We show that emotion vectors in LLMs are organized by a two-dimensional valence-arousal (VA) subspace exhibiting circular geometry. Through principal component decomposition and ridge regression, we recover meaningful VA axes underlying emotion steering vectors whose projections correlate with human affect ratings across 44,728 words. Steering along these axes produces monotonic control over the affective properties of generated text, and further affords bidirectional control over multiple downstream behaviors (refusal and sycophancy) from a single subspace. These effects replicate across Llama-3.1-8B, Qwen3-8B, and Qwen3-14B. We propose lexical mediation to explain why these effects and prior emotionally framed controls work: refusal and compliance tokens occupy distinct VA regions, and VA steering directly modulates their emission probabilities.

Scaling autoregressive large language models (LLMs) has driven unprecedented progress but comes with vast computational costs. In this work, we tackle these costs by leveraging unstructured sparsity within an LLM's feedforward layers, the components accounting for most of the model parameters and execution FLOPs. To achieve this, we introduce a new sparse packing format and a set of CUDA kernels designed to seamlessly integrate with the optimized execution pipelines of modern GPUs, enabling efficient sparse computation during LLM inference and training. To substantiate our gains, we provide a quantitative study of LLM sparsity, demonstrating that simple L1 regularization can induce over 99% sparsity with negligible impact on downstream performance. When paired with our kernels, we show that these sparsity levels translate into substantial throughput, energy efficiency, and memory usage benefits that increase with model scale. We will release all code and kernels under an open-source license to promote adoption and accelerate research toward establishing sparsity as a practical axis for improving the efficiency and scalability of modern foundation models.

Recently, it has been shown that the Stochastic Gradient Bandit (SGB) algorithm converges to a globally optimal policy with a constant learning rate. However, these guarantees rely on unrealistic assumptions about the learning process, namely that the probability of the optimal action is always bounded away from zero. We attribute this to the lack of an explicit exploration mechanism in SGB. To address these limitations, we propose to regularize the SGB objective with a log-barrier on the parametric policy, structurally enforcing a minimal amount of exploration. We prove that Log-Barrier Stochastic Gradient Bandit (LB-SGB) matches the sample complexity of SGB, but also converges (at a slower rate) without any assumptions on the learning process. We also show a connection between the log-barrier regularization and Natural Policy Gradient, as both exploit the geometry of the policy space by controlling the Fisher information. We validate our theoretical findings through numerical simulations, showing the benefits of the log-barrier regularization.

Neural oscillators that originate from second-order ordinary differential equations (ODEs) have shown competitive performance in learning mappings between dynamic loads and responses of complex nonlinear structural systems. Despite this empirical success, theoretically quantifying the generalization capacities of their neural network architectures remains undeveloped. In this study, the neural oscillator consisting of a second-order ODE followed by a multilayer perceptron (MLP) is considered. Its upper probably approximately correct (PAC) generalization bound for approximating causal and uniformly continuous operators between continuous temporal function spaces and that for approximating the uniformly asymptotically incrementally stable second-order dynamical systems are derived by leveraging the Rademacher complexity framework. These bounds are further extended to the squared Wasserstein-1 distances between the probability measures of quantities of interest calculated from target causal operators and the corresponding learned neural oscillators. The theoretical results show that the estimation errors grow polynomially with respect to both MLP sizes and the time length, thereby avoiding the curse of parametric complexity. Furthermore, the derived error bounds demonstrate that constraining the Lipschitz constants of the MLPs via loss function regularization can improve the generalization ability of the neural oscillator. Numerical studies considering a Bouc-Wen nonlinear system under stochastic seismic excitation validates the theoretically predicted power laws of the estimation errors with respect to the sample size and time length, and confirms the effectiveness of constraining MLPs' matrix and vector norms in enhancing the performance of the neural oscillator under limited training data.

