Papers

Discrete diffusion models offer a promising alternative to autoregressive generation by enabling parallel updates, but their sampling efficiency can depend strongly on the choice of the forward process and the sampler. For the uniform forward process, existing lower bounds for the standard $\tau$-leaping sampler scale linearly with the ambient dimension $d$, raising the question of whether this dependence is intrinsic to the forward process. We answer this question in the negative. We consider a first-order sampler based on the leave-one-out denoiser for uniform and remasking processes whose coordinate updates can be performed in parallel. In both cases, the sampler can correct denoising mistakes during the sampling process, which becomes necessary when many coordinates are updated together. Our main result establishes an adaptive sampling guarantee: up to logarithmic factors, $N = O(\mathrm{DTC}(X_0) / \varepsilon)$ discretization steps suffice to achieve sampling error $O(\varepsilon_{\mathrm{score}}+\varepsilon)$, where $\varepsilon_{\mathrm{score}}$ is the error in score estimation. Thus, the sampling complexity is governed by the intrinsic dependence structure of the target distribution, as measured by its dual total correlation $\mathrm{DTC}(X_0)$, rather than directly by the ambient dimension $d$. Our analysis proceeds through a Bayes-optimal auxiliary sampler that separates discretization error from score-estimation error. We also derive an exact information-theoretic representation of the discretization error in terms of the mutual information between different coordinates of the forward process at different times. This representation applies to general forward processes and, in the uniform and remasking cases, can be controlled by $\mathrm{DTC}(X_0)$. Numerical experiments on structured synthetic distributions illustrate the predicted dimension-adaptive behavior.

Multi-vector retrieval has become an important primitive for fine-grained matching in information retrieval, with emerging applications in areas such as recommender systems and bioinformatics. However, its high computational complexity and memory costs make low-latency retrieval difficult. Prior systems have attempted to optimize query latency, but their designs remain CPU-centric. While GPUs offer substantial computational advantages, their limited memory capacity necessitates a heterogeneous architecture in which the dataset resides in host memory and the GPU serves as an accelerator. Existing GPU-based system, PLAID, is bottlenecked by CPU-GPU data movement, as vector data must be transferred from host memory to the GPU at query time. We propose Chimera, a GPU-CPU co-processing system for multi-vector retrieval that eliminates this transfer bottleneck. Chimera stores highly compressed, low-precision quantization codes on the GPU while maintaining high-precision data in CPU memory. At query time, it leverages GPU-resident data for efficient candidate generation and filtering, and further refines results through a GPU-CPU collaborative scoring scheme that completely avoids vector data transfer while enabling computation overlap. Experiments on real-world datasets demonstrate that Chimera significantly outperforms existing approaches, achieving up to 59.5x higher QPS at the same recall level.

Language models are sequential processors, but long-horizon agency requires external information and computation beyond model weights and active context. Prime Agent is an open-source harness for long-horizon evaluation and coding-agent workflows. A persistent IPython REPL follows the Recursive Language Model abstraction for programmatic context processing and test-time compute, while Continual Harness preserves histories, memories, skills, prompts, and subagent specifications across trajectories. Recursive subagents coordinate through direct agent-to-agent communication, and the Agents View lets humans inspect and manage daemon-backed sessions. Prime Agent standardizes execution, recovery, verification, and resource accounting while leaving strategy construction to the model. This low-friction, expressive membrane prevents harness failures from becoming model failures and pushes measurement toward the model's true maximal underlying capability. Prime Agent raises ARC-AGI-3 RHAE Best@1 from 30% to 95.5% and matches or exceeds native and popular harnesses across long-context coding, GPU-kernel generation, emulator construction, and autonomous nanoGPT speedruns. On Factorio, we find refinement allows for continuous technology progression and dedicated subagents enable parallelized work. Code is available at https://github.com/PrimeIntellect-ai/prime-agent.

Recent advances in continuous diffusion and flow-based language models (LMs) have achieved performance competitive with discrete LMs. However, existing continuous frameworks still rely on decoders supervised with cross entropy (CE) because the flow trajectories are not guaranteed to terminate at valid token embeddings. Motivated by this limitation, we introduce ConvergeFlow, an embedding-space flow-based LM, which constrains the data predictor to the convex hull of token embeddings and trains it solely with the mean squared error objective induced by flow matching. Under suitable regularity conditions, we prove that the resulting flow converges to valid token embeddings despite errors in the data predictor, enabling direct token prediction without a CE-supervised decoder. We further develop three sampling mechanisms for controlling the trade-off between the generative perplexity and entropy. Experiments on OpenWebText demonstrate that ConvergeFlow achieves performance competitive with existing continuous and discrete diffusion LMs. These findings demonstrate the potential of the flow-based paradigm for language modeling. Our code is available at https://github.com/Na-Li66/ConvergeFlow.

