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The past year has seen over 20 open-source document parsing models, yet thefield still benchmarks almost exclusively on OmniDocBench, a 1,355-pagemanually annotated dataset whose top scores have saturated above 90%. Athree-stage audit pipeline we run on OmniDocBench screens its 21,353evaluator-scored blocks and confirms 2,580 errors (12.08%); combined with overa year of public availability, both annotation quality and contamination riskcall its rankings into question. To address these issues, we presentPureDocBench, a programmatically generated, source-traceable benchmark thatrenders document images from HTML/CSS and produces verifiable annotations fromthe same source, covering 10 domains, 66 subcategories, and 1,475 pages, eachin three versions: clean, digitally degraded, and real-degraded (4,425 imagestotal). Evaluating 40 models spanning pipeline specialists, end-to-endspecialists, and general-purpose VLMs, we find: (i) document parsing is farfrom solved: the best model scores only ~74 out of 100, with a 44.6-point gapbetween the strongest and weakest models; (ii) specialist parsers with <=4Bparameters rival or surpass general VLMs that are 5-100x larger, yet formularecognition remains a shared bottleneck where no model exceeds 67% whenaveraging the formula metric across all three tracks; (iii) general VLMs loseonly 0.99/8.52 Overall points under digital/real degradation versus 4.90/14.21for pipeline specialists, producing ranking reversals that make clean-onlyevaluation misleading for deployment. All data, code, and artifacts arepublicly released.

Implicit neural representations (INRs) encode images as neural-network weights, making image classification a problem of weight-space classifiability. A natural geometric hypothesis is that classifier feedback should make image-specific weights cluster by class in the shared-anchor coordinate. We test this hypothesis in the SIREN-based Meta Weight Transformer (MWT) regime, where end-to-end training meta-learns a shared initialization and inner-loop update schedule for fitting image-specific SIRENs. We find that this prediction fails. Exposed weight-space geometry and supervised clustering pressure do not reliably track trained-reader accuracy; clustering can even make local neighborhoods more class-consistent while making the trained reader worse. Crucially, the reader constructs rather than inherits class-aligned geometry: token-flow diagnostics show that class-aligned neighborhoods become strongly predictive of trained-reader accuracy only after late reader interactions, not in the input coordinate. We further identify the native SIREN bias column in the augmented weight token as a low-dimensional, sample-dependent causal readout route for the trained reader; targeted controls rule out generic scalar-column and marginal-distribution artifacts. The diagnosis motivates interventions that strengthen reader routing, add an explicit bias route, or use denser inner-loop fitting; under the lane-specific training conventions used here, route-directed variants often outperform the shared-anchor baseline but interact non-additively. Task-induced INR weights are classifiable not because they form raw geometric clusters, but because their class signal is routed through the reader.

V2X can warn an autonomous vehicle about hazards beyond line-of-sight, but it also brings uncertainty: messages may be delayed, dropped, or even forged. Meanwhile, map knowledge may change during a trip, forcing the vehicle to replan under tight real-time budgets. This paper studies how to make motion planning and low-level control robust to such uncertain, event-driven updates. We present MORPH-U, a CARLA-based closed-loop stack that fuses LiDAR/radar/camera with V2X (CAM/DENM) into a Local Dynamic Map (LDM) and triggers Hybrid-A* replanning when validated hazards or map changes affect the planned route. We expose the planning/control trade-offs via a multi-objective formulation over tracking error, safety margin (minimum TTC), responsiveness, and smoothness, and select operating points using Pareto-frontier analysis. To avoid unsafe replanning from faulty V2X triggers, MORPH-U adds a lightweight Byzantine-inspired acceptance gate that combines a quorum rule with an on-board sensor veto. Experiments in dynamic CARLA scenarios show that V2X-augmented LDM improves downstream safety, Pareto tuning provides controllable accuracy-comfort trade-offs, and the gate prevents replanning under saturated false-DENM injection ($p_{\text{attack}}=1.0$).

