimate the local behavior of each functional component, aligns operators sequentially under the intermediate activation of the partially merged model, and subsequently factorizes the merged operators back into valid transformer parameters. We empirically show that this sequential step reduces error accumulation across layers. Furthermore, the proposed operator factorization step enables rank expansion, providing a principled mechanism for increasing multi-task capacity. We demonstrate that our approach generalizes across modalities, model scales, and varying numbers of tasks, from CLIP and RoBERTa to billion-parameter LLMs, and further extends naturally to the merging of LoRA-fine-tuned models. The results indicate improvements over strong merging baselines without requiring rank expansion, while optional expansion provides a further accuracy-inference-cost trade-off. Project link: https://akansh12.github.io/SLOA-Merge/

The performance of stationary iterative methods is memory-bound, due to the low arithmetic intensity. So, we propose a mixed-precision technique to reduce the amount of data movement in matrix-splitting iterative methods. We demonstrate both theoretically and experimentally that this technique will generally converge at a similar rate as an exact-precision iteration, depending on the precision used and the conditioning of the $M$ matrix. Furthermore, we demonstrate that iterative refinement can be used to refine the solution to full double-precision accuracy. Using this approach, we mixed half and double precision to achieve an average speedup over uniform double precision of $1.60\times$ for scalar and block Jacobi and $1.25\times$ for scalar and block Gauss-Seidel. Furthermore, we reduced the precision in the SSOR iteration used by OVERFLOW, a NASA code for compressible fluid dynamics simulations, and achieved a $1.14\times$ speedup to the overall application.

Thinking-enabled vision-language models (VLMs) report ever-higher accuracy on spatial benchmarks, yet final-answer scores cannot reveal whether a correct prediction reflects faithful spatial reasoning or a linguistic shortcut. We introduce SpatialChain, a dataset of 28,350 training and 899 test examples pairing spatially-oriented GQA questions with scene-graph-grounded reasoning chains, retained only when the generated answer matches the symbolic ground truth, and a two-axis evaluation combining objective chain-overlap metrics with a scene-graph-aware LLM judge that scores faithfulness and completeness independently of the final answer. Applied to nine thinking-enabled VLMs, the protocol surfaces three findings invisible to standard accuracy: (i) four of nine models achieve $\geq$79% VQA accuracy while exhibiting shortcut rates above 39%, i.e., correct answers whose reasoning the judge marks as unfaithful; (ii) chain quality significantly predicts answer correctness for seven of nine models, but the two exceptions (Claude Sonnet 4.6, InternVL3.5-8B) reveal qualitatively distinct failure modes, terse output vs. verbose-decorative reasoning, that benchmark accuracy alone conflates; (iii) SFT on SpatialChain improves Qwen3-VL-8B by +6.2 pp in-domain and reduces its shortcut rate to 22%, while a stylistic specialization effect on external benchmarks motivates replay-augmented training as mitigation. The faithfulness judge is validated against 198 human-annotated items, where judge-human agreement matches human-human agreement, and against a second judge from a different provider, which preserves the model ranking ($\rho$ = 0.88). Data, generation scripts, and evaluation code are released at https://github.com/spatialchain/SpatialChainBenchmark.

Trade-sign errors can change measured trading costs even when classification accuracy is high. We validate the side of Polymarket's public trade prints against the taker leg of each print's on-chain settlement. On twelve selected days between April and August 2026, spanning both exchange generations, 92.1% to 100.0% of prints match a settled taker leg, with exact side and token agreement on all 24.5 million matched pairs. Mint-and-merge settlement makes that taker leg essential: pooling maker and taker legs changes the measured buy share. Signing the full cached tape before settlement selection yields 16.6 million prints signed by every rule; equal-day balanced accuracy is 0.942 for Lee-Ready, 0.768 for the tick test and 0.670 for retrospective bulk volume classification. On 16.4 million identical eligible fills, Lee-Ready raises effective spread by 0.429 cents per share under equal-fill weights; its realised-spread difference is -0.209 cents. Under share-volume weights, taker five-minute midpoint impact is 0.689 cents, while tick and bulk classifications give -0.374 and -0.119 cents. That aggregate sign reversal disappears when tied print rows are excluded. Distortion depends on error-weighted signed outcomes, sample selection and weighting. Receipt-time ordering and unobserved future-quote age limit these delivered-quote accounting quantities; they do not identify causal impact or private information. Supporting venue and collector analyses provide descriptive diagnostics.