In CLAUDE.md, "do not" is a natural-language instruction that the model interprets. Claude Code's deny is a built-in control that blocks an action before the agent can take it. Both can express the same security goal, but they control the agent in different ways. We measure this gap in 481 public CLAUDE.md files. An LLM matched the extracted candidate rules against Claude Code's documented controls, and two security practitioners independently checked a sample without seeing the model's answers or each other's labels. Depending on how closely a control had to match the written rule, only about 4-16% of the retrieved security rules had a matching built-in control. Under the strictest standard the estimate was 4.4% (95% CI: 2.6-6.7%), and the two annotators agreed closely on which rules had a match. A manual review of complete files found that our extraction method captured 66.3% of eligible security rules; the reported rates therefore apply to the rules it captured. This is a usable security problem: CLAUDE.md is a write-only channel. A developer writes a security rule but gets no feedback on whether a control will enforce it. The same plain-text form hides two kinds of rule: those a permission rule, mode, or sandbox can enforce, and those left to the model to interpret.

Rendering views using 3D scene representations such as Gaussian Splatting (3DGS), Neural Radiance Fields (NeRF), meshes, or even point clouds produces artifacts when input views are sparse or target views lie far from the input. Recent work mitigates these artifacts using diffusion-based generative priors, but is specialized to individual representations and require custom architectures or extensive retraining. We present FixAnything, a single model for fixing a wide range of rendering artifacts. It does so by repurposing a pretrained video generative model, leveraging its implicit multi-view priors with only minimal modification and lightweight finetuning. Our key insight is that even noisily-rendered sequences preserve camera motion and coarse scene structure, allowing cleanup to be formulated as video-to-video translation. To control what scene structure should be preserved, we introduce a binary mask denoting the clean pixels, enabling the model to anchor its output to high-quality inputs (e.g. training views) while refining the rest. To encourage FixAnything to produce 3D-consistent renderings that support downstream reconstruction, we use camera pose accuracy (recovered via structure-from-motion) as a reward signal for direct preference optimization (DPO). Across four distinct 3D representations, FixAnything consistently improves rendering quality with lightweight finetuning, demonstrating that a single generalist video prior can replace multiple specialist refinement pipelines. The simplicity of the framework enables immediate adoption of stronger future video models without architectural redesign.

Machine-learning-based anomaly detection is increasingly used in industrial control systems (ICS), yet most studies assume that detector training data is trustworthy. In practice, training data may be corrupted through compromised logs, labeling errors, manipulated historian records, or unsafe retraining processes. This paper evaluates the robustness of offline ICS anomaly-detection pipelines on the Secure Water Treatment (SWaT) benchmark under training-time contamination. We assess 11 heterogeneous anomaly detectors under three contamination strategies: random injection, similarity-targeted injection, and feature-noise injection. The first two insert attack samples into the nominal training pool, while the third adds bounded Gaussian noise to selected normal training samples. These attacks are contamination-based rather than gradient-driven poisoning methods. Contamination budgets from 1% to 10% are evaluated using clean validation and test sets under a unified offline protocol. The results show that robustness is strongly model-dependent and cannot be predicted from clean-data performance alone. Injection-based contamination causes the greatest degradation, particularly for local-density and distance-based detectors, whereas feature-noise contamination has a comparatively limited effect. PCA, SVM, HBOS, and IForest remain relatively stable, while the tuned neural detectors demonstrate intermediate robustness. Overall, the findings highlight the importance of training-data integrity in ML-enabled ICS monitoring, subject to the evaluated dataset, models, and threat assumptions.

In this paper, we introduce the Inertial Manifold Neural Operator (IMNO) for solving dissipative time-dependent partial differential equations (PDEs). The long-time dynamics of such systems often exhibit an effective low-dimensional structure due to dissipation. Unlike standard neural operator architectures such as the Fourier Neural Operator (FNO), IMNO explicitly leverages the low-dimensional structure to achieve better physical interpretability, accuracy, and stability in long-horizon autoregressive training and prediction for nonlinear dissipative PDEs. For shift-equivariant PDEs, we further introduce a shift-equivariant variant (IMNO-SE) of the proposed neural operator, ensuring that a spatial shift in the input induces the same spatial shift in the output. This symmetry-preserving inductive bias substantially improves its performance in shift-equivariant PDEs. Extensive benchmark experiments are presented to evaluate IMNO's performance numerically.