Flight delays impose cascading operational and financial burdens across the aviation network, costing the U.S. economy billions of dollars annually by disrupting interconnected aircraft rotation systems. While prior machine learning approaches have demonstrated strong predictive performance, most treat upstream delays as static input variables rather than explicitly modeling how delays propagate dynamically through aircraft rotation chains, and none have deployed such systems alongside a live weather-aware conversational AI interface for end-user interaction. This paper presents FlightSense, an end-to-end MLOps platform for real-time flight delay prediction built through a progressive three-version feature engineering framework. Version 1 trains an XGBoost classifier on 11 schedule-based features establishing a baseline ROC AUC of 0.732 on 7.07 million BTS 2018 On-Time Performance records. Version 2 introduces 11 delay propagation features derived from aircraft rotation chains via tail-number tracking, yielding the dominant performance gain (AUC 0.732 to 0.875) and surpassing the single-stage XGBoost baseline reported by Zhou (2025). Version 3 integrates five NOAA meteorological features across 10 major U.S. airports, achieving a final test set AUC of 0.879. FlightSense is deployed as a production AWS MLOps pipeline incorporating live weather ingestion via Lambda, real-time SageMaker inference, an interactive Streamlit dashboard, and an Amazon Bedrock Nova Micro conversational assistant answering natural-language delay queries via a tool-use architecture.

Most existing LLM diagnoses are evaluated on static, single-turn settings where complete patient information is provided upfront, an oversimplification of real clinical practice. We study active diagnosis: the real-life clinical process of starting from initial observation, ordering tests, interpreting results, and updating a differential diagnosis across multiple turns. Through systematic analysis, we identify three recurring failure modes in current LLMs: ungrounded test ordering, unreliable diagnostic update, and degraded multi-turn coherence. Together, these failures reveal a core deficit: existing medical training data teaches models to reason from complete information but not to act under evolving, partial evidence. To address this gap, we introduce MedAction, a tree-structured distillation pipeline that synthesizes diverse and high-quality multi-turn diagnostic trajectories via LLM-environment interaction. We propose two knowledge-graph-grounded metrics to filter trajectory quality: Disease Trajectory Consistency (DTC), which tracks whether the model's hypothesis converges toward the correct diagnosis, and Reasoning-Action Consistency (RAC), which verifies that belief updates are driven by gathered evidence. Using this pipeline, we construct MedAction-32K, a dataset of 32,681 trajectories from 2,896 PMC cases. Fine-tuning an 8B model on MedAction-32K achieves state-of-the-art performance among open-source models on both MedR-Bench and our curated MedAction-300-Hard benchmark, pushing the edge for open-source medical LLMs.

Personalized healthcare decisions require reasoning about how physiological and behavioral variables influence an individual patient over time. Existing temporal causal discovery methods are poorly matched to this setting: cohort-level models provide stable but non-personalized structures, while per-patient discovery is unreliable because individual trajectories are short, noisy, irregular, and non-stationary. This creates a fundamental gap between population-level causal modeling and the patient-specific, time-varying mechanisms needed for intervention reasoning. We introduce PerCaM-Health, a framework for learning personalized dynamic causal graphs from longitudinal health data. The framework learns a knowledge-guided population temporal graph, then conservatively adapts and evolves it using patient-specific temporal evidence and rolling-window updates, producing interpretable and auditable graph sequences. By coupling these graphs with temporal structural equations, the framework enables patient-level counterfactual queries, such as estimating short-horizon outcome changes under hypothetical behavioral interventions. Experiments on a semi-synthetic dynamic health benchmark show that PerCaM-Health improves graph recovery, dynamic edge tracking, and intervention direction accuracy compared to cohort-level, per-patient, and non-personalized temporal baselines. These results demonstrate that jointly modeling personalization and temporal evolution yields more reliable causal structure and intervention reasoning.

We present PicoEyes, a unified gaze estimation framework that directly predicts all key attributes of gaze, including 3D eye parameters, eye-region segmentation, optical axis, visual axis, and depth maps, from either monocular or binocular inputs. The framework simultaneously addresses calibration, gaze forecasting, and varying device postures, while also supporting 3D eye reconstruction via joint estimation of eye parameters and depth maps in an end-to-end manner. In addition, we introduce a large-scale multi-view near-eye dataset containing comprehensive 2D and 3D annotations under diverse conditions, including train, test, rewear-test, and calibration sessions. Extensive experiments demonstrate that PicoEyes achieves state-ofthe-art performance, consistently outperforming both academic and industrial gaze tracking methods across nocalibration, calibration, rewear-after-calibration, and forecasting settings. This work establishes a practical, end-toend paradigm for robust and generalizable gaze estimation in mixed reality (MR) applications.