With the rapid advancement of Large Language Models (LLMs) in code generation, human-AI interaction is evolving from static text responses to dynamic, interactive HTML-based applications, which we term MiniApps. These applications require models to not only render visual interfaces but also construct customized interaction logic that adheres to real-world principles. However, existing benchmarks primarily focus on algorithmic correctness or static layout reconstruction, failing to capture the capabilities required for this new paradigm. To address this gap, we introduce MiniAppBench, the first comprehensive benchmark designed to evaluate principle-driven, interactive application generation. Sourced from a real-world application with 10M+ generations, MiniAppBench distills 500 tasks across six domains (e.g., Games, Science, and Tools). Furthermore, to tackle the challenge of evaluating open-ended interactions where no single ground truth exists, we propose MiniAppEval, an agentic evaluation framework. Leveraging browser automation, it performs human-like exploratory testing to systematically assess applications across three dimensions: Intention, Static, and Dynamic. Our experiments reveal that current LLMs still face significant challenges in generating high-quality MiniApps, while MiniAppEval demonstrates high alignment with human judgment, establishing a reliable standard for future research. Our homepage is available in miniappbench.github.io.

Removing an agent from a cooperative team to measure its contribution seems natural, yet in multi-agent LLM systems this evaluation distorts the result it claims to measure. This failure is not isolated: learned critics, trajectory-level baselines, and agent-removal counterfactuals all inherit from standard multi-agent reinforcement learning a premise that exact counterfactual evaluation requires privileged environment access, and therefore approximate. In cooperative LLM systems, this premise is false. Interaction histories are deterministic functions of observable text with no hidden state, so any decision point can be restored exactly, making direct causal measurement possible without parametric approximation. C3 exploits this property by fixing the complete history at each decision point, sampling alternative actions under a frozen behavior policy, and computing unbiased per-decision advantages through a parameter-free leave-one-out baseline. Across six benchmarks spanning math reasoning and code generation, two model families, and two multi-agent topologies, C3 consistently outperforms all baselines; a controlled decomposition confirms gains originate from credit quality, not architecture, while checkpoint restoration reduces training token consumption. The exact solution proves simpler, cheaper, and more effective than all approximate alternatives. The same structural property that enables exact credit also enables exact verification: three independently computable diagnostics, credit fidelity, within-group variance, and inter-agent influence, constitute the first method-agnostic auditing tool for multi-agent LLM credit assignment. Our code is available at https://github.com/EIT-EAST-Lab/C3

With many organizations struggling to gain value from AI deployments, pressure to evaluate AI in an informed manner has intensified. Status quo AI evaluation approaches often mask the operational realities that ultimately determine deployment success, making it difficult for organizational decision makers to know whether and how AI tools will deliver durable value. We introduce and describe context specification as a process to support and inform this decision making process. Context specification turns diffuse stakeholder perspectives about what matters in a given setting into clear, named constructs: explicit definitions of the properties, behaviors, and outcomes that evaluations aim to capture, so they can be observed and measured in context. The process serves as a foundational roadmap for evaluating what AI systems are likely to do in the deployment contexts that organizations actually manage.

We introduce VDCook: a self-evolving video data operating system, a configurable video data construction platform for researchers and vertical domain teams. Users initiate data requests via natural language queries and adjustable parameters (scale, retrieval-synthesis ratio, quality threshold). The system automatically performs query optimization, concurrently running real video retrieval and controlled synthesis modules. It ultimately generates in-domain data packages with complete provenance and metadata, along with reproducible Notebooks. Unlike traditional static, one-time-built datasets, VDCook enables continuous updates and domain expansion through its automated data ingestion mechanism based on MCP (Model Context Protocol)\cite{mcp2024anthropic}, transforming datasets into dynamically evolving open ecosystems. The system also provides multi-dimensional metadata annotation (scene segmentation, motion scoring, OCR ratio, automatic captioning, etc.), laying the foundation for flexible subsequent data `cooking' and indexing\cite{vlogger}. This platform aims to significantly lower the barrier to constructing specialized video training datasets through infrastructure-level solutions, while supporting community contributions and a governance-enabled data expansion paradigm. \textbf{Project demo:} https://screenapp.io/app/v/WP0SvffgsH