Agentic systems increasingly coordinate molecular-design tools, but it is unclear which layer of the stack limits outcomes on real projects. We developed MAGI, an open modular agent that authors objectives, launches and monitors optimization, interprets structure–activity relationships, and revises its strategy accordingly. MAGI generates molecules either directly through the LLM or by delegating to REINVENT 4, with scoring services interchangeable behind a common contract. We tested it across nine retrospective lead-optimization campaigns from three pharmaceutical companies, replayed under fixed temporal cutoffs. Both routes produced valid structures: LLM proposals stayed closer to local chemistry and reached comparable or higher primary activity in fewer operations, whereas REINVENT explored broader chemical space. Whether a campaign met its objective depended on the predictive models, not on the generation route: attainment followed model accuracy on the chemistry proposed, dropping once that chemistry moved outside the model's applicability domain. Separately, a blinded evaluation asked whether the MAGI's output could pass as expert work: chemists were not able to discriminate agentic proposals from held-out compounds, and judged the SAR reasoning broadly plausible yet incomplete. Together, these results position MAGI as a coordination layer pluggable into existing computational chemistry workflows. The ceiling on real projects, however, remains currently set by scorer applicability rather than by tool orchestration.

Traditional technosignature and transient searches commonly operate on beamformed time–frequency products. Interferometric imaging adds spatial context and allows time-domain searches to be performed across many image pixels simultaneously. We report the development and testing of a GPU-accelerated interferometric imaging and image-domain dispersion-measure (DM) search pipeline for Allen Telescope Array (ATA) post-correlation UVH5 visibility data, integrated with the CyberEther streaming framework to replay recorded visibility data and work toward real-time operation. The pipeline forms Stokes-I dirty images from correlated visibilities, incorporates Inter-Quartile Range Mitigation (IQRM) flags into the imaging weights, images 48 frequency subbands spanning 287.5\,MHz, subtracts a temporal mean over the full observation from each subband and pixel, applies IQRM-informed subband masking, and performs a blind trial-DM search using a short-history image ring buffer. On a controlled 10-minute three-spectral-window test observation containing a periodic dispersed pulsed injection (DM\,$\approx$\,150\,pc\,cm$^{-3}$), the pipeline recovers the injected source at the phase centre with a best-fit DM\,$=$\,150\,pc\,cm$^{-3}$, with individual dispersed pulses reaching a median image-plane S/N of $\approx$52. When integrated into CyberEther, the core processing requires approximately 63\,ms per integration compared with a native integration time of approximately 98\,ms, demonstrating that the core science-processing operations can be completed within the available integration time. The present implementation operates on recorded visibility data and relies on a temporal mean and MAD noise estimate precomputed over the full observation. For live operation, these quantities will instead need to be estimated from data available up to the current integration.

Machine-learned interatomic potentials extend atomistic simulations beyond the length- and timescales accessible to electronic-structure methods. However, the computational cost of equivariant architectures limits the local correlations they can represent in practice and therefore their achievable accuracy. Here we introduce FlashCart, which makes higher-order correlations affordable by combining generated GPU kernels with an architecture that recursively builds equivariant features and compresses them to a fixed width at each step. We express tensor products in independent Cartesian components and symbolically simplify them and their derivatives, producing fused kernels that often outperform optimized spherical counterparts. We then show that increasing correlation order improves accuracy more efficiently than increasing width, depth, or tensor rank. On SPICE-MACE-OFF, FlashCart models advance the measured accuracy-efficiency frontier: a model with $5.6$ million parameters achieves lower energy and force errors and $10\times$ faster inference than a transformer with $189$ million parameters.

We consider nonlocal divergence-form operators of the type $$PV\int_{\mathbb{R}^n}(u(x)-u(y))K(x, y) dy=0\quad \text{in} \; B_2,$$ where the kernel $K$ is symmetric ($K(x, y) = K(y, x)$). We first show that there exists a kernel satisfying the conditions of \cite[Open Question 2.1]{FRRO24} for which this problem admits a bounded discontinuous weak solution, answering that question negatively. We then impose the stronger one-sided lower bound suggested in \cite{CS20,IS20}, together with an $L^p$ bound of $K$ over annuli, and prove a coercivity estimate and interior Hölder regularity of weak solutions. In particular, this establishes the coercivity conjecture of \cite{CS20,IS20} under the additional $L^p$ hypothesis for $p>1$.