The interaction of robots with bendable objects in midair presents significant challenges in control, often resulting in performance degradation and potential crashes, especially for aerial robots due to their limited actuation capabilities and constant need to remain airborne. This paper presents an adaptive controller that enables two aerial vehicles to collaboratively follow a trajectory while transporting a bendable object without relying on explicit elasticity models. Our method allows on-the-fly adaptation to the object's unknown deformable properties, ensuring stability and performance in trajectory-tracking tasks. We use Lyapunov analysis to demonstrate that our adaptive controller is asymptotically stable. Our method is evaluated through hardware experiments in various scenarios, demonstrating the capabilities of using multirotor aerial vehicles to handle bendable objects.

Architectural code smells erode software maintainability and are costly to repair manually, yet unlike localized bugs, they require cross-module reasoning about design intent that challenges both developers and automated tools. While large language model agents excel at bug fixing and code-level refactoring, their ability to repair architectural code smells remains unexplored. We present the first empirical evaluation of LLM agents on architectural code smell repair. We contribute SmellBench, a task orchestration framework that incorporates smell-type-specific optimized prompts and supports iterative multi-step execution, together with a scoring methodology that separately evaluates repair effectiveness, false positive identification, and net codebase impact. We evaluate 11 agent configurations from four model families (GPT, Claude, Gemini, Mistral) on 65 hard-severity architectural smells detected by PyExamine in the Python project scikit-learn, validated against expert judgments. Expert validation reveals that 63.1% of detected smells are false positives, while the best agent achieves a 47.7% resolution rate. Agents identify false positives with up to $κ= 0.94$ expert agreement, but repair aggressiveness and net codebase quality are inversely related: the most aggressive agent introduces 140 new smells. These findings expose a gap between current LLM capabilities in localized code transformations and the architectural understanding needed for cross-module refactoring. SmellBench provides reusable infrastructure for tracking progress on this underexplored dimension of automated software engineering. We release our code and data at https://doi.org/10.5281/zenodo.19247588.

Aligning large language models (LLMs) to human preferences typically relies on aggregating pooled feedback into a single reward model. However, this standard approach assumes that all labelers share the same underlying preferences, ignoring the fact that real-world labelers are highly heterogeneous and usually anonymous. Consequently, relying solely on binary choice data fundamentally distorts the learned policy, making the true population-average preference unidentifiable. To overcome this critical limitation, we demonstrate that augmenting preference datasets with a simple, secondary signal -- the user's response time -- can restore the identifiability of the population's average preference. By modeling each decision as a Drift-Diffusion Model (DDM), we introduce a novel, consistent estimator of heterogeneous preferences that successfully corrects the distortions of standard choice-only labels. We prove that our estimator asymptotically converges to the true average preference even in extreme cases where each anonymous labeler contributes only a single choice. Empirically, across both synthetic and real-world datasets, our method consistently outperforms standard baselines that otherwise fail and plateau at a bias floor. Because response times are essentially free to record and require zero user tracking or identification, our results bring promises and open up new opportunities for future data-collection pipelines to improve the social benefit without requiring user-level identifiers or repeated elicitations.

We augment the Slotine--Li adaptive controller for Euler--Lagrange systems with three learned components: a structured-quadratic Lyapunov function $V_ψ$ whose positive-definiteness follows from a Cholesky parameterization, a residual Soft Actor--Critic policy that adds bounded torque corrections to the analytic baseline, and a physics-informed neural network that estimates unmodeled dynamics. A closed-form safety filter, derived from the single affine constraint $\dot V_ψ+ αV_ψ\le 0$, projects every policy output onto the safe set without requiring an online QP solver. We prove: global feasibility of the filter under a drift-decay condition on the control-degeneracy set; exponential stability under exact shielding, with a robust extension whose margin depends on the PINN approximation error; almost-sure convergence of the three-timescale policy--certificate--multiplier updates to a KKT point; and a PAC generalization bound for the certificate over compacts. On a 2-DOF manipulator with nonlinear friction and variable payload, the learned certificate accounts for most of the empirical gain: tracking error drops by 41% on nominal friction and 24% on aggressive friction at the centroid of the training distribution. A 7-DOF scalability study on a Franka Emika Panda confirms clean convergence of the full pipeline at industrial scale, identifies the conditions under which gains over exact model-based baselines should and should not be expected, and documents a warm-start pathology of the learned certificate that has practical implications for deployment.

Synthesizing consistent and coherent long video remains a fundamental challenge. Existing methods suffer from semantic drift and narrative collapse over long horizons. We present A$^2$RD, an Agentic Auto-Regressive Diffusion architecture that decouples creative synthesis from consistency enforcement. A$^2$RD formulates long video synthesis as a closed-loop process that synthesizes and self-improves video segment-by-segment through a Retrieve--Synthesize--Refine--Update cycle. It comprises three core components: (i) Multimodal Video Memory that tracks video progression across modalities; (ii) Adaptive Segment Generation that switches among generation modes for natural progression and visual consistency; and (iii) Hierarchical Test-Time Self-Improvement that self-improves each segment at frame and video levels to prevent error propagation. We further introduce LVBench-C, a challenging benchmark with non-linear entity and environment transitions to stress-test long-horizon consistency. Across public and LVBench-C benchmarks spanning one- to ten-minute videos, A$^2$RD outperforms state-of-the-art baselines by up to 30% in consistency and 20% in narrative coherence. Human evaluations corroborate these gains while also highlighting notable improvements in motion and transition smoothness.

Large language models are now embedded in everyday writing workflows, making reliable AI-generated text detection important for academic integrity, content moderation, and provenance tracking. In practice, however, a detector must do more than achieve high aggregate AUROC on clean, in-distribution human and AI text: it should remain robust to attacks and adversarial rewrites, transfer to unseen generators and domains, and operate at low false-positive rates (FPR). Most existing detectors optimize a single AI/Human objective, giving the representation little incentive to learn generator, attack, or domain structure once the binary task saturates. We introduce MELD (Multi-Task Equilibrated Learning Detector), a deployable detector for AI-generated text that enriches binary detection with auxiliary supervision. MELD attaches generator-family, attack-type, and source-domain heads to a shared encoder, and balances the four losses with learned homoscedastic uncertainty weights. To improve robustness, an EMA teacher predicts on clean inputs while an attack-augmented student is distilled toward the teacher. MELD further uses a hard-negative pairwise ranking loss to enlarge the score margin between AI-generated texts and the most confusable human texts. At inference, all auxiliary heads are discarded, giving MELD the same interface and cost as a standard detector. On the public RAID leaderboard, MELD is the strongest open-source detector and is competitive with leading commercial models, especially under attack and at low FPR. Across standard held-out benchmarks, MELD matches or outperforms supervised baselines. We further introduce MELD-eval, a held-out evaluation pool built from recent chat models released by four major LLM providers. Without additional finetuning, MELD achieves 99.9% TPR at 1% FPR on MELD-eval, while many baselines degrade sharply.

Adversarial robustness has been studied extensively for offline deep networks, but less is known about strict single-pass streaming neural learners. This paper studies adversarial robustness in Fuzzy ARTMAP, an Adaptive Resonance Theory architecture based on category competition, complement coding, match tracking, and replay-free prototype updates. We introduce WB-Softmax, a differentiable white-box attack surrogate aligned with ARTMAP's category-competition and map-field prediction mechanism, and formalize a streaming evaluation principle requiring robustness to be assessed on the final deployed model. Across four image benchmarks, WB-Softmax achieves 89-100% attack success on vanilla Fuzzy ARTMAP models. We show that defense rankings can reverse across protocols: offline adversarial training may appear strong under transfer attacks yet collapse under adaptive white-box evaluation, whereas progressive two-stage selective training provides the strongest overall replay-free robustness. We further show that ART's explicit category geometry enables interpretable diagnosis of separation collapse and match-score inversion. These results provide a mechanism-aligned, protocol-aware framework for adversarial robustness in streaming prototype-based learners.

The rise of Internet of Things (IoT) devices in the physical world necessitates voice-based interfaces capable of handling complex user experiences. While modern Large Language Models (LLMs) already demonstrate strong tool-usage capabilities, modeling real-world IoT devices presents a difficult, understudied challenge which combines modeling spatiotemporal constraints with speech inputs, dynamic state tracking, and mixed-initiative interaction patterns. We introduce MIST (the Multimodal Interactive Speech-based Tool-calling Dataset), a synthetic multi-turn, voice-driven code generation task that operates over IoT devices. We find that there is a significant gap between open- and closed-weight multimodal LLMs on MIST, and that even frontier closed-weight LLMs have substantial headroom. We release MIST and an extensible data generation framework to build related datasets in order to facilitate research on mixed-initiative voice assistants which reason about physical world constraints.

We contribute Bi3, a dataset of social robot navigation among groups of people in a constrained lab space. Compared to prior data collection efforts for social robot navigation, our dataset is unique in that it features: an original experiment design giving rise to close navigation encounters between two humans and a robot; five different navigation algorithms; two different robot platforms; a diverse participant pool of 74 people recruited from two sites in the USA and France; multimodal data streams including 10.5 hours of human and robot ground-truth motion tracks, RGB video, and user impressions over robot performance. Our analysis of the collected dataset through metrics like interaction density and human velocity suggests that Bi3 represents a benchmark of unique diversity and modeling complexity. Bi3 contributes towards understanding how humans and robots can productively mesh their activities in constrained environments, and can be a resource for training models of human motion prediction and robot control policies for navigation in densely crowded spaces.

In model-based learning, the agent learns behaviors by simulating trajectories based on world model predictions. Standard world models typically learn a stationary transition function that maps states and actions to next states, when an action and an outcome frequently co-occur in training data, the model tends to internalize this correlation as a general causal rule while ignoring action preconditions. In interactive environments, however, agent actions can reshape the future affordance space. At each timestep, an action may becomes executable only after its prerequisites are met, or non-executable when they are destroyed. We term such events structure-changing events (SC events). As a result, a conventional world model often fails to determine whether a given action is executable in the current state, especially in multi-step predictions. Each imagined step is conditioned on an incorrect affordance state, and therefore the prediction error compounds over the rollout horizon. In this paper, we propose AGWM (Affordance-Grounded World Model), which learns an abstract affordance structure represented as a DAG of prerequisite dependencies to explicitly track the dynamic executability of actions. Experiments on game-based simulated environments demonstrate the effectiveness of our method by achieving lower multi-step prediction error, better generalization to novel configurations, and improved interpretability.

Cohen et al. (arXiv:2207.14484) observed that adaptive gradient methods such as Adam operate at the edge of stability. While there has been significant work on continuous-time modeling of gradient descent at the edge of stability, extending these models to momentum methods remains underdeveloped. In the gradient descent setting, Regis et al. (arXiv:2602.01480) introduced rod flow, which models consecutive iterates as an extended one-dimensional object -- a "rod." Here we extend rod flow to Adam by working in the joint phase space of parameters and first moment $(w, m)$ and treating the second moment $ν$ as a smooth auxiliary variable. We also develop rod flows for heavy ball momentum, Nesterov momentum, and scalar and per-component versions of RMSProp, Adam, and NAdam. For all eight optimizers, we empirically evaluate rod flow on representative machine learning architectures, where it tracks the discrete iterates through the edge-of-stability regime significantly more accurately than the corresponding stable flow.

Eye movement biometrics (EMB) use subject-specific gaze dynamics for user authentication and identification. Recent deep learning-based EMB systems achieve strong performance by modeling temporal eye movement behavior. However, these systems typically overlook continuous gaze offset, despite prior evidence that it contains user-discriminative information. This work examines whether continuous gaze offset can improve biometric performance when combined with existing biometric features. We evaluate linear and nonlinear fusion methods on two publicly available datasets, collected via the lab-grade eye tracker and virtual reality headset across multiple tasks and observation durations. Results indicate that fusion offers performance benefits on both datasets, particularly when using nonlinear fusion. Additionally, fusing biometric information across multiple tasks further improves authentication performance. These findings support the hypothesis that continuous gaze offset may serve as useful auxiliary information under conditions of degraded or noisy eye tracking.

We introduce the AI co-mathematician, a workbench for mathematicians to interactively leverage AI agents to pursue open-ended research. The AI co-mathematician is optimized to provide holistic support for the exploratory and iterative reality of mathematical workflows, including ideation, literature search, computational exploration, theorem proving and theory building. By providing an asynchronous, stateful workspace that manages uncertainty, refines user intent, tracks failed hypotheses, and outputs native mathematical artifacts, the system mirrors human collaborative workflows. In early tests, the AI co-mathematician helped researchers solve open problems, identify new research directions, and uncover overlooked literature references. Besides demonstrating a highly interactive paradigm for AI-assisted mathematical discovery, the AI co-mathematician also achieves state of the art results on hard problem-solving benchmarks, including scoring 48% on FrontierMath Tier 4, a new high score among all AI systems evaluated.

Bayesian model calibration is central to digital twins and computer experiments, as it aligns model outputs with field observations by estimating calibration parameters and correcting systematic model bias. Classical Bayesian calibration introduces latent parameters and a discrepancy function to model bias, but suffers from parameter--discrepancy confounding and is typically formulated as an offline procedure under a stationary data-generating assumption. These limitations are restrictive in modern digital twin applications, where systems evolve over time and may exhibit gradual drift and abrupt regime shifts. While data assimilation methods enable sequential updates, they generally do not explicitly model systematic bias and are less effective under abrupt changes. We propose Bayesian Recursive Projected Calibration (BRPC), an online Bayesian calibration framework for streaming data under simulator mismatch and nonstationarity. BRPC extends projected calibration to the online setting by separating a discrepancy-free particle update for calibration parameters from a conditional Gaussian process update for discrepancy, preserving identifiability while enabling bias-aware adaptation under gradual system evolution. To handle abrupt changes, BRPC is integrated with restart mechanisms that detect regime shifts and reset the calibration process. We establish theoretical guarantees for both components, including tracking performance under gradual evolution and false-alarm and detection behavior for restart mechanisms. Empirical studies on synthetic and plant-simulation benchmarks show that BRPC improves calibration accuracy under gradual changes, while restart-augmented BRPC further improves robustness and predictive performance under abrupt regime shifts compared to sliding-window Bayesian calibration and data assimilation baselines.

Retargeting human kinematic reference motion onto a robot's morphology remains a formidable challenge. Existing methods often produce physical inconsistencies, such as foot sliding, self-collisions, or dynamically infeasible motions, which hinder downstream imitation learning. We propose a bilevel optimization framework that jointly adapts reference motions to a robot's morphology while training a tracking policy using reinforcement learning. To make the optimization tractable, we derive an approximate gradient for the upper-level loss. Our framework requires only a sparse set of semantic rigid-body correspondences and eliminates the need for manual tuning by identifying optimal values for a parameterization expressive enough to preserve characteristic motion across different embodiments. Moreover, by integrating retargeting directly with physics simulation, we produce physically plausible motions that facilitate robust imitation learning. We validate our method in simulation and on hardware, demonstrating challenging motions for morphologies that differ significantly from a human, including retargeting onto a quadruped.

We study online prediction under distribution shift, where inputs arrive chronologically and outcomes are revealed only after prediction. In this setting, predictors must remain stable in quiet regimes yet adapt when regimes shift, and the right adaptation memory is unknown in advance. We propose MELO (Memory-hedged Exponentially Weighted Least-Squares Online aggregation), a model-agnostic method that hedges across adaptation scales: it wraps any non-anticipating base-predictor pool with exponentially weighted least-squares (EWLS) adaptation experts at multiple forgetting factors, and aggregates raw and EWLS-adapted forecasts with MLpol, a parameter-free online aggregation rule. Under boundedness conditions, we establish deterministic oracle inequalities showing that it competes with both the best raw predictor and the best bounded, time-varying affine combinations of the base predictions, up to a path-length-dependent tracking cost and a sublinear aggregation overhead. We evaluate MELO on French national electricity-load forecasting through the COVID-19 lockdown using no regime indicators, lockdown dates, or policy covariates. MELO reduces overall RMSE by 34.7% relative to base-only MLpol and achieves lower overall RMSE than a TabICL reference supplied with an external COVID policy-response covariate. Moreover, MELO requires only lightweight per-step recursive updates without model retraining.