We investigate a quantum-inspired approach to supervised multi-class classification based on the Pretty Good Measurement (PGM), viewed as an operator-valued decision rule derived from quantum state discrimination. The method associates each class with an encoded mixed state and performs classification through a single POVM construction, thus providing a genuinely multi-class strategy without reduction to pairwise or one-vs-rest schemes. In this perspective, classification is reformulated as the discrimination of a finite ensemble of class-dependent density operators, with performance governed by the geometry induced by the encoding map and by the overlap structure among classes. To assess the practical scope of this framework, we apply the PGM-based classifier to two biomedical radiomics case studies: histopathological subtyping of non-small-cell lung carcinoma (NSCLC) and prostate cancer (PCa) risk stratification. The evaluation is conducted under protocols aligned with previously reported radiomics studies, enabling direct comparison with established classical baselines. The results show that the PGM-based classifier is consistently competitive and, in several settings, improves upon standard methods. In particular, the method performs especially well in the NSCLC binary and three-class tasks, while remaining competitive in the four-class case, where increased class overlap yields a more demanding discrimination geometry. In the PCa study, the PGM classifier remains close to the strongest ensemble baseline and exhibits clinically relevant sensitivity--specificity trade-offs across feature-selection scenarios.

Causal machine learning (ML) recovers graphical structures that inform us about potential cause-and-effect relationships. Most progress has focused on cross-sectional data with no explicit time order, whereas recovering causal structures from time series data remains the subject of ongoing research in causal ML. In addition to traditional causal ML, this study assesses econometric methods that some argue can recover causal structures from time series data. The use of these methods can be explained by the significant attention the field of econometrics has given to causality, and specifically to time series, over the years. This presents the possibility of comparing the causal discovery performance between econometric and traditional causal ML algorithms. We seek to understand if there are lessons to be incorporated into causal ML from econometrics, and provide code to translate the results of these econometric methods to the most widely used Bayesian Network R library, bnlearn. We investigate the benefits and challenges that these algorithms present in supporting policy decision-making, using the real-world case of COVID-19 in the UK as an example. Four econometric methods are evaluated in terms of graphical structure, model dimensionality, and their ability to recover causal effects, and these results are compared with those of eleven causal ML algorithms. Amongst our main results, we see that econometric methods provide clear rules for temporal structures, whereas causal-ML algorithms offer broader discovery by exploring a larger space of graph structures that tends to lead to denser graphs that capture more identifiable causal relationships.

Our understanding of the oceans remains limited by sparse and infrequent observations, primarily because current methods are constrained by the high cost and logistical effort of underwater monitoring, relying either on sporadic surveys across broad areas or on long-term measurements at fixed locations. To overcome these limitations, monitoring systems must enable persistent and autonomous operations without the need for continuous surface support. Despite recent advances, resident underwater vehicles remain uncommon due to persistent challenges in autonomy, robotic resilience, and mechanical robustness, particularly under long-term deployment in harsh and remote environments. This work addresses these problems by presenting the development, deployment, and operation of a resident infrastructure using a docking station with a mini-class Remotely Operated Vehicle (ROV) at 90 m depth. The ROV is equipped with enhanced onboard processing and perception, allowing it to autonomously navigate using USBL signals, dock via ArUco marker-based visual localisation fused through an Extended Kalman Filter, and carry out local inspection routines. The system demonstrated a 90 % autonomous docking success rate and completed full inspection missions within four minutes, validating the integration of acoustic and visual navigation in real-world conditions. These results show that reliable, untethered operations at depth are feasible, highlighting the potential of resident ROV systems for scalable, cost-effective underwater monitoring.

Reinforcement learning has emerged as a powerful paradigm for unlocking reasoning capabilities in language models. However, relying on sparse rewards makes this process highly sample-inefficient, as models must navigate vast search spaces with minimal feedback. While classic curriculum learning aims to mitigate this by ordering data based on complexity, prior works have primarily targeted small datasets and do not directly transfer to the large-scale settings typical of modern LM training. Furthermore, the right ordering for a specific model is often unclear. To address this, we propose Goldilocks, a novel teacher-driven data sampling strategy that aims to predict each question's difficulty for the student model. The teacher model selects questions of appropriate difficulty for the student model, i.e., questions that are neither too easy nor too hard (Goldilocks principle), while training the student with GRPO. By leveraging the student's performance on seen samples, the teacher continuously adapts to the student's evolving abilities. On the OpenMathReasoning dataset, Goldilocks data sampling improves the performance of models trained with standard GRPO under the same compute budget.

This paper investigates the relationship between convolutional neural network (CNN) topology and image recognition performance through a comparative study of the VGG, ResNet, and GoogLