Papers

We present a machine-learning pipeline for determining stellar parameters and chemical abundances from spectra observed by the Dark Energy Spectroscopic Instrument (DESI). Building on the model-driven Payne framework, we train an artificial neural network on ~370,000 synthetic spectra spanning FGK stars, and fit the network directly to the flux-calibrated, un-normalised spectral energy distribution (SED) of each star, rather than to a continuum-normalised spectrum as done by DESI's official Stellar Parameter (SP) pipeline. Internal accuracy tests show a median interpolation error of less than 0.3% for 90% of a synthetic verification sample, and the full fitting workflow recovers input labels to high accuracy even at low signal-to-noise ratio (S/N). Validating our method on cross-matched samples of 6719 APOGEE and 3455 GALAH stars observed by DESI with S/N > 20, we recover Teff and logg with smaller systematic offsets than the DESI SP pipeline, an improvement we attribute to fitting the full SED shape rather than a normalised spectrum. We further recover 12 elemental abundances (Na, Mg, Al, Si, Ca, Ti, V, Cr, Mn, Ni, Ba, and Y) to an accuracy that matches or exceeds SP where a comparison is possible, and provide four abundances, Mn, V, Ba, and Y, that SP does not report at all. Applying this pipeline to the DESI Data Release 1 stellar sample, we deliver a catalogue of stellar parameters and abundances for 3.2 million stars.

Exclusive $\gamma\gamma\to J/\psi+\gamma$ production is studied in the color-singlet channel at leading order in the heavy-quark velocity. The conventional next-to-leading-order (NLO) result $B+V$, comprising Born production and its interference with the renormalized one-loop amplitude, is compared with $B+V+Q$, where $Q$ retains the complete one-loop square. At photon-photon energies $W=80~\mathrm{GeV}$ and $160~\mathrm{GeV}$, the conventional spectrum becomes negative over finite high-$p_T$ intervals already at renormalization scale $\mu_R=W$, whereas the complete square remains non-negative. In contrast, the total partonic cross section exceeds Born at the larger energies in the energy scan, owing to positive virtual contributions from other scattering directions. For $p$-$p$ collisions at $14~\mathrm{TeV}$ and $Pb$-$Pb$ collisions at $\sqrt{s_{NN}}=5.52~\mathrm{TeV}$, $Q$ raises the central integrated ultraperipheral rates by $11.6\%$–$18.4\%$. Their absolute scale widths over $\mu_R=\{W/2,W,2W\}$ decrease by $36\%$–$67\%$. Retaining the complete one-loop square changes both the predicted integrated rates and the shapes of the differential distributions.

LLM-based agents are increasingly capable of generating complex 3D structures, with the potential to reshape how objects are designed and realized in the physical world. Yet, producing elegant geometry is fundamentally different from producing objects that can be built and perform their intended functions. Existing evaluations largely focus on geometric quality while overlooking physical realizability. We introduce LMBuild, a benchmark for evaluating LLM agents on generating buildable and functional structures. LMBuild represents generated objects as assembled structures comprising part decompositions, joints, materials, and sequences. To support reproducible evaluation, we provide a unified framework consisting of: (1) an interactive environment in which agents can use tools to retrieve, create, and place components to construct objects; (2) a curated benchmark that repurposes established CAD datasets and augments them with knowledge from Wikipedia; and (3) a evaluation framework covering structural soundness, functional affordance, design quality, and physical realization. Evaluations across 30 systems reveal several intriguing findings: (a) Soundness and alignment are no longer the primary bottlenecks for frontier closed-source models, while functional affordance and physical operability remain substantially more challenging; (b) stronger models more effectively create new components, whereas weaker models tend to rely on retrieval; and (c) providing functional specifications substantially improves part completeness, kinematics, and physical operability. These results show that generating real-world structures requires deeper reasoning about functional affordances, mechanics, and designing and creating novel components. We expect LMBuild to provide a foundation for measuring progress and incentivizing research toward agents that generate buildable and functional structures.

Sparse causal discovery calls for methods that exploit graph structure without estimating high-dimensional densities. We introduce Fisher Information Completion Search (FiCS), a source-first algorithm for additive noise models that uses one local Fisher score for both ordering and parent selection. Under regularity and nonconstant-parent conditions, we prove that a node's local Fisher information equals the noise Fisher information exactly when the conditioning set contains all parents, provided that it contains no descendants. This Fisher parent completion identifies the parent set as the unique minimal Fisher completion. With a maximum conditioning set size $q$ at least the maximum indegree $d$, population FiCS queries marginals of at most $q+1$ variables and recovers the true directed acyclic graph under a positive ordering margin. Bounded conditioning also has a population advantage: reducing $q$ toward $d$ cannot decrease, and can strictly increase, the ordering margin. A growing non-Gaussian family separates local Fisher selection from conditional-variance and leaf-first Fisher ordering. For the regularized kernel Stein estimator, we establish high-dimensional DAG consistency under $q\{1+\log(p/q)\}+\log p=o(n)$, uniform Fisher separation, local approximation, and compatible ridge and parent penalty parameters. Experiments show the strongest gains when $n$ is small relative to $p$, quantify the effect of the conditioning size, and demonstrate competitive reference-graph recovery on three real-data benchmarks.

We investigate Sb square net-based Dirac semimetallic ternary antimonides La$T$Sb$_2$ ($T$ = Cu, Ag) using magnetotransport and photoelectron spectroscopic studies, complemented by density functional theory (DFT) based ab initio calculations. Our results show that both compounds exhibit a positive temperature coefficient of resistivity, linear magnetoresistance (MR), and a deviation from Fermi liquid behaviour at low temperatures (2-30 K). But only $T$ = Ag compound exhibit signature of charge density wave (CDW) phenomena and the results of its temperature dependent MR data suggest that single-band semiclassical transport is not sufficient to understand the transport behaviour. $\text{DFT}+U$ studies show that in both samples, an on-site Coulomb interaction ($U$) for Cu 3$d$ and Ag 4$d$ electrons, in the presence of spin-orbit coupling (SOC) is required to reproduce experimental valence band spectra. Sb 3$d$, 4$d$ core-level spectra combined with $\text{DFT}+U$ calculations and La 3$d$ spectra confirm the presence and effects of inequivalent Sb sites for both the samples. In contrast to the $T$ = Cu compound, which follows expected temperature-dependent core-level sharpening, the $T$ = Ag compound exhibits an anomalous low-temperature broadening in the CDW phase. The analysis of Sb 3$d$ spectra suggests Sb square nets are linked to CDW phenomena in the $T$ = Ag compound. Temperature-dependent ultraviolet photoemission spectroscopic studies on $T$ = Ag show a small decrement in spectral DOS at the $\epsilon_F$ for the temperature below the CDW transition temperature. These core-level studies provide a valuable spectroscopic benchmark for comparing CDW and non-CDW systems and clarifying the role of local electronic environments in CDW formation.

Wireless foundation models learn representations from unlabeled radio signals for reuse across downstream tasks. Scaling model capacity is a common strategy for learning richer representations and improving downstream performance. However, its gains are less consistent in wireless self-supervised learning when pretraining data are limited. We investigate objective diversity as an alternative scaling axis: different self-supervised objectives emphasize different signal properties, and combining their representations can preserve more information to enable diverse tasks. We develop a fusion framework that combines frozen representations from independent encoders trained through reconstructive, predictive, and contrastive learning. This provides a reference for the benefits of diversity, but requires the maintenance of multiple encoders. To retain these benefits within the parameter budget of a standard single-objective encoder, we introduce a jointly trained multi-branch architecture with a shared trunk and objective-specific branches. We pretrain on a heterogeneous corpus of spectrogram and channel state information data and evaluate six downstream tasks that span communication, sensing, and positioning. At an equal output embedding dimension, fusion outperforms the evaluated single-objective encoders on all six tasks while using roughly one-third of their parameters. The multi-branch architecture retains much of the fusion benefit within a single-encoder parameter budget. Representation analyses indicate complementary contributions across objectives, with much of the added benefit retained in components orthogonal to the reconstruction representation subspace. These findings support objective diversity as an effective strategy for scaling wireless foundation models.

One-way local operations and classical communication (LOCC) can fail to distinguish four orthogonal maximally entangled states in every local dimension $d\ge4$. We show that every set of $k$ pairwise orthogonal maximally entangled states in $\mathbb C^d\otimes\mathbb C^d$ is perfectly distinguishable by an $A\to B\to A$ protocol whenever $d\ge Ck^4[\log(2k)]^\nu$, for universal constants $C,\nu>0$. A single feedback message therefore raises the number of candidates that can always be distinguished from a constant to $\Omega\!\left(d^{1/4}/(\log d)^{\nu/4}\right)$, establishing a polynomial separation between one-way and two-way LOCC. In our protocol, Alice preserves exact orthogonality while reducing overlaps between Bob's conditional subspaces. Bob reduces the candidates to a singleton or an orthogonal pair and refines his outcome so that Alice can complete the discrimination. As a corollary, nine copies suffice for perfect two-way LOCC discrimination of any orthogonal maximally entangled set in all sufficiently large local dimensions.

Enterprise agents should improve from delayed feedback without allowing every correction to rewrite system behavior. We study continual harness learning for corpus-level spreadsheet question answering. Building on FiCo (Find-then-Compute), a static retrieval-and-execution backbone, we introduce VIGIL (Verifier-Informed Gated Improvement Loop). Within a question, VIGIL verifies and repairs diversely prompted Structured Query Language (SQL) candidates. Across episodes, delayed labels update only a contract calibrator and query/result-column selector. The base model, prompts, retriever, and recorded candidate pool remain fixed in the continual-learning protocol. With the gold workbook and expected type supplied, the ungated and dual-gated full-replay variants reach 82.4% and 82.0% forward accuracy over 79 documents, from a 75.8% static baseline. The dual gate has the larger retrospective gain (2.7 versus 2.3 points), and its 6.3-point forward gain has a 95% t-interval of 5.6-6.9. In a separate stricter split that excludes 16 documents and 380 questions from fitting and online promotion, the accuracy-only gate raises mean held-out accuracy across ten final harnesses from 80.3% to 86.7%. Calibrator-only adaptation gains 5.9 points, close to the combined 6.4-point gain. Yet three of 26 gate-approved updates reduce held-out accuracy relative to their incumbents, so replay-buffer non-regression does not imply held-out non-regression. MiMoTable and external-task case studies test within-task verification and reuse the same promote-or-retain discipline. Overall, the results support bounded, auditable harness adaptation while revealing where finite replay gates fail to generalize beyond their promotion buffers.

Distributed Energy Resource (DER) environments rely on network communication protocols to coordinate control commands, measurements, and device states across edge assets and cloud systems. Edge anomaly detection systems (ADS) monitor this traffic to identify deviations from normal communication behavior, flagging suspicious flows for further investigation. When the ADS flags abnormal network traffic, a single attack label is often insufficient for operational response: the label reports the detector's selected class but does not expose alternative threat interpretations that may warrant investigation. This paper presents Cybersecurity Threat Reasoning with Explainable Artificial Intelligence (CyTReX), an evidence-grounded threat reasoning framework for DER security that transforms network-level anomaly alerts into ranked, analyst-facing threat hypotheses designed to support Security Operations Center (SOC) triage and investigation. CyTReX constrains large language model (LLM) reasoning through a structured evidence packet, defined as a consolidated record of detection outputs, model explanations, and cyber threat intelligence (CTI) context. The evidence packet integrates edge-layer anomaly detection evidence, cloud reasoning layer attack interpretation, Shapley Additive Explanations (SHAP) network-feature attributions, surrogate decision rules, and Model Context Protocol (MCP)-enabled CTI enrichment. This ensures that every ranked hypothesis and attack-tree branch is traceable to explicit evidence rather than free-form LLM inference, and that incomplete or conflicting evidence is communicated rather than suppressed. Evaluation across five configurations shows that additional reasoning components improve hypothesis specificity, evidence traceability, and analytical grounding, with the complete pipeline providing the richest evidence-grounded reasoning context.

We develop an amortized, grid-free implementation of continuous Langevin dynamics based policy-value iteration for entropy-regularized, infinite-horizon relaxed stochastic control problems. The improvement rate of the exact iteration is a discounted aggregate of relative Fisher information between the policy and the Gibbs law of its Hamiltonian. The associated score residual is the velocity with which the control's Langevin dynamics transport its law. We project this velocity onto a conditional sampler shared across states, instead of one Langevin dynamics per state, and the value dynamics onto a parametric critic, estimating both projections at sampled states to obtain coupled actor–critic flows. The score loss measures the actor's agreement with the current critic, while the policy-evaluation residual measures the critic's agreement with the actor. We also derive gradient and Hessian residuals, including a Feynman–Kac representation for the gradient equation, to control errors not detected by the projected value iteration. An exact decomposition of the HJB residual combines these errors into a policy-suboptimality bound under verification and logarithmic Sobolev assumptions. In the linear-quadratic class, both projections are exact and recover the pointwise iteration, and we provide numerical experiments on general models to demonstrate the coupled actor–critic learning in high-dimensions.

