Papers

Supervised fine-tuning (SFT) on offline agent trajectories is the standard approach for training specialized tool-using agents, but forcing models to imitate reasoning and actions token by token may harm other capabilities (e.g., general reasoning, tool calling, code generation) of the base model. In this work, we focus on studying how to better balance the trade-off between acquiring new capabilities and preserving existing ones during agent trace SFT. By comparing several baselines in our setup, standard SFT improves the target benchmark while lowering several non-target benchmark scores; meanwhile, simply constraining distributional drift using KL penalty or limiting the update magnitude did not avoid this regression trend. Motivated by recent token-wise adaptive learning objectives, this work proposes Privilege-Guided SFT (PG-SFT) to leverage turn-level information gain of agent trajectories as an indicator to adjust supervision strength. PG-SFT yields a more favorable observed trade-off on the evaluated benchmarks, substantially reducing distributional drift and broad capability degradation at the cost of slight degradation in target-task performance. Our findings suggest that balancing the acquisition–retention trade-off depends not only on whether the model is anchored to its base behavior, but also on where and how strongly supervision should depart from that behavior.}

The executable harness surrounding a GUI model determines how observations are assembled, actions are executed, and verification, recovery, and termination are controlled. Compared with harness optimization for non-GUI agents, automatically optimizing this harness poses three coupled challenges: reconciling model intent with observed visual effects, diagnosing failures under variable execution outcomes, and identifying recurrent failure patterns across tasks and translating them into reusable runtime changes. We introduce GUI-HARVEST, an automatic harness optimizer that enables self-improving GUI agents with frozen backbone models. First, to ground diagnosis in observed action effects, it aligns model outputs and executed actions with before-and-after screenshots, tying findings to specific interface transitions. Second, to account for execution variability, it treats repeated runs of the same task as a joint evidence unit, using within-task comparisons to locate outcome-relevant behavioral differences. Third, it consolidates verified findings across tasks into recurring failure patterns, maps them to bounded source-code edits with predictions recorded before evaluation, and checks the predicted behavioral effects alongside task performance through repeated execution. Experiments on OSWorld-Verified show consistent held-out gains across six general-purpose open, GUI-specialized open, and proprietary backbone models; Qwen3-VL-32B-Instruct gains 12.33 points on the full suite. Frozen-harness transfer improves GPT-5 by 13.87 percentage points on WindowsAgentArena at 50 steps without further optimization. With the same backbone and initial harness, GUI-HARVEST outperforms Self-Harness and Meta-Harness, suggesting that GUI-specific diagnosis and validation help harness improvements generalize to unseen tasks. The code is available at https://github.com/GaryYang12345/GUI-HARVEST.

ABDA-NL adds a natural-language interface to ABDA, a system for argument-based discussion using ASPIC- knowledge bases under grounded semantics. Users see which conclusions are accepted, rejected, or undecided, open an interactive rendering of the grounded discussion game to learn why, explore what-if alternatives by suspending assumptions and rules or changing preferences, ask questions that are answered from a scenario's reference documents, and author new facts, assumptions, and rules in plain English. A large language model provides the bridge between language and formalism: it answers questions from the documents and the current state of the scenario, and it translates plain-English edits into candidate formal statements. The deterministic ABDA engine remains the sole source of arguments, attacks, and acceptance labels, and every proposal of the model is validated and confirmed by the user before it takes effect.

In this paper, we construct an explicit correspondence between Engel and Pierce expansion digit sequences, obtained by adding $n-2$ to the $n$th Engel expansion digit, and show that it induces a homeomorphism from the set of irrationals in the unit interval onto the complement of a countable dense subset of this set. This yields a transfer principle for Baire category between the two expansions, and we determine exactly which Borel classes are preserved. We then identify this homeomorphism with the composition of two maps considered by Moroz (2027), and study the continuity of the second map, which sends modified Engel expansions to Pierce expansions. We determine its set of discontinuities, show that every discontinuity is a jump, and prove that the map is nowhere monotone. In particular, this confirms, for this map, the nowhere monotonicity and the continuity outside the exceptional set conjectured by Moroz (2027). As applications, we characterize the non-increasing position-dependent weights for which the associated series of Pierce expansion digits diverges on a comeager set, and we relate the convergence exponents of the Engel and Pierce expansion digit sequences.

One of the most important initial steps in quantum computing is high-fidelity quantum state preparation, because errors in it can affect the final computational result. Therefore, one of the major challenges is to design a quantum circuit that can achieve the desired target state accurately with a smaller number of gates. Traditionally, circuits are designed using predefined rules and mathematical decompositions, but this makes it difficult to design circuits for different and complex target states. This paper presents TATVA, a reinforcement learning (RL) system for synthesizing quantum circuits. TATVA views circuit synthesis as a sequential decision problem in which the agents select one gate at a time and calculate the fidelity after each applied gate, with the gate producing the highest fidelity selected for the circuit. The system introduces a parallel architecture that uses two RL agents, Deep Q-Network (DQN) and Proximal Policy Optimization (PPO), along with Qiskit's statevector simulator. The system can synthesize up to 5 qubits while achieving a fidelity of 0.999999 and producing compact circuits. After achieving the desired fidelity, it performs a post-hoc optimization step that reduces the circuit depth while preserving the achieved fidelity. The circuit is finalized using fidelity, success rate, gate count, and circuit depth. Target states that are not used during training are used to test whether the system has learned effectively and can generalize beyond the training states. This approach aims to enable automatic quantum circuit synthesis with high fidelity using reinforcement learning.

Traditional guided wave methods for structural health monitoring typically assume uniform material properties, which limit their ability to characterize heterogeneous structures with spatially varying thickness, damage, or material properties. These are challenges commonly encountered in corrosion assessment, composite delamination detection, and structural degradation monitoring. This paper presents a wave physics-informed regression approach that enables spatially resolved characterization of material properties by extracting local dispersion curves across a structure. Our approach focuses on a highly interpretable but flexible physics-informed framework that can be solved using fast algorithms and achieve robust numerical solutions. This paper discusses the mathematical design of the framework, the algorithm, and its interpretation. The framework was applied to a guided wave wavefield imaging dataset from a thin aluminum plate with non-uniform thickness around a hole to validate its practicality. The framework creates an accurate thickness map (correlation coefficient 0.94 with x-ray CT validation) as well as extracts the frequency-dependent velocities of waves within those regions.

We present CAFES, a correlation-aware agentic framework for electronic-structure simulations of strongly correlated systems. CAFES addresses two challenges: the fragmented software landscape for many-body calculations and the difficulty of selecting appropriate methods across diverse correlation regimes. It combines correlation diagnostics, adaptive method selection, and large language model (LLM) assistance for molecular, crystalline, and model-Hamiltonian systems. A study-task architecture separates study-level planning from task-level execution, while a curated scientific knowledge layer provides reusable guidance for method selection, workflow design, and result interpretation. We demonstrate CAFES through three research-level studies: calculating the low-lying electronic states of lutein using DMRG-CASSCF, probing phase competition in the extended honeycomb Hubbard model using DMET, and generating a quantum-chemical dataset with CCSD labels. These calculations demonstrate the potential of agentic workflows for strongly correlated electronic-structure problems, a regime that has received limited attention in existing agentic computational frameworks.

Given a $\mathbb{Q}$-Gorenstein normal projective Calabi-Yau variety $Y$ with ordinary double points as singularities and a small crepant resolution $\pi\colon X\to Y$ with $X$ in the Fujiki class $\mathcal{C}$, we establish uniform estimates away from the exceptional locus where the given metrics may degenerate. When $Y$ is a threefold, we prove that these metrics also converge in a Gromov-Hausdorff sense to the metric completion of $Y$ on the regular locus. In particular, our results extend the work of Song on a conjecture of Candelas and de la Ossa.

The viewshed of a point $v$ on a grid terrain $T$, viewshed$_T(v)$, is defined as the set of grid points in $T$ that are visible from $v$. We describe a novel algorithm for computing viewshed$_T(v)$ using a multi-resolution approach: Given a parameter $k >1$ that represents the block size, we create a grid $T'$ which is a lower-resolution version of $T$, such that each point in $T'$ corresponds to a block of $\lceil \sqrt k \rceil $-by-$\lceil \sqrt k \rceil$ points in $T$. The key of our approach is using $T'$ to speed up the computation of viewshed$_T(v)$ while not introducing approximation. We compute viewshed$_T(v)$ in two steps: First we compute the viewshed of $v$ on $T'$, while maintaining the invariant that any block in $T'$ that is labeled as invisible may not contain any visible points. Thus, the first step's role is to use $T'$ to filter out blocks in $T$ that are guaranteed to be invisible. The second step considers the blocks that were labeled as visible in $T'$ and computes the visibility of their points with full accuracy using the data in $T$. Overall the algorithm runs in $O(n + \frac nk \lg \frac nk + k \lg k + l \cdot \lg n)$, where $l$ is the total size of visible blocks in $T'$. When $k = \Omega(1)$ and $l = o(n) $, the running time of our algorithm improves on the previous best bound of $O(n \lg n)$. Our experimental results show the performance of the new algorithm in practice and a speedup of more than an order of magnitude compared to previous algorithms.

We propose ReHoPER, an inference-only, zero-shot method that improves large language models' reasoning by generating and answering intermediate questions along multiple paths before the final answer. It iteratively plans a horizon of candidate intermediate questions, selects one to answer, and replans from the updated history. ReHoPER is task-agnostic, using the same generic instructions across datasets and models without labeled data or task-specific prompt design. Across multiple datasets, including iLLC, a new controlled benchmark for compositional reasoning, ReHoPER outperforms strong baselines, with the largest gains in the most compositional settings. Our implementation and the iLLC generator are publicly available to support future work.

The cyclic steepest descent method computes the exact steepest descent stepsize at the start of each cycle and reuses it for a fixed number $m$ of iterations. For strictly convex quadratics in $n$ variables, it has been suggested that the method converges $R$-superlinearly whenever $m\ge(n+1)/2$. We show that this cannot hold for every initial point, already at the threshold cycle length. For $n=m=2$ we exhibit an initial point from which the method follows the classical zigzag trajectory of steepest descent: the stepsize never changes and the error is halved at every iteration. The same mechanism yields linearly convergent trajectories for every Hessian with at least two distinct eigenvalues and every cycle length. For $n=3$ and $m=2$ we construct a second, genuinely three-dimensional counterexample: all components of the gradient remain nonzero, consecutive cycles use two different stepsizes, and every four iterations reduce the gradient exactly by the factor $1/49$. Both trajectories are given in closed form. Consequently, any $R$-superlinear convergence result for this method at the threshold must exclude a set of initial points, as recent almost-everywhere results do.

We prove that every event invariant under swaps has probability zero or one for either the free or the wired spanning forest on any connected, locally finite, infinite network. Applications include the constancy of the number of components and of the total number of excessive ends. For the free forest, these results resolve longstanding questions of Benjamini, Lyons, Peres, and Schramm [Ann. Probab. (2001), Question 15.7] on constancy of the component count and of Lyons, Morris, and Schramm [Electron. J. Probab. (2008), Question 7.7] on the zero-one law for one-endedness. In the latter case, we obtain the stronger conclusion that the total number of excessive ends is deterministic.

Let $A$ be a string algebra. We identify its Gorenstein-projective support $\tau$-tilting pairs with a distinguished class of maximal good collections and give a finite compatibility graph for them. Under the G-condition, we construct an explicit labelled tiled-surface model for $\mathrm{End}_A(T)$ for every nonzero basic Gorenstein-projective module $T$. Under the same condition, we show that $A$ is representation-finite if and only if $\End_A(T)$ is representation-finite for every basic Gorenstein-projective module $T$.

With the global population rapidly aging, maintaining independence in Activities of Daily Living (ADLs), particularly bathing or showering, has become a critical challenge. Older adults who sit while showering currently have limited options, often relying on rigid overhead showerheads or flexible hand-held hoses that require continuous gripping and precarious user maneuvers, increasing the risk of falls. To address this need, this paper introduces a highly articulated, pseudo-static balanced continuum mechanism designed specifically for accessible bathing assistance. The proposed mechanism features a modular continuum architecture composed of friction-locked ball-and-socket joints (loc-line), seamlessly integrated with a retractable spring-loaded reel for effective gravity compensation. This hybrid design achieves an intuitive "Push-and-Stay" interaction logic, maintaining an approximate static equilibrium with ergonomically low actuation force, without any external electronic power, while significantly minimizing the force needed for repositioning. Theoretically, we established a recursive forward kinematics framework to construct the geometric model of the structure, coupled with a comprehensive static equilibrium analysis to evaluate the system's holding capacity across its 51-DOF structure. Numerical simulations utilizing Monte Carlo methods validate the system's morphological adaptability and stability at various extreme positions within a standard bath space. Physical experiments further validate the prototype's real-world performance, confirming its intrinsic static stability against gravity and ensuring that the actuation force remains well within the ergonomic capabilities of older adults. Ultimately, this research provides a low-cost, intrinsically safe showerhead design that reduces physical strain, restoring dignity and autonomy in personal hygiene.

Embodied assistants in domestic environments must infer what happened, where and when it occurred, and how to respond. To address this, we introduce RMS-AQA, a spatial audio question answering (SAQA) benchmark for real-world domestic environments. The benchmark features a two-stage question-answering (QA) format to comprehensively assess the ability of audio-language models (ALMs) to first ground audible sound events and subsequently perform complex spatio-temporal reasoning based on that grounding. To maximize acoustic realism, our dataset combines authentic real-world first-order Ambisonics (FOA) recordings with high-fidelity synthetic data generated using measured room impulse responses (RIRs). Furthermore, we provide a lightweight spatial plug-in that injects FOA-format data into frozen audio-language backbones. Experimental results reveal that the primary challenges stem from concurrent sources, far distance, and sim-to-real domain gap between RIR-synthesized and authentic recordings.

We examine the relationship between trees and narrow systems. In particular, we prove that if a tree of height $\kappa$ admits a narrow subsystem, it must contain a well-pruned subtree of height $\kappa$. We extend these results to two-cardinal trees.

Research on modelling peer effects has predominantly relied on linear-in-means models. However, averaging peer responses prevents these models from capturing the effects of extreme peer behavior. To address this limitation, we propose a quantile social autoregressive model based on a novel quantile social norm, which uses empirical quantiles of peer responses. By treating the quantile level as an unknown parameter estimated directly from the data, our approach identifies which segment of the peer response distribution most strongly influences individual behavior. To estimate the model, we introduce new moment conditions using pseudo-response instruments. Because the quantile social norm is nonsmooth, we apply kernel smoothing to the instruments and residuals, ensuring valid statistical inference. Additionally, we establish equilibrium existence and uniqueness and derive the identification conditions. Furthermore, we prove the consistency and asymptotic normality of our proposed estimator. Finally, Monte Carlo experiments examine the finite-sample performance of the estimator, and an empirical application illustrates the interpretation of the estimated quantile levels and their corresponding peer effects.

We present a continuous Galerkin, Deferred Correction (cG-DeC) method for the equations of Lagrangian hydrodynamics. The proposed scheme combines a high-order continuous finite element discretization with an explicit Deferred Correction time integrator, yielding a formulation that avoids the inversion of a global sparse mass matrix at each update. To stabilize the method in the presence of strong shocks we introduce a modification of the hyperviscosity model that is compatible with the cG-DeC framework and likewise does not require a global solve to construct the finite element approximation to the polyharmonic operator. We further present an alternative reformulation of the DeC iteration which admits a simple recursive algorithmic structure and provides insight into previously observed convergence behavior of explicit DeC applied to hyperbolic partial differential equations. Conservation of momentum and total energy of the resulting fully discrete scheme is analyzed. A set of numerical experiments illustrates the accuracy and robustness of the cG-DeC scheme. Comparisons with a continuous Galerkin Runge-Kutta (cG-RK) method are provided.

We investigated the nucleation, growth, and solid-to-solid phase transition processes of spherical six-fold symmetric crystals (C6) and ten-fold symmetric quasicrystals (DQC) using the Lifshitz-Petrich model. By combining the spherical-harmonic pseudospectral method with a nullspace-preserving saddle-point search technique, we resolved the critical nucleus structures and phase transition pathways. Although both transitions from the homogeneous state to the ordered state involve the formation of localized critical nuclei, their subsequent growth processes exhibit distinct modes of accommodating geometric mismatch: C6 forms branched domain structures and persistent line defects associated with orientation and phase mismatches, whereas DQC relaxes collision-induced defects through local coordination rearrangements. The resolved DQC-to-C6 pathway proceeds through a series of metastable intermediates that progressively connect these distinct modes of mismatch accommodation. Its multi-step character reflects the coupled adjustment of local coordination and compatibility between the emerging C6 domains. These results reveal the intrinsic link between the multi-step nature of the phase transition and the distinct structural requirements for accommodating geometric mismatch.

Post-training quantization for diffusion models increasingly exploits timestep, feature, and layer structure. While recent work has begun incorporating CFG structure into diffusion quantization, activation quantization still operates independently across conditional and unconditional coordinates, leaving cross-activation structure unexploited. We show that matched CFG activations form a strongly correlated two-dimensional source and that, under a fixed bit budget, the choice of branch coding basis materially affects quantization fidelity. Motivated by this observation, we introduce branch-space transform coding, which rotates matched CFG branches via an offline derived 2x2 orthogonal matrix, requiring minimal modifications to model parameters or the quantization pipeline. We further derive the Guidance-Correlation Branch Transform (GCBT), which jointly incorporates the CFG guidance direction and cross-branch second moments. Under an equal-rate quantization-noise surrogate, GCBT admits a closed-form per-layer solution without gradient optimization or angle search. Applied on top of existing diffusion PTQ methods, GCBT yields statistically significant fidelity gains in most evaluated comparisons with no statistically significant degradation, while leaving the underlying host quantization pipeline unchanged.

Distinct pre-trained models specialized for the same task converge to closely similar behavior, yet the parameter updates that produce it share no common coordinate system. Weight-space task arithmetic is therefore confined to a single model, and transporting an update between models requires a structural correspondence. Drawing on Plato's allegory of the cave, we hypothesize that these model-specific updates are shadows cast by one shared, model-agnostic object, the platonic task vector. To make it operational across models of different architectures, we introduce Universal Task Descriptors, matrices whose shape is independent of architecture and embedding dimension, which record a task's functional effect and admit addition and negation as ordinary matrix operations, and we transfer a descriptor into a target in two ways. A single least-squares solve returns a linear operator folded into the target's last layer, and a bank of such operators, one per source and task, realizes any composition as a signed sum of its entries. Alternatively, a low-rank adapter of the target's encoder is trained on the same objective at the price of one optimization per edit. Despite a model-specific residual comparable in norm to the shared component, transfer from another model retains 74 to 80 percent of the gain the target's own descriptors attain. Experiments across six model families, eight tasks and audio-text models confirm both realizations.

As large language models are increasingly deployed across diverse downstream tasks, efficient task adaptation has emerged as a central challenge. In response, a wide range of task adaptation methods have been proposed, spanning parameter-efficient fine-tuning, in-context learning, and embedding-injection approaches. However, these lines of work have largely evolved within individual paradigms, leaving their cross-paradigm relationships and trade-offs underexplored, especially for recently emerging embedding-based adaptations. This survey presents a unified framework that categorizes task adaptation methods by where and how task information is encoded: model weights, input prompts, or injected task embeddings. We provide a comprehensive taxonomy that integrates these paradigms, analyze their key strengths and limitations to explain how different adaptation paradigms have evolved, clarify relationships across paradigms, and highlight open problems for future research.

We study episodic adversarial linear constrained Markov decision processes (CMDPs) with unknown transitions, where both the loss and constraint functions may vary adversarially across episodes. The best previous algorithm achieves $\widetilde{\mathcal{O}}(K^{3/4})$ regret and cumulative constraint violation, leaving a gap to the optimal $\widetilde{\mathcal{O}}(\sqrt{K})$ dependence on the number of episodes $K$. We close this gap by proposing a new primal dual algorithm that achieves $\widetilde{\mathcal{O}}(\sqrt{K})$ regret and cumulative constraint violation without assuming Slater's condition. We further extend the algorithm to achieve the same $\widetilde{\mathcal{O}}(\sqrt{K})$ guarantees for regret and hard constraint violation, which does not allow constraint violations to cancel across episodes. The main challenge is that learning linear CMDPs requires uniform concentration over a value function class with a controlled covering number, whereas standard techniques in constrained online learning, such as policy mixing, can make this class more complex. Our algorithm combines adaptive Follow the Regularized Leader (FTRL), contracted value estimation, and an exponential Lyapunov function. An adaptive dual regularizer offsets the dependence on the dual weights in the primal regret bound, removing the need for policy mixing. We further show that the normalization in the FTRL update bounds the policy parameters independently of the magnitudes of the dual weights, which explains why the resulting policy class remains compatible with uniform concentration. Under feature access, the computational complexity is independent of the size of the state space.

Autonomous driving is a cornerstone technology for the future of intelligent transportation, where end-to-end learning has emerged as a transformative paradigm that directly maps multimodal sensory inputs to driving actions through unified differentiable models. While offering advantages, the effectiveness of end-to-end autonomous driving (E2E-AD) is ultimately determined by the quality of its training ecosystem. This paper provides a comprehensive review of training methods and ecosystem for E2E-AD. We introduce a Data-Strategy-Platform taxonomy that conceptualizes training as an interdependent system. The data layer defines what can be learned, the strategy layer governs how learning aligns with driving objectives, and the platform layer supports scalability and continuous evolution. Within this framework, we survey recent advances across data-centric pipelines, learning paradigms, and training infrastructures, and analyze their interplay in shaping model performance, robustness, and deployability. Finally, we reflect on current limitations and articulate a forward-looking vision that emphasizes a shift from data quantity to data value, from isolated optimization to foundation-driven generalization, and from static training to integrated training-testing loops, aiming toward robust, scalable, and trustworthy autonomous driving systems. We maintain a continuously updated repository tracking cutting-edge literature and works at \href{https://github.com/Jiaaqiliu/Awesome-Training-Ecosystem-for-E2E-AD}{Our Project Page}.

This paper studies communication-aware safe control for discrete-time linear multi-agent systems under limited information exchange. The main challenge lies in the coupling between remote-state estimation and safe controller design, since estimation errors affect the state evolution through the controller gains, while the controller design must account for the resulting observer-induced state perturbations to guarantee safety. To address this challenge, a distributed k-hop observer is developed to reconstruct unavailable remote states, and a uniform observer-error bound is derived. The effect of the observer-induced state perturbation on closed-loop safety is accounted for in both the construction of local {\epsilon}i-robust safe invariant (RSI) sets and the enforcement of pairwise relative-state safety constraints. The resulting safety conditions ensure that all agents remain within their local RSI sets while all pairwise relative-state safety constraints are satisfied. A linear matrix inequality (LMI)-based optimization method is developed to jointly synthesize the distributed observers, local controllers, and RSI sets. A case study illustrates the effectiveness of the proposed method.

Let $\delta^*_{k,r}$ be the fractional $K_r^{(k)}$-decomposition threshold in minimum codegree. For fixed $k\ge2$, $r\ge k+1$ and $\varepsilon>0$, we prove that every $n$-vertex $k$-uniform hypergraph $G$ with minimum codegree at least $(\delta^*_{k,r}+\varepsilon)n$ admits, with high probability, a fractional $K_r^{(k)}$-decomposition after retaining each edge independently with probability $p \ge C(\log n/n^{r-k})^{1/(\binom{r}{k}-1)}$. The bound on $p$ is sharp up to a constant factor, confirming the conjectured threshold order in the graph case. The proof develops a probabilistic matrix-scaling approach.

Multimodal RAG retrieves text, tables, images, and videos, but choosing a retrieval granularity does not determine how much context to retain within each item. Coarse units include irrelevant content, while uniformly fine selection can remove context needed to interpret the evidence. Existing compressors address this trade-off with modality-specific mechanisms, leaving open a shared procedure for adapting the retained extent region by region across heterogeneous items. We introduce CANOPY (Canonical Projection over Hierarchy), a framework for adaptive-granularity post-retrieval evidence compression. CANOPY represents retrieved items as hierarchies and uses a node encoder fine-tuned on gold evidence to score regions against the query. Parent-relative refinement compares these scores to select multiple regions at different granularities without LLM calls for node-level pruning. Because compression cannot recover evidence that was never retrieved, a critic requests targeted follow-up retrieval when it judges the accumulated evidence insufficient; newly retrieved items are compressed before being added. Across five QA benchmarks over a 33M-item heterogeneous corpus, CANOPY achieves higher average answer accuracy than the evaluated retrieval baselines. Ablations indicate that additional retrieval drives the main accuracy gains on multi-hop QA. In the unrouted Qwen3-VL-8B-Instruct setting, compression reduces reader-input evidence tokens by 14.2-27.7% relative to the same iterative pipeline without compression, with comparable answer accuracy.

Gaze estimation under natural head-eye motion underpins applications from driver monitoring to human-computer interaction. Single-frame methods predict each frame independently, so consecutive outputs fluctuate as jitter. Multi-frame methods reduce this, but they learn motion implicitly inside appearance features, so the gaze trajectory is never an explicit variable. We propose EyeTAG (Eye Trajectory-Aware Gaze Estimation), a causal multi-frame framework built around an explicit first-order gaze prior: at each step it differentiates its own recent predictions and feeds the resulting trajectory back as a compact kinematic token. Because differencing is translation-invariant in gaze space, this token carries subject-invariant motion rather than personal gaze offsets. Face and eye streams supply visual evidence, fused by cross-attention and a causal Transformer decoder. EyeTAG reduces the mean angular error by about 1.0$^\circ$ on Gaze360 and performs on par with the strongest baseline on EVE (2.56$^\circ$ vs. 2.58$^\circ$). Within-model ablations, which keep the encoder and the rest of the architecture fixed and vary only the gaze history, show that the differential formulation, rather than temporal context alone, removes the systematic saccade bias that persists even with an absolute gaze-history prior. Our code is available at https://github.com/peter8366/EyeTAG.

The cross-entropy method (CEM) uses world-model scores to select action sequences and fit the distribution sampled in its next iteration. A scoring error can therefore change both the present decision and the candidates considered later. We evaluate these two roles separately. Four types of predictive model generate CEM traces, and every model rescores every saved candidate pool. Executing the same candidates in the environment provides a reference elite set and proposal update. Across twelve independently trained task-seed units on Walker and Cheetah, the pre-specified proposal distance falls from the first to the final CEM iteration in every unit. Proposal widths contract and fitted means separate relative to the remaining search width. Pairwise ranking agreement stays near chance on Walker and declines on Cheetah; elite-set agreement does not improve. This comparison shows greater variation between scorers than between pool sources on Cheetah; Walker has variation in both and in their pairings. We use the original six units to select Random nonlinear for a one-update intervention, without inspecting intervention outcomes. Replacing its first model-ranked update with an environment-ranked update lowers final realised selected-sequence cost in those six units and in six further units held out from the selection.

We consider the weighted matroid intersection problem in the independence-oracle model. A sequence of works by Huang–Kakimura–Kamiyama~[SODA'16 & Math. Program'19], Chekuri–Quanrud~[SODA'16], Quanrud~[ICALP'24], and Dudeja–Grilnberger~[IPCO'26] has developed efficient $(1-\varepsilon)$-approximation algorithms for this problem. We present a simple deterministic auction algorithm that, given two matroids on a common ground set of size $n$, computes a $(1-\varepsilon)$-approximate maximum-weight common independent set using $O(n \varepsilon^{-2} \log^2(n))$ independence-oracle queries. This is the first deterministic $(1-\varepsilon)$-approximation algorithm for the weighted matroid intersection problem whose query complexity is nearly linear in $n$ and polynomial in $1/\varepsilon$. Our algorithm builds on the auction algorithm for unweighted matroid intersection by Huang–Kobayashi~['26].