Underwater Wireless Optical Communications (UWOC) provide essential high data rates for Autonomous Underwater Vehicles (AUVs), but reliable connectivity is critically affected by transmitter-receiver misalignment. This work addresses the beam pointing problem for a moving AUV subject to unknown ocean currents through a Deep Reinforcement Learning (DRL) framework. We develop a comprehensive 3D UWOC channel model incorporating depth-dependent attenuation, turbulence, and a discrete-ray method to accurately quantify geometric and misalignment losses. The resulting agent jointly optimizes beam steering and divergence angles, learning a policy that prioritizes continuous link maintenance. Evaluated using real oceanographic data, the framework's performance is assessed via the excess outage metric, which isolates outages occurring exclusively due to pointing errors. Relative to perfect alignment between nodes, the proposed method bounds this metric to 8.5% under ocean current-free tracking conditions and limits it to 16.2% when subjected to current-induced drift. The findings obtained in this work confirms that DRL-enabled beam control is capable of adaptive tracking and mitigating link outages in dynamic underwater environments.

As agents take on long-horizon tasks, users shift from making individual decisions to overseeing autonomous execution. Yet the volume of agent activity and the fragmentation of supporting evidence make it difficult to determine which decisions warrant user verification. We study monitors that identify consequential decisions and locate evidence to help users assess their implications. We introduce AgentMonBench, a software-engineering benchmark comprising three subsets that cover two complementary dimensions: alignment between requirements and behavior, and awareness of consequential autonomous decisions for verification. To support these judgments, we propose the Evidence-Grounded Behavior Graph (EBG), a training-free method that groups source-linked evidence into behaviors and organizes their relationships into a graph. EBG presents task-oriented views of this graph to help monitors interpret behavior in context. Experiments across eight models show that EBG improves decision identification and evidence localization in most settings compared with direct access to the original context. Further experiments show that EBG's evidence-localization gains persist across input scales and hyperparameter settings, while real-world applications illustrate its practical value for human oversight.

We're often in a situation where we have models of measles transmission that are stuck at a coarse population scale. This paper is about increasing their resolution or, said differently, creating consistent models for the population's subcommunities. We pay special attention to the fact that even if the full population is isolated, subcommunities are open to measles importations and related consequences of population movement. It turns out that the resolution issue can be productively framed as a constrained optimization problem, where the constraint is aggregation to the coarse model. That mathematical scaffolding allows us to make epidemiologically motivated approximations concentrated at the large population scale, where they're more valid, which leaves the estimates at the fine subcommunity scale atypically unstructured. We develop the idea in the context of the pre-vaccination-era 60 city UK dataset, building transmission models for all 60 cities. We find that they have intuitive seasonality, volatility, and importation elements, but that they depend on nontrivial dynamics in their case reporting probabilities. Potential interpretations of those surveillance processes are discussed in some detail, and we also describe how they influence inference on the balance between competing cryptic transmission and transient elimination dynamics.

We consider the stability of multi-step reasoning processes, which have extensive applications in language models, including chain-of-thought and algorithmic reasoning. While longer sequences of reasoning can improve a model's generation capability at test time, the errors due to intermediate reasoning steps can accumulate in autoregressive generation, and thus grow substantially at the end. In this paper, we ask: What are the key factors determining the stability of multi-step reasoning? First, we show an inference error bound governed by the product of spectral norms of the Jacobians taken through the input space across generation steps. This product can be viewed as an error amplification factor, which could scale exponentially with the number of reasoning steps, serving as a quantitative measure of reasoning stability. Second, we analyze this measure in transformer models trained to predict simple tasks like linear and quadratic functions. We theoretically prove that the transformer model converges to a solution where the stability measure decays, thus yielding nearly zero inference loss over (arbitrarily) long steps. Finally, the stability analysis leads to several algorithmic implications for controlling the stability, through (i) chain-of-thought length compression that reduces the sensitivity of each step, and (ii) quantization-aware training that regularizes the input Jacobian norms. We validate the proposed algorithms by fine-tuning language models on graph-algorithmic reasoning tasks and symbolic state-tracking tasks. Across seven evaluations, our algorithms improve over baseline comparisons by 3.5% on average, and by 8.2% for longer-length inputs. Ablation analysis validates that the stability measure is drastically reduced by 3-8$\times$, confirming the regularization effect on the spectral norms of the (input space) Jacobians.