Modelling cold dark matter as dust makes the matter congruence geodesic and therefore removes any intrinsic dipole from the local Hubble flow. The dust model breaks down as stream crossing develops, whereas a collisionless gas accommodates stream crossing via velocity dispersion in phase space. We develop a covariant kinetic framework for this regime without assuming a background spacetime or any geometrical symmetry. Starting from the exact massive Vlasov hierarchy, we construct its energy-integrated moments and organise these by velocity weight. A self-consistent truncation at the quadrupole closes the dynamics on the matter energy density, isotropic pressure and anisotropic pressure. Their gradients generate a matter-frame 4-acceleration, for which we find an exact nonlinear solution of the momentum constraint, valid in the general case without truncation. This goes beyond previous work in which an arbitrary 4-acceleration is introduced. Velocity dispersion also sources vorticity through the curl of 4-acceleration, and we derive the nonlinear expression for vorticity evolution. We then propagate the non-geodesic matter flow into covariant local cosmography, where the 4-acceleration is the intrinsic Hubble dipole and also enters the deceleration multipoles. Our construction provides a covariant kinetic completion of dust cosmography and identifies the quantities required to test collisionless matter directly with local distance–redshift data. A companion paper specialises the hierarchy to perturbed FLRW spacetime and predicts the size of the resulting cosmographic signals.

Activation steering exploits interpretable directions in the residual stream to enable inference-time manipulation of model behavior. Composing steering vectors to apply multiple target behaviors simultaneously is important in various fields-including AI alignment and safety-but remains a challenge for existing activation steering methods. In contrast, prior work in model merging shows that target behaviors represented by learned weight adaptations can be combined with high accuracy. A method that translates weight adaptations into activation steering vectors could therefore extend prior work in model merging to generate composable steering vectors that better enable simultaneous inference-time behavioral control. For this, we introduce First-Order Steering, a formulation of activation steering as a first-order approximation of weight update matrices parameterized by a vector of steering strengths, and establish theoretical bounds on the approximation error of first-order steering. We then develop a novel model merging procedure, HeRD-Merging, which minimizes the first-order approximation error terms to enable higher first-order steering accuracy. Together, our method produces steering vectors that control both individual and composed behaviors more accurately than existing activation steering methods. Furthermore, HeRD-Merging matches the performance of conventional model-merging baselines, while producing weight adaptations that admit more accurate first-order steering vectors.

A dark-matter core and a soft nuclear equation of state can produce similar mass–radius signatures, motivating a complementary probe through the $f$-mode spectrum. We compute quadrupolar $f$-mode frequencies and gravitational-wave damping times in full general relativity for cold, nonrotating neutron stars admixed with self-interacting bosonic dark matter (DM). Our two-fluid survey spans 21 nuclear equations of state covering nucleonic, hyperonic, $\Delta$-admixed, and combined hyperon–$\Delta$ compositions at $F_{\rm DM}=1$–$20\%$. The main sequences use $\lambda=\pi$ and boson masses of $500$ and $100\,\mathrm{MeV}$ for the core and halo studies, respectively. Independent normal-matter (NM) and DM displacements couple through the metric, yielding NM-led and DM-led $f$-mode branches whose radiative damping is determined by outgoing-wave boundary conditions. At $1.4\,M_\odot$, the core DM-led damping time decreases from order $10^3\,\mathrm{s}$ at $F_{\rm DM}=1\%$ to order $1\,\mathrm{s}$ at $20\%$, approximately following an empirical $F_{\rm DM}^{-2}$ dependence, while NM-led damping times remain within $0.12$–$0.33\,\mathrm{s}$. Halo DM-led damping instead increases with dark fraction: at the same stellar mass and $F_{\rm DM}=20\%$, dark radii approach $88\,\mathrm{km}$, frequencies fall to $0.14\,\mathrm{kHz}$, and damping times reach approximately $450\,\mathrm{s}$. Selected high-mass core sequences exhibit strong DM-led damping-time upturns not reproduced by the leading mass-quadrupole diagnostic. Representative core calculations show greater DM-led sensitivity to the bosonic self-coupling and retain both branches at $\ell=3$. Under the adopted nonrotating, circular-binary prescriptions, no evaluated configuration satisfies all geometric and perturbative conditions for a controlled linear tidal resonance.

Lossless triangle mesh compression must preserve both vertex positions and connectivity. Octrees support learned point cloud geometry coding and progressive refinement, but extending them to meshes requires a compatible connectivity representation. Unlike the eight occupancy decisions of a voxel, a parent edge can develop into varied child connections, making edge refinement difficult to model with a compact prediction prior. We propose OctMesh, a learned framework that codes geometry and connectivity on a shared octree hierarchy. Its key observation is that octree pooling produces parents with either one child or two to eight children. Child edges are then grouped by their endpoint parents' types and whether the endpoints share a parent. Each candidate group contains children from just one parent or two connected parents. The resulting four categories define small, fixed-shape prediction tasks: connections uniquely determined by the parent graph are inherited without bits, while three neural predictors estimate probabilities for the remaining candidates. These probabilities guide arithmetic coding of the actual edge symbols. Binarized predictions of within-parent connections provide context for predicting connections between different parents. A graph-aware parent feature extractor combines local geometry, parent connectivity and global shape. The connectivity models use dedicated weights at coarse levels and share weights at fine levels. Residual edges and a finest-level face-selection payload complete the reconstruction. On 256 frames from eight MPEG V-DMC test sequences, OctMesh losslessly recovers the finest-level vertex-coordinate, edge and unoriented face sets at an average of 7.033 bits per face, 12.8% below V-Mesh. The same hierarchical representation supports nine levels of progressive vertex-and-edge refinement.

Geometry reasoning is naturally stateful: solving a problem repeatedly alternates between structural proposals and exact deductions. We formulate this process as dense neural-symbolic coupling, in which neural guidance and symbolic execution share a typed state and communicate through executable actions at every search step. Neural proposals contribute theorem instances, constructions, and algebraic bridges; the symbolic runtime applies registered rules, propagates exact constraints, and records provenance. A nested controller allocates computation first between neural and symbolic proposal sources and then among admitted actions. We instantiate the framework in OmniGeo, a single solver for plane, analytic, and solid geometry. With Claude Sonnet 4.6, OmniGeo reaches 94.2%, 88.5%, and 89.8% on FormalGeo7K, Conic10K, and SolidFGeo, respectively (90.8% macro average), and solves 21/30 IMO-AG-30 problems.

We develop a cutting-plane algorithm for computing pure Nash equilibria in finite integer games with shared constraints, where a deviation may be feasible against one opponent profile and infeasible against another. Conditional equilibrium inequalities capture this dependence through an explicit activation term. We give affine encodings of costs and activation conditions and prove that the resulting inequalities characterize the equilibrium set exactly. Embedded as lazy constraints in branch-and-cut, they yield the Generalized Zero-Regret algorithm for optimizing a linear objective over exact or approximate equilibria; a bisection procedure maintains certified bounds on the smallest achievable approximation factor. We also prove that, when the conditional polytopes have integral vertices, a concave cost is constant on the minimal face containing an equilibrium strategy, so strict concavity forces vertex strategies; for uniform integer-splittable bin packing, a cost-preserving transformation yields vertex equilibria even without strict concavity. We give formulations for bin packing, network formation, and knapsack games with shared capacities and evaluate the algorithm on 3,300 instances, computing a socially optimal equilibrium on all but 43, certifying nonexistence on 16, and certifying approximation factors within a few percent where no exact equilibrium exists.

Deep remaining-useful-life (RUL) models on NASA C-MAPSS are now routine, and so are heatmaps that colour sensors and timesteps. A heatmap that looks mechanical is not the same as an explanation an engineer can act on. We train three standard architectures - a 1D CNN, an LSTM, and a small Transformer encoder - on the official FD001 and FD003 splits with the piecewise RUL cap of 125 cycles and the official PHM08 asymmetric score. We then attach three attribution maps (Integrated Gradients, occlusion, last-layer attention) and evaluate them with the checks the XAI-for-PdM literature still under-reports: deletion/insertion faithfulness, Spearman stability under sensor-scale noise, agreement across training seeds, and cosine consistency inside RUL bins. Prediction error is a prerequisite, not the claim. The headline is which explanation method moves the RUL output when its top cells are removed, and which map survives a 5% input perturbation. Integrated Gradients and occlusion are similarly faithful on the LSTM; Transformer attention is cheap and temporally smooth but weakly faithful. All three maps are almost unchanged under 5% input noise, yet IG/occlusion agree only moderately across two LSTM seeds - stability to sensor jitter is not the same as stability to retraining. A secondary tabular check on the AI4I 2020 failure dataset shows the same deletion pattern for tree importances. We recommend occlusion or IG for any C-MAPSS-style report that will be read by a maintenance engineer, and we treat raw attention weights as a visualisation only.

New AI accelerators arrive before the kernels that make them fast, because peak kernel performance requires architecture-specific expertise in operand pipelines and data-movement techniques. Coding agents can now write, compile, and tune kernels on their own, so they could greatly accelerate kernel development and optimization. What agents produce depends on the interfaces they are given. These interfaces may expose a machine's raw capabilities or encode the known-good methods for exploiting its hardware features efficiently. We test the performance impact of these two interfaces on Intel GPUs through controlled experiments with three coding models on three kernels. With raw SYCL and execution feedback, Opus 4.8, the strongest of the three models tested, writes a single-GPU GEMM kernel reaching only 57.5% of Intel's tuned oneDNN library. We present SyclKittens, a hardware-aware tile programming model for Intel GPUs that encodes these known-good methods, so its operations place operands in matrix-engine layouts, prefetch through the L1 cache, and communicate over the fabric that links GPU stacks into a node. With SyclKittens under the same agent, task, and feedback budget, the agent reaches 82.1%, showing that encoded methods turn hardware capabilities into performance. Workload-specific policies stay programmable, and engineers and agents jointly refine these schedules in SyclKittens to build a kernel suite that reaches ~96% of oneDNN in geometric mean across GEMM shapes. The suite runs Llama-3.1-8B inference 1.59x faster than torch$.$compile on one GPU and up to 2.91x faster than a matched multi-GPU decode path on Intel's oneCCL. SyclKittens is open source and available at https://github.com/intel/SyclKittens.

We pose stealthy attack scheduling on a sensor-to-estimator link under a resource constraint with a budget \bar{\Gamma} on the fraction of corrupted transmissions and a model-free whiteness constraint on the received innovations. For a discrete-time linear plant with non-Gaussian noise, the worst attack, innovation sign flip, preserves the innovation magnitude and is exactly stealthy against every magnitude-measurable detector, the damage-optimal schedule being a memoryless threshold; but the tail concentration that maximizes damage also manufactures serial correlation, where an innovation-whiteness monitor gains power. We dualize the whiteness constraint and show the optimum is a threshold rule on corrected innovation energy using memory of recent magnitudes and the previous decision. We further trace that correction to a second degree of freedom and set the damage by the location of the firing set in magnitude space and set exposure by the boundary density of its run structure. We realize it as a hysteresis set by one split-conformal order statistic without any plant model, using one counter and two comparisons per step. It keeps 80–96% of the memoryless damage at 2.3 to 71 times lower lag-one whiteness power, validated on a real truck CAN record.

Formal theorem proving increasingly combines learned semantic guidance with verified symbolic execution. The quality of the symbolic search substrate therefore determines how much useful mathematical structure can be accumulated, reused, and exposed under a finite inference budget. We introduce ViaLean, a Lean4 prover that organizes symbolic reasoning as bounded exploration of a persistent proof-state graph. Its search preserves coverage across complementary reasoning modes, merges semantically equivalent goals, retains verified intermediate structure, and observes short symbolic futures before committing to a transition. On the complete miniF2F test split, the model-free configuration solves 122/244 problems (50.0% pass@1). Historical and recent symbolic reference points range from Lean's earlier tidy search to modern grind and SMT-backed verification, showing that proof-space organization remains a substantial source of capability. The same persistent state also provides a natural interface for neural–symbolic agents: neural reasoning can operate over verified regions and intermediate objects while Lean continuously expands and validates the local proof space.

For a set $\mathcal P$ of odd primes, let $\operatorname{CT}_{\mathcal P}(\mathbb{Z})$ denote the group generated by all class transpositions whose moduli have no odd prime divisors outside $\mathcal P$. We prove that \[ \bigl\langle \operatorname{CT}_{\mathcal P_1}(\mathbb{Z}),\operatorname{CT}_{\mathcal P_2}(\mathbb{Z}) \bigr\rangle = \operatorname{CT}_{\mathcal P_1\cup\mathcal P_2}(\mathbb{Z}) \] for any sets $\mathcal P_1$ and $\mathcal P_2$ of odd primes. This gives a negative answer to Question 21.75 in the Kourovka Notebook.

We study supervised classification problems with missing feature values. Existing approaches often decouple imputation from classification, producing imputations that may be plausible but uninformative for prediction. Instead, we propose the Integrated Imputation and Classification Network (IICN), which jointly trains an imputer and an ${(n{+}1)}$-classdiscriminator adversarially with a single class supervised classification objective, where the discriminator learns to distinguish among the $n$ true classes and an additional “imputed" class. We prove that at the global optimum, the imputer and discriminator together implement marginalization over missing coordinates and yield a Bayes-optimal classifier. We evaluate IICN on FashionMNIST, CIFAR-10, and tabular datasets with naturally occurring missingness. IICN outperforms classical impute-then-classify pipelines and recent generative baselines, showing strong robustness and accuracy in challenging settings.

Combining capabilities of multiple expert models trained starting from the same base checkpoint has become increasingly common in frontier language-model post-training. Recent trends suggest that multi-teacher on-policy distillation (MOPD) outperforms conventional off-policy methods. However, despite the higher inference and environment interaction costs incurred by MOPD, we find that much of its reported accuracy gain is due to certain training design choices and hyperparameter optimization, rather than the algorithm itself. We conduct a controlled self-distillation study across two multi-teacher settings, four models, and eleven benchmarks, comparing off-policy methods, namely supervised fine-tuning (SFT) and soft-label distillation, to hybrid teacher-prefix distillation and MOPD. We found that all four methods achieve nearly identical accuracy. However, MOPD uses $14.8$–$23.1\times$ SFT's training GPU-hours. We also revisit four recently published comparisons between on-policy and off-policy distillation and find that the reported on-policy gains shrink substantially when SFT baselines are trained on rejection-sampled teacher trajectories and use independently tuned hyperparameters. As a training-free alternative, we also find that simple weight-merging methods can recover expert capabilities with minutes of CPU merging time, although their accuracy degrades as model size decreases and task interference increases. Overall, our results question recent gains reported due to MOPD and suggest careful tuning of more efficient off-policy baselines as a viable alternative.

How far from finite can an amenable group be? Every finite piece of an amenable group can be imitated by permutations of a finite set, and Cornulier's sofic profile counts how many points such an imitation needs at accuracy $1/r$. We build a finitely presented elementary amenable group with a finite piece whose profile is $\exp(r^{1+o(1)})$, close to the most our counting method can ever detect. The construction is a lamplighter with its lamps on configurations rather than on points. Houghton's group moves the points of three rays, finitely supported affine maps act on their binary configurations, and a copy of $S_3$ sits on every configuration. Then $N$ points carry $2^N$ lamps, yet any two lamps can be brought together by moves that each involve at most three points. The group embeds in Brin's group $3V$, so $3V$ too has a finite piece of nearly exponential profile. The group also gives an explicit quantum channel on $\mathbb C^{873}$ that is cheap to use once and expensive to use many times. A device that applies it $n$ times, releasing each output before the next input arrives, needs about $n/B$ qubits of memory when it may spend $B$ bits of purity, and exact devices achieve this up to polylogarithmic factors. With exchange at the optimal rate, the least memory is about $\sqrt n$, attained with purity of the same order. The channel is factorizable and lies in the closure of channels with finite maximally mixed baths, yet any such bath that imitates it to accuracy $u$ needs dimension $\exp(u^{-1+o(1)})$, although its minimal Stinespring dilation implements it exactly with a pure environment of dimension $130$. The engine is a one-round theorem: after a single use, the memory of any such device carries an approximate representation of the group.

A family of $k$-subspaces of an $n$-dimensional vector space over a finite field is $t$-intersecting if any two members intersect in a subspace of dimension at least $t$. A $t$-intersecting family is nontrivial if no $t$-subspace is contained in all its members. In this paper, we determine the largest nontrivial $t$-intersecting families for $k\geq t+2$ and $n\geq 2k+1$. As a result, the complete nontrivial-intersection theorem for vector spaces is established.

Large language model (LLM) agents are increasingly deployed in tool-augmented environments, but their reliance on external inputs makes them highly vulnerable to prompt injection attacks that can hijack task objectives. Existing safety alignment methods rely on static expert trajectories or preference optimization, limiting their ability to generalize to adaptive attack patterns. In this work, we propose Self-Reflection Fine-Tuning (SRFT), a training framework that enables agents to improve robustness by learning from their own failure experiences under adversarial conditions. Instead of passively imitating expert behaviors, SRFT exposes the agent to compromised trajectories constructed via injected attacks, and leverages an expert model to generate structured self-reflection reasoning that contrasts unsafe and optimal actions. This reflective supervision teaches the agent to identify malicious instructions, reason about their consequences, and maintain alignment with the original user intent. We instantiate this framework in SR-Agent, built on Llama-3.1-8B-Instruct and Qwen3-8B, and evaluate it on both static and adaptive prompt injection benchmarks. Experimental results show that SRFT substantially reduces attack success rates while preserving task performance, and demonstrates strong generalization under adaptive attacks. These findings suggest that learning from failure via self-reflection is a promising direction for building robust and secure LLM agents. Our code is released at https://github.com/Eden-Wang1710/srft-repo.