While AI assistance can improve human task performance in the short term, it may also undermine the development of skills in the longer term. We examine this tension in a controlled logic-puzzle experiment involving on-demand AI assistance, where participants complete tasks before, during, and after AI is available. By experimentally varying AI request costs, we find that lower-cost assistance induces more frequent AI use. We also find that participants who request AI assistance during the AI-access phase perform worse at the task after assistance is removed, and their subsequent unassisted performance is overestimated when predicted from earlier AI-assisted performance. We use a Bayesian latent ability model to separate initial ability, post-AI ability, and participant-specific skill change, while estimating how independent reasoning during the AI-access phase relates to skill development. The results show that greater independent problem-solving effort is associated with larger gains in latent ability, consistent with the interpretation that skill development is weaker when AI assistance substitutes for independent reasoning.

Does multi-agent LLM interaction help or hurt? Some work reports gains from debate (Du et al., 2024), critique loops (Chen et al., 2025), and mixture-of-agents synthesis (Wang et al., 2025), while other work finds that interaction adds cost without improving quality under equal budgets (Tran & Kiela, 2026; Xu et al., 2026; Jarrett et al., 2025), or that independent sampling already captures multi-agent gains (Li et al., 2024). We argue this contradiction partly reflects a missing distinction, because not all multi-agent communication is equal. Different model families find structurally different solutions, but when agents read each other's complete outputs, their proposals converge within one round, erasing the diversity that motivates using multiple models. We call this the interaction tax. We test 11 verifier-scored optimization tasks under matched budgets and find that full-solution interaction is a weak default. Independent proposal generation avoids this collapse. Full-solution interaction mainly makes agents stay close to the first solution they see instead of trying different approaches, and critique helps only if the violated rule is easy for the LLM to find and fix. These results suggest that multi-agent performance depends less on the number of agents than on the information they exchange, and interaction helps only when agents share the right information at the right time.

The boxicity of a graph $G$, denoted by $box(G)$, is the minimum integer $d\geq 0$ such that $G$ is the intersection graph of axis-parallel boxes in $\mathbb{R}^d$. The class of zero divisor graphs introduced by Beck (1988) is a popular class of graphs and has been studied extensively by several researchers. Suppose $Z(R)$ is the set of zero divisors of a ring $R$. The zero divisor graph $\Gamma(R)$ for a ring $R $ is defined as the graph with the vertex set $V(\Gamma(R))=Z(R)$ and $E(\Gamma(R))=\{\{x,y\}\colon x,y\in Z(R)\text{ with }x\neq y\text{ and }x y=0\}$. One can define an equivalence relation $\sim$ on $V(\Gamma(R))$ such that for vertices $x$ and $y$, one has $x\sim y$ if and only if $x$ and $y$ have the same annihilator, i.e., $Ann(x)=Ann(y)$. The compressed zero divisor graph $\Gamma_E(R)$ for a ring $R$ is the simple graph obtained from $\Gamma(R)$ by retaining exactly one vertex from each equivalence class induced by $\sim$. In this paper, we completely answer two open questions posed in Discrete Applied Mathematics 391 (2026), pp. 127-136. Let $N=\prod_{i=1}^a p_i^{n_i}$ be the prime factorization of a positive integer $N$ and let $\mathbb{Z}_N$ be the ring of integers modulo $N$. We determine the exact boxicity of the compressed zero divisor graph $\Gamma_E(\mathbb{Z}_N)$. We show that when $a\geq 2$, $box(\Gamma_E(\mathbb{Z}_N))= a-1$ if and only if one of the following is true: $(i)$ $a\geq 2$ and $N$ is the product of two coprime integers $x$ and $y$ such that $x$ is a square-free integer and $y$ is the cube of a prime number; $(ii)$ $a\geq 3$ and $N$ is square-free; $(iii)$ $a\geq 2$, $N$ is cube-free, not square-free, and contains at least one prime divisor $p_i$ such that $n_i=1$. If $a=2$ and $n_1=n_2=1$, then $\Gamma_{E}(\mathbb{Z}_N)$ is a clique, and so, $box(\Gamma_{E}(\mathbb{Z}_N))=0$. In all other cases, $box(\Gamma_{E}(\mathbb{Z}_N))=a$.

Modern AI models such as tabular foundation models and gradient-boosted ensembles can outpredict classical methods, but provide little basis for reasoning about their predictions. High-stakes decisions call for models that are both accurate and interpretable as built. Local linear modeling offers a path forward: a smooth regression function is locally well approximated by a linear one, allowing a linear fit near each query point to achieve high accuracy without sacrificing transparency. The challenges lie in learning what is "local" and developing statistical tools for interpretation. Here, we propose local distillation, in which a black-box "teacher" guides a regularized linear "student" model at each query point. The teacher (1) defines locality by upweighting training observations with similar predicted outcomes, and (2) anchors the fit with its prediction at the query point, included as a pseudo-observation whose weight is estimated from the data. For interpretation, we add a small amount of Gaussian randomization to the local objective and use refits to assess stability: selection frequencies identify reliable features at a query point, and clustering the randomized fits identifies stable subgroups across the data. Under the lasso penalty, we prove that this randomization yields feature-selection probabilities that are stable under small perturbations of the training responses. Across 17 benchmark datasets, local distillation nearly matches its AI teacher's accuracy while producing a sparse linear model at each test point. In a high-dimensional cancer gene expression example, the framework identifies patient subgroups whose local models use different genes; this heterogeneity is invisible to a global linear model, and difficult to surface in a black-box model.

The continual evolution of malware variants necessitates detection systems that can adapt to new threats without retraining from scratch. However, continually updating models on new data often leads to catastrophic forgetting, where previously learned knowledge is overwritten. While continual learning has been increasingly explored for malware detection, the specific setting of Few-Shot Class-Incremental Learning (FSCIL), where new malware classes must be learned from only a small number of labeled examples, remains comparatively underexplored. Therefore, this work investigates the FSCIL setting for malware classification. To address the stability-plasticity dilemma, we propose a hybrid framework that leverages a Self-Supervised Learning (SSL) backbone initialized through domain-specific pre-training on malware packets. Our method incorporates Low-Rank Adaptation (LoRA) to efficiently adapt the model during the base session while freezing the core backbone to preserve previously learned representations, alongside a prototype-based classification head for incremental sessions to establish robust decision boundaries from limited samples. Extensive experiments across several datasets demonstrate that our approach consistently outperforms prior malware FSCIL baselines and achieves state-of-the-art performance.

Older adults recovering after lower-limb fracture or hip replacement may experience complex recovery trajectories. Most of the time, these clinical aspects are studied in isolation, masking their joint impact on recovery. This study used the MAISON-LLF dataset, which contains multimodal sensor and clinical assessment data from 18 older adults recovering in the community after lower-limb fracture or hip replacement. Participants were monitored for up to eight weeks, corresponding to a maximum of 1,008 participant-days of sensor monitoring. Forty-six daily features were extracted from indoor motion, acceleration, step count, heart rate, out-of-home mobility, and sleep data. Five clinical outcomes were assessed every two weeks: the Social Isolation Scale, Oxford Hip Score, Oxford Knee Score, Timed Up and Go test, and 30-second Chair Stand test. We utilize an inherent relationship between multi-modal sensor data and different clinical scores and formulate it as a multi-output regression problem. We tested various machine learning and deep learning single- and multi-output regression algorithms to predict these scores simultaneously. The results showed that predicting clinical scores jointly was better than separately. The tabular DL multi-output regressor, NODE, gave a remarkable performance of MSE=3.96 and MAE=1.02 in comparison to other multi- and single-output regressors. The SHAP feature analysis further showed the importance of including multimodal sensors to provide a good estimate of patients' recovery trajectory. This work may support the simultaneous assessment of functional recovery and social engagement among community-dwelling older adults and ultimately help improve their care and quality of life.

World models can predict video without learning dynamics that they reliably preserve. We test whether a frozen DreamerV3 trained only on pendulum video learns a scalar that its own latent transition treats as approximately conserved. A label-free search recovers the same energy-like invariant across independently trained conservative models, while the same procedure finds no comparable invariant in matched damped models. During autonomous rollouts, this quantity drifts. Projecting the latent state back toward its initial level set reduces rollout error in all three conservative models, whereas matched random constraints usually increase it. These results distinguish a dynamically meaningful invariant from a merely decodable correlate and reveal a concrete failure mode: a world model can learn a physical constraint from pixels yet violate that constraint when it imagines forward.

Earth-system analysis reconstructs changing physical processes from observations that differ in source, scale, timing, and modality. Natural hazards make this work consequential because incomplete evidence can change estimates of severity, exposure, and mechanism. We introduce EarthVerse, a benchmark that evaluates scientific agents through package-scoped investigations. Its 405 reproducible tasks are grounded in 199 documented events and 19 hazard families. Agents inspect heterogeneous event packages, choose compatible evidence, execute transparent calculations, reconcile source differences, and preserve provenance in the final answer. We provide executable ground truth that decomposes each task into fine-grained answer units, together with task-specific rubrics that assess the supporting research process while allowing multiple valid paths. We evaluate 25 model and agent systems under a controlled tool-using protocol, then use controlled studies to locate failures in evidence access, tool selection, memory, reasoning, interaction, and scientific execution. Across systems, the best mean answer-unit accuracy is 84.65%, while the highest Strict@95 is only 34.81%. The gap shows that current agents often complete individual steps without maintaining a consistent chain across evidence, scales, units, calculations, and physical interpretation. EarthVerse provides a reproducible basis for measuring end-to-end scientific reliability in dynamic Earth systems.

Artificial intelligence (AI) is transforming measurement in economics. AI models convert unstructured data, such as text and images, into structured variables at low cost, making previously prohibitive measurement feasible at scale. This shifts the bottleneck from finding any scalable measure of a phenomenon to choosing among many plausible ones, which may support different empirical conclusions. This review provides guidance for navigating that shift. We describe three stages at which AI enters the measurement pipeline—discovery, construct definition, and observation—and what each demands of researchers. We argue that credible inference with AI-generated variables requires appropriately designed validation: anchoring measurement to explicit criteria, rather than informal claims that a proxy is reasonable. We then examine how validation samples support valid inference even when AI predictions are arbitrarily biased, and what can be done when a random validation sample is unavailable.

Vision-Language Models (VLMs) achieve strong performance in visual reasoning tasks, but it remains unclear whether they understand visual relations, or simply employ shortcuts such as language cues or priors. To investigate this, we use the Qwen3-VL-4B (Bai et al., 2025), a modern VLM, to decode how visual information is encoded across depths. For this, we propose a synthetic dataset of simple geometric shapes for controlled analysis, along with queries crafted to precisely test language cues. Furthermore, the dataset is modified to test causal reliance on visual evidence. Our results show that current VLMs combine genuine visual reasoning with shortcut strategies primarily rooted in language cues.

Earth System Models (ESMs) rely heavily on High-Performance Computing (HPC) resources to simulate global climate. As these models evolve, their computational demands continue to grow, driven by three factors: (1) finer spatial grid resolutions, (2) the integration of complex biogeochemical processes (e.g., atmospheric chemistry, interactive vegetation, land use, and ice sheets), and (3) larger climate ensembles to manage uncertainty. Historically, growth in peak computing performance (FLOP/s) has outpaced improvements in energy efficiency (FLOP/Watt), increasing total HPC power consumption. Despite the central role of Model Intercomparison Projects (MIPs) in climate research, quantifying their computational and environmental costs has received limited systematic attention. This paper examines the evolution of climate model carbon accounting from voluntary post-hoc estimation in the Coupled Model Intercomparison Project phase 6 (CMIP6) to standardized accounting under the newly established CMIP7 Task Team on Energy Consumption. Using high-resolution Destination Earth simulations on MareNostrum 5, we empirically evaluate how different accounting boundaries (operational, active-only, and embodied carbon) impact reported energy, carbon emissions, and financial costs. Finally, we outline key methodological considerations for standardizing energy and carbon accounting for Model Intercomparison Projects (MIPs).

Historical people may appear under different languages, scripts, and transcription traditions, while distinct individuals may share highly similar or even identical names. This makes historical identity reconciliation more than a problem of string matching or transliteration. We introduce MHER, a provenance-controlled benchmark for pairwise reconciliation of person-name attestations from the Mongol world. MHER contains a balanced 396-pair Name-only core over 84 primary historical persons and a stricter 160-pair Source-grounded subset constructed from mention-by-source evidence, with entity-disjoint development and test splits. Across five generative systems, correctly Source-grounded evidence improves paired TEST accuracy by 12.96 to 94.44 percentage points relative to Name-only input. On five identical-surface different-person cases, all models fail under names alone (0/25 model-item decisions), whereas Source-grounded evidence yields 24/25 correct resolutions, with the remaining output an abstention. Context-only ablations show that historical descriptions often carry substantial identity information, while explicitly signaled misgrounding controls produce substantially lower performance. We also find that names are not uniformly beneficial: for Qwen3-8B, restoring surface forms converts ten otherwise correct Context-only distinctions into false identity merges. These results show that historical entity reconciliation depends not only on surface correspondence, but on whether identity judgments respond appropriately to provenance-controlled historical evidence. MHER therefore provides a controlled framework for studying evidence use, abstention, and failure modes in historical NLP.

We prove that minimum Riesz $s$-energy subset selection in the Euclidean plane is NP-complete already for the fixed exponent $s=2$. To our knowledge, this is the first Euclidean hardness result for exact Riesz-energy subset selection in which both the ambient dimension and the exponent are fixed. The reduction uses Barahona's planar cubic Ising model with uniform field. A spin is encoded by one diagonal of a four-point square. Axis-aligned selector chains implement ferromagnetic consistency, while a $45^\circ$ terminal geometry yields an antiferromagnetic source interaction. Rational diagonal perturbations realize the magnetic field, and all remaining interactions are dominated by polynomial separation. Because $s=2$ and all coordinates are rational, every constructed energy and the decision threshold are rational exactly.

Text-based person anomaly search requires distinguishing individuals based on fine-grained, context-dependent behaviors rather than mere appearance. Existing methods struggle to capture these context-conditioned actions, frequently relying on isolated skeletal geometry, discarding raw query details during reformulation, or utilizing absolute pointwise scoring for multimodal verification. To address these limitations, we propose ActPair, a unified three-stage coarse-to-fine framework that combines action-aligned retrieval with pairwise multimodal reranking to bridge the pose-semantic gap. First, we fine-tune a vision-language model (VLM) with an action-aligned multi-task objective that encourages the representations to encode action-discriminative semantics. Second, we perform parallel late-fusion retrieval using the original query and a large language model (LLM)-generated context-grounded rewrite, retaining complementary details from both semantic views. Finally, we propose an efficient off-the-shelf reranking module that leverages a pivot-promote algorithm to perform direct pairwise visual comparisons, mitigating residual spatial and compositional ambiguities without the prohibitive inference costs of exhaustive evaluation. Extensive experiments demonstrate that our framework achieves the best results among the compared methods on the Pedestrian Anomaly Behavior (PAB) public test and transfers effectively to an unseen, non-anomaly-specific dataset.

Consider the canonical universal hash family $h(x)= ((ax+b)\text{ mod } p)\text{ mod } m$, where $a,b$ are chosen uniformly from $\mathbb Z_p$, which we call linear hashing, being used to hash $n$ elements into $m=\Theta(n)$ buckets. For any universal family, the expected size of the largest bucket is at least $\Omega(\log n / \log\log n)$ and at most $O(\sqrt{n})$. The only improvement upon these trivial bounds for linear hashing is a 2019 upper bound of $\tilde{O}(n^{1/3})$ by Knudsen. We show that for any $p$ sufficiently larger than $n$, there is a set of $n$ keys whose expected maximum load is $n^{\Omega(1/\log\log n)}$, proving linear hashing does not have a polylogarithmic maximum load. We extend the same bounds to the classical multiply-shift hash family of Dietzfelbinger, Hagerup, Katajainen, and Penttonen. Our main contribution is an equivalence between the maximum load problem to a density variant of arithmetic Kakeya sets. We then complete the lower bound using a construction of Green and Ruzsa of a small set containing long arithmetic progressions with every difference in a prescribed range. Surprisingly, our equivalence also implies that any substantial improvement over Knudsen's upper bound would imply new results about standard arithmetic Kakeya sets. More precisely, an $O(n^{1/3-\varepsilon})$ upper bound would improve known bounds for unions of complete integer arithmetic progressions, while an $n^{o(1)}$ upper bound would imply Bourgain's arithmetic-progression criterion.

Finding people from a natural-language description (“ML engineers transitioning to research roles in biotech”) is increasingly delegated to LLM agents and framed as information retrieval. We argue that it is fundamentally a requirements engineering task: such a request is an under-determined requirement with implicit constraints, many valid answers, and no acceptance criterion, so useful answers require eliciting, validating, and verifying the requirement before search can matter. We present \sys{}, to our knowledge the first interactive, requirements-driven candidate-sourcing agent (it elicits, validates, retrieves, and verifies a vague people-request into a justified slate through bounded elicitation, workflow templates, a two-stage commit protocol, and bidirectional termination guards) and \bench{}, a benchmark that runs the requirements lifecycle (criteria-anchored validation, multi-model evidence-grounded oracle construction, and cost-aware verification). Across $21$ systems and all $691$ requirements, \sys{} dominates breadth ($100%$ coverage at $2.5\times$ the yield) and is near-orthogonal to the field, with $90%$ of the people it returns are surfaced by none of $20$ strong LLM-plus-web baselines combined. Beyond breadth, an evidence-grounded judging of every system shows \sys{} recalls the most relevant real people: $0.241$ of the union pool, $1.9\times$ the next system, with a bootstrap $95%$ interval disjoint from every baseline. \sys{} is thus the strongest sourcing engine (the deepest real, reachable candidate pool), while precision-ranking LLMs serve as~complementary verifiers.

Let $\lambda(n)=(-1)^{\Omega(n)}$ be the Liouville function. We prove a fixed power-logarithmic bound for its logarithmically weighted two-point correlations across the full shift range. There is an absolute $c>0$ such that every sufficiently large $x$ admits a single set $\mathcal E_x\subseteq[1,x]$ with $|\mathcal E_x\cap[1,H]|\ll_A H(\log x)^{-A}$ $(1\le H\le x)$ for every fixed $A>0$, while $\max_{\substack{1\le h\le x\ h\notin\mathcal E_x}}\sup_{1\le y\le x}\left|\sum_{n\le y}\frac{\lambda(n)\lambda(n+h)}{n}\right|\ll(\log x)^{1-c}$. The same exceptional-set formulation extends, without an upper cutoff, to all positive integer shifts. Earlier full-range theorems average over the shift; here a fixed saving holds pointwise outside one set whose density in every initial segment is smaller than every fixed negative power of $\log x$. The new middle-scale argument combines a general-good-modulus Liouville deletion lemma with a linear bad-modulus score, a progression Fourier estimate, and a Mellin-localized dilation that separates divisor-dependent endpoints. Maximal fixed-moment bounds evacuate the low prefix and control the long-shift range. Assuming GRH for primitive Dirichlet $L$-functions, we also prove, uniformly for $h\in\mathbb N$ and $1\le y\le x$, $\left|\sum_{n\le y}\frac{\lambda(n)\lambda(n+h)}{n}\right|\le\log(2\min{h,y})+O((\log x)^{1-c_{\mathrm G}})$ for an absolute $c_{\mathrm G}>0$, with no exceptional shifts.

We present a method for analyzing the internal representations of Vision Transformers (ViTs) exploiting the geometry of their learned parameters. Each affine layer's weight matrix is factored via Singular Value Decomposition (SVD), and activations are projected onto the leading right singular vectors to obtain compact, layer-intrinsic representations. A class-conditional density model is then fitted at each layer, producing per-class typicality scores that are stacked across depth into typicality maps: two-dimensional summaries of how class-specific evidence evolves through the network. From these maps, we derive two post-hoc scores for Out-Of-Distribution (OOD) detection: a Prototype Alignment Score (PAS), measuring agreement with class reference prototype patterns, and a Multi-Layer Soft Voting (MLSV) score, capturing cross-layer consensus without stored prototypes. On ViT-B/16 fine-tuned on CIFAR-100, the proposed scores achieve competitive detection performance without retraining or OOD exposure.

Reasoning-Induced Misalignment, where fine-tuning on reasoning data containing no harmful content, including mathematics, code, and problem-solving with chain-of-thought traces can induce harmful behaviors of LLM, posing a serious challenge to the safety of LLM reasoning. Cross-architecture, cross-scale, and cross-dataset checks show that RIM does not always emerge. Previous work attributed RIM to neuron-level entanglement, but did not identify the geometry of the representation space underlying this entanglement or propose a training-time fix. We provide both: a representation-space analysis of RIM and the Safety-Direction Penalty (SDP), which penalizes movement along a learned safety direction during reasoning fine-tuning. The analysis extracts two activation-space directions, one encoding reasoning ability and the other safety behavior. These directions are coupled: fine-tuning that improves reasoning shifts safety representations, and prompts with larger shifts show larger safety degradation. CKA distance ratios and probes locate the safety-decision layers where this shift is most relevant. These findings guide the design of SDP: the coupling motivates penalizing displacement along the safety direction, and the layer localization sets the initial scope. When the initial scope leaves compensatory shifts beyond the penalized layers, the same diagnostics guide iterative expansion. On Qwen2.5-3B and 7B, SDP restores safety while preserving benchmark reasoning performance.

Self-reflection is a powerful mechanism for credit assignment in human learning, converting sparse outcome feedback into actionable guidance. However, its potential for post-training Large Language Models (LLMs) remains underexplored. We propose Self-Reflective Policy Optimization (SRPO), a framework that internalizes this capability. SRPO enables LLMs to analyze their own completed trajectories, synthesize errors into concise "reflection patches," and use reflection-conditioned teacher scores on student on-policy rollouts as dense token-level training signals. This process effectively transforms sparse terminal supervision into dense, token-level learning signals without requiring external critics, separate reward models, or larger teacher models. We demonstrate that SRPO achieves state-of-the-art performance across mathematical reasoning and long-horizon agentic benchmarks with exceptional data efficiency. Using a Qwen3-8B base model, SRPO attains 73.3% on AIME'24 using only 8% (0.08x) of the training FLOPs required by scaled supervised fine-tuning, while significantly improving success rates on WebShop (64.7%), ALFWorld (76.8%), and SWE-Bench-Lite (31.2%). Code is available at https://github.com/Galleons2029/SRPO

The capacity of Low Earth Orbit (LEO) to sustain space operations is under mounting pressure from megaconstellations, legacy fragmentation debris, and new payload classes. Existing assessments of orbital capacity and debris evolution are largely deterministic, tracking mean populations of intact satellites and fragments with ordinary differential equations; they cannot capture the inherent randomness of collisions, breakup sizes, and launch schedules. We develop a stochastic extension of the two-species Lotka–Volterra model of Bradley and Wein, formulated as a density-dependent Markov chain, and study its deterministic and stochastic scaling limits. Because intacts and fragments differ by many orders of magnitude, these limits emerge on distinct time-scales, and different pathways to a collisional Kessler cascade become visible only on the appropriate time horizon. On a fast intact time-scale we obtain an ODE approximation and a Gaussian SDE approximation; on an intermediate fragment time-scale we obtain an ODE approximation, a Gaussian SDE approximation, and the critical Kessler threshold, above which the ODE approximation runs away in Kessler syndrome. Crucially, on a third, slow time-scale at the critical threshold, the fragment count converges to a Feller diffusion, in which runaway is triggered purely by fluctuations rather than by the drift—an effect the ODE approximations and their Gaussian SDE approximations cannot see. Debris runaway may occur sooner, and with higher probability, than deterministic models predict: the intact population can appear well-behaved while fragments quietly accumulate risk. Constellation deployment, debris-removal investment, and slot allocation should account for these stochastic effects, and planning for runaway must depend on the variance of the collision dynamics, not on the mean alone.

World action models (WAMs) have recently gained increasing attention as a framework for jointly modeling scene evolution and ego actions in autonomous driving. Most existing WAMs learn scene dynamics in pixel space by combining a video-generation backbone for future-observation prediction with an action head for ego-trajectory prediction. Pixels, however, provide only an indirect representation of these dynamics: they entangle geometry and motion with appearance, texture, and illumination, forcing the model to infer three-dimensional transformations from two-dimensional observations. We argue that point-based geometry provides a more natural state space for driving. It explicitly captures spatial structure and both rigid and non-rigid scene dynamics while remaining aligned with the 3D space of driving actions. Building on this insight, we introduce GeoWAM, a visual geometry world action model for autonomous driving. Rather than predicting future images, GeoWAM is pretrained to forecast future scene geometry, yielding representations that jointly encode spatial structure and temporal evolution. A geometry-conditioned action head then leverages these learned geometric dynamics to predict future ego-trajectories. Extensive experiments show that GeoWAM outperforms image-based alternatives, achieving a combined EPDMS of 36.6 on navhard without PDMS supervision and strong zero-shot generalization to nuScenes, with a collision rate of 0.24%. Scaling geometry pretraining with unlabeled data further improves performance, increasing the navhard score by 8.2% to 39.6 and strengthening zero-shot transfer to nuScenes, where the collision rate is reduced by 50% to 0.12%. Together, these results establish geometry as an effective state representation for autonomous driving and geometry pretraining as a general, scalable strategy for downstream planning.