The Davey-Stewartson (DS) system is a canonical model for a weakly nonlinear wave packet in two spatial dimensions that is resonantly coupled to the slowly varying mean flow it generates, and as such it governs modulated wave trains in settings as different as finite-depth water waves, quadratic optical media and magnetic films. Here we develop the Whitham modulation theory for the DS system and use it to study the stability of its periodic traveling wave solutions. Specifically: 1. We perform a detailed study of the parametric dependence of the periodic solutions of all four variants of the DS system, including their harmonic and soliton limits. 2. We present the formulation of Whitham modulation theory for the DS system and write down the resulting Whitham modulation equations for all four variants of the DS system. 3. We use the resulting modulation equations to study the stability of the periodic traveling wave solutions of all four variants of the DS system. 4. We validate the theoretical predictions by comparing them with a direct linearization of the DS system as well as with the direct numerical simulations of the DS system, showing excellent agreement. The results indicate that the periodic solutions of the defocusing DSII system are linearly stable, whereas those of all other variants of the DS system are unstable. The calculations also evidence many structural features (non-evolutionary modulation equations, constraints on the admissible initial data, and auxiliary mean-field constants absent from the traveling wave solutions yet indispensable to the modulation system) are expected to recur in any two-dimensional envelope equation with mean-field coupling.

We study semi-Clifford and generalized semi-Clifford structures in the Clifford hierarchy as a function of hierarchy level $k$ and qubit number $n$. We show that $\mathcal{C}_k(n)$ is semi-Clifford if and only if $k\le2$, $n\le2$, or $k=3$ and $n\le6$. We also establish that $\mathcal{C}_k(n)$ is generalized semi-Clifford when $k\le4$ or $n\le3$ and construct counterexamples when $k,n \geq 5$. For $n=4$ and $k\ge5$, we show that every gate defined over $\mathbb{Q}(i)$ up to a scalar is generalized semi-Clifford, reduce the general case to a single level, and propose a strategy to prove our conjecture that $\mathcal{C}_k(n)$ is generalized semi-Clifford if and only if $k\le4$ or $n\le4$. Lastly, we go beyond this structure by introducing $n_c$-generalized semi-Clifford gates, which we show are exactly the gates of the form $\sum_x|\pi(x)\rangle\langle x|\otimes V_x$ up to Clifford gates on both sides, where $\pi$ permutes the computational basis states of $n_c$ control qubits. We conjecture that for $k\ge3$ every gate in $\mathcal{C}_k(n)$ has this form for some $n_c\ge1$ with every $V_x\in\mathcal{C}_{k-3}(n-n_c)$, refining the conjecture of Zeng, Chen, and Chuang.

Tool-using language-model agents are vulnerable to indirect prompt injection because they must act on untrusted external content. Existing training-time defenses can reduce attack success rates, but often at the cost of general capabilities. We show that training-based defenses induce substantial drift in the model's output distribution, altering its behavior even in benign settings and providing a potential mechanism for utility degradation. We further identify a failure mode of these defenses: On benign tool-use tasks, the model refrains from a step needed to finish an authorized task, particularly when that step is indicated by a tool output. To address these limitations, we introduce RAISED (Robust Attack Invariance through Self-Distillation), a training framework that combines self-generation and self-distillation. The model first generates its own tool-use scenarios, with an emphasis on cases where task completion requires acting on legitimate guidance from tool outputs. Then, through self-distillation, the student is trained to match the teacher's clean-context behavior on both clean and injected variants of the same trajectory. RAISED substantially reduces the attack success rate of prompt injections in tool responses while, unlike prior training-based defenses, preserving utility on both agentic and general-purpose benchmarks.

Swarm robotics presents a robust and cost-effective paradigm for advanced automation in complex, dynamic environments, such as those encountered in search and rescue or environmental monitoring. A fundamental challenge for this field is the data-driven design of decentralized controllers capable of generating emergent collective behaviors. This paper proposes a novel, AI-driven hybrid methodology for the automatic synthesis of swarm robotic controllers for autonomous visual navigation. This approach synergistically combines multi-agent reinforcement learning with neuro-evolutionary strategies, specifically leveraging implementations of the cross-entropy method and the covariance matrix adaptation evolution strategy to optimize a pre-trained individual navigation policy. The underlying deep architecture is engineered for low-cost, resource-constrained platforms, utilizing a compact neural network that relies exclusively on monocular camera imagery. This vision-based design emphasizes computational and energy efficiency, a critical requirement for practical swarm deployments. Experiments, performed in a high-fidelity physics simulator, demonstrate that the resulting controllers enable robust and scalable collective exploration of diverse indoor environments. The controller trained using our cross-entropy method achieves superior exploration coverage, visiting 36.20% more regions compared to the covariance matrix adaptation evolution strategy. Critically, our best vision-based policy achieves exploration performance statistically comparable to traditional methods relying on more expensive distance sensors, while delivering a significant 31.40% average reduction in energy consumption. These findings validate an effective and economically viable autonomous control system, establishing a path for deploying highly efficient collective intelligence in real-world engineering applications.