We consider the ill-posed inverse problem of recovering the drift potential of an overdamped Langevin diffusion from discrete, possibly irregular position observations. Specializing the suboptimality gap for inverse stochastic control to drift-potential recovery, we parametrize the associated value function in a finite basis. Under a basis nondegeneracy condition, the resulting Galerkin estimator is obtained from one positive-definite linear system whose entries are smooth functionals of the empirical time marginals; no transition density is required. The gap equals one half of the squared energy distance to the true potential, yielding a best-approximation identity and energy-seminorm consistency as the basis becomes complete. At a fixed basis, we separate the sample fluctuation from the time-quadrature error, thereby avoiding the Euler–Maruyama $O(\Delta t)$ drift-discretization bias. We also analyze the finite basis as regularization, give a dimension-dependent convergence rate for a concrete basis family, and bound observation-noise bias. One- and two-dimensional experiments verify the predicted sampling-interval behavior. An application to irregular animal telemetry illustrates the method on a single long trajectory.

Generating multiple-choice questions is increasingly scalable, but establishing their assessment quality remains difficult. We present a focused narrative review of automated item-writing flaw detection, revision, psychometric screening, and NLP benchmark auditing. Database searches, citation retrieval, and nominated sources yield fourteen research reports reviewed in full text. We distinguish surface checks from content-sensitive judgments and map a 19-criterion rubric to detection methods and reported evidence. High label-level accuracy often coexists with weak positive case detection, while rubric definitions and reference standards vary. Revision evidence is mixed, and the associations reported in prior work do not establish the effects of repair. We propose evaluating quality assurance as a sequence of independently validated decisions, with criterion-specific reporting, calibrated human review, and outcome-based assessment of revisions.

This paper presents a conformal-seeded hybrid strategy for solving inverse kinematics of offset, redundant 7-DoF robot arms of the humanoid class. Analytical inverse kinematics (AIK) provides closed-form solutions with very low computational cost. However, for offset kinematic structures, the exact closed-form solution is generally unavailable, and practical AIK must rely on an approximate or simplified kinematic model. In contrast, numerical inverse kinematics (NIK) can achieve high-precision solutions on the full kinematic model. However, its convergence is highly sensitive to initialization. To overcome these limitations, we propose a two-stage hybrid inverse kinematics framework with conformal-calibrated seed selection. First, an approximate analytical model efficiently enumerates a finite set of candidate joint solutions. Second, we rank these candidates using a lightweight learned predictor of post-refinement difficulty, wrapped by split-conformal prediction into a calibrated upper bound that serves as the selection score. The best-ranked seed is then refined using a Levenberg-Marquardt solver on the full kinematic model. The proposed method combines fast candidate generation, learned seed ranking with a calibrated difficulty bound, and accurate numerical refinement, achieving real-time performance of less than 40us and a success rate of 100% in our evaluation on reachable targets. We validate the approach through large-scale stochastic simulation across the workspace and experimental demonstrations with motion planning on a humanoid robot arm. Demonstration videos are available at https://youtu.be/aeiBmw1XRbw.

Coherent motion of light scalar fields in the early Universe is typically attributed to an initial displacement, a primordial velocity, or a prescribed temperature-dependent potential. We identify a distinct microscopic mechanism in which differential thermal evolution of multiple non-aligned symmetry-breaking sources rotates the effective vacuum direction of a pseudo-Nambu–Goldstone boson (pNGB), driving motion from an initially stationary minimum. The mechanism is realized in the Majoron sector of a Type-I seesaw mechanism, where heavy neutrinos with separated thermal thresholds supply the required differential thermal evolution. For a representative benchmark, the thermal source direction rotates by $|\Delta\theta_T|\simeq0.76$~rad and drives the Majoron to a peak velocity $|\dot\theta|/H\simeq0.62$, while the field tracks the moving minimum to sub-milliradian accuracy. This establishes a microscopic finite-temperature origin for pNGB motion, with implications for spontaneous leptogenesis and, more generally, for any system with multiple non-aligned symmetry-breaking sources that evolve differently with temperature.