We introduce PACZero, a family of PAC-private zeroth-order mechanisms for fine-tuning large language models that delivers usable utility at $I(S^*; Y_{1:T})=0$. This privacy regime bounds the membership-inference attack (MIA) posterior success rate at the prior, an MIA-resistance level the DP framework matches only at $\varepsilon=0$ and infinite noise. All DP-ZO comparisons below are matched at the MIA posterior level. The key insight is that PAC Privacy charges mutual information only when the release depends on which candidate subset is the secret. Sign-quantizing subset-aggregated zeroth-order gradients creates frequent unanimity, steps at which every candidate subset agrees on the update direction; at these steps the released sign costs zero conditional mutual information. We propose two variants that span the privacy-utility trade-off: PACZero-MI (budgeted MI via exact calibration on the binary release) and PACZero-ZPL ($I=0$ via a uniform coin flip on disagreement steps). We evaluate on SST-2 and SQuAD with OPT-1.3B and OPT-6.7B in both LoRA and full-parameter tracks. On SST-2 OPT-1.3B full fine-tuning at $I=0$, PACZero-ZPL reaches ${88.99\pm0.91}$, within $2.1$pp of the non-private MeZO baseline ($91.1$ FT). No prior method produces usable utility in the high-privacy regime $\varepsilon<1$, and PACZero-ZPL obtains competitive SST-2 accuracy and nontrivial SQuAD F1 across OPT-1.3B and OPT-6.7B at $I=0$.

Optimizers that exploit the matrix structure of gradients are central to modern LLM pre-training, with two distinct frontiers: explicit Kronecker-factored preconditioning -- most recently KL-Shampoo, which estimates the preconditioner via KL divergence minimization -- and orthogonalization of the gradient momentum, exemplified by Muon and analyzed as steepest descent under the spectral norm. The two routes are typically developed in isolation. We make a structural observation about KL-Shampoo's Kronecker preconditioners: their eigenvalue spectra exhibit a \emph{spike-and-flat} shape -- a few dominant eigenvalues followed by an approximately uniform tail -- across layers and training stages, holding exactly under a rank-$ρ$ signal-plus-noise gradient model. We exploit this structure by restricting one of KL-Shampoo's Kronecker factors to a parametric family aligned with the spike-and-flat shape: full spectral structure on a tracked $r$-dimensional subspace, single shared eigenvalue across the remaining $n-r$ directions. On these directions, we apply orthogonalization. An identity shows that this orthogonalization recovers the algebraic form of full KL-Shampoo's preconditioner. On four pre-training scales (GPT-2 124M / 350M, LLaMA 134M / 450M), Pro-KLShampoo consistently outperforms KL-Shampoo at every subspace rank we test in validation loss, peak per-GPU memory, and wallclock time to reach each loss level.

It remains unclear whether graph language models learn structural regularities or merely memorize training graphs; this cannot be resolved by current aggregate fidelity metrics alone. We develop a calibrated diagnostic protocol that combines frequent subgraph mining, a graph-level bootstrap baseline, and three-level frequency stratification to disentangle memorization from structural alignment. Using this framework, we show that graph language models can acquire structural regularities beyond memorization at scale, primarily in the high-frequency regime. This is supported by the following empirical evidence: On five TU benchmarks, LLaMA-style graph language models reach high subgraph-rank correlation, yet their alignment is matched or exceeded by the memorization bootstrap in most cases. At small scale, under our bootstrap diagnostic, fidelity is largely indistinguishable from verbatim recall. In contrast, at large scale with 3.75M graphs, verbatim memorization drops sharply while rank correlation remains near ceiling. Crucially, in a separate fixed-subsample analysis, frequent subgraph mining restricted to the novel-only subset closely tracks the corresponding all-generation Spearman correlation, providing evidence that the alignment is not driven solely by verbatim recall. Across all scales, high-frequency patterns are well reproduced, while rare patterns remain poorly covered, and this deficit narrows only marginally as capacity increases. We observe the same scale-dependent crossover under two distinct graph serializations (canonical DFS code and action sequences), providing evidence of robustness in our analysis.

Scaling Diffusion Transformers (DiTs) to hundreds of layers introduces a structural vulnerability: networks can enter a silent, mean-dominated collapse state that homogenizes token representations and suppresses centered variation. Through mechanistic auditing, we isolate the trigger event of this collapse as Mean Mode Screaming (MMS). MMS can occur even when training appears stable, with a mean-coherent backward shock on residual writers that opens deep residual branches and drives the network into a mean-dominated state. We show this behavior is driven by an exact decomposition of these gradients into mean-coherent and centered components, compounded by the structural suppression of attention-logit gradients through the null space of the Softmax Jacobian once values homogenize. To address this, we propose Mean-Variance Split (MV-Split) Residuals, which combine a separately gained centered residual update with a leaky trunk-mean replacement. On a 400-layer single-stream DiT, MV-Split prevents the divergent collapse that crashes the un-stabilized baseline; it tracks close to the baseline's pre-crash trajectory while remaining substantially better than token-isotropic gating methods such as LayerScale across the full schedule. Finally, we present a 1000-layer DiT as a scale-validation run at boundary scales, establishing that the architecture remains stably trainable at extreme depth.

Discrete image tokenizers are commonly trained in two stages: first for reconstruction, and then with a prior model fitted to the frozen token sequences. This decoupling leaves the tokenizer unaware of the model that will later generate its tokens. As a result, the learned tokens may preserve image information well but still be difficult for an autoregressive (AR) prior to predict from left to right. We analyze this mismatch using Tripartite Variational Consistency (TVC), which decomposes latent-variable learning into three consistency conditions: conditional-likelihood consistency, prior consistency, and posterior consistency. TVC shows that two-stage training preserves the reconstruction side but leaves prior consistency outside the tokenizer objective: the overall token distribution is fixed before the AR prior participates in training. Motivated by this view, we add a distribution-level prior-matching signal during tokenizer training, while keeping the reconstruction objective unchanged. We optimize this signal with a Wasserstein-gradient-flow update. For hard categorical tokens, the update reduces to a token-level contrast between an auxiliary AR model that tracks the tokenizer's current token distribution and the target AR prior. It requires only forward passes through the two AR models and does not backpropagate through either of them. The resulting tokenizer, wAR-Tok, reduces AR loss and improves generation FID on CIFAR-10 and ImageNet at comparable reconstruction quality.

Augmented Lagrangian and optimistic primal--dual methods stabilize equality-constrained optimization through seemingly different mechanisms: the former adds constraint-dependent primal curvature, while the latter adds dual memory. Recent work has shown that these mechanisms are equivalent for scalar parameters. We extend this equivalence to matrix-valued correction. We prove an additivity principle: for symmetric matrix parameters, the ideal primal trajectory depends only on the summed correction matrix, not on how it is split between augmented and optimistic channels. This exposes a design freedom: algebraically equivalent decompositions can have different finite-step feasibility because augmented correction affects primal curvature, whereas optimistic correction affects the scale of the dual memory correction. We formulate the resulting step-size-limited design problem and derive a closed-form hybrid rule that selects a matrix correction, splits it between the two channels, and chooses primal and dual steps using local spectral weights. Experiments on nonlinear equality-constrained problems with controlled constraint-Jacobian conditioning show that the hybrid design improves over pure augmented and pure optimistic endpoints, closely tracks a grid-search hybrid oracle, and is competitive with first-order primal--dual baselines under mild-to-moderate ill-conditioning. The experiments also identify the expected limitation: exact cancellation requires increasingly large matrix corrections as the constraint Jacobian becomes ill-conditioned.

The "Locate-then-Update" paradigm has become a predominant approach in the post-training of large language models (LLMs), identifying critical components via mechanistic interpretability for targeted parameter updates. However, this paradigm rests on a fundamental yet unverified assumption: can mechanisms derived from current static parameters reliably guide future dynamic parameter updates? To investigate this, we systematically track the structural evolution of Transformer circuits throughout the supervised fine-tuning (SFT) process, revealing the underlying dynamics of task mechanisms. We introduce three novel metrics-Circuit Distance, Circuit Stability, and Circuit Conflict-to analyze circuit evolution across three dimensions: neural migration, semantic stability, and cross-task interference. Our empirical results reveal that circuits inherently exhibit "Free Evolution" during parameter updates. Consequently, static mechanisms extracted from current states inevitably suffer from temporal latency, making them fundamentally inadequate for guiding future states. Moreover, by deconstructing the "illusion of effectiveness" in existing methods, this work underscores the necessity of "foresight" in mechanistic localization and proposes a predictive framework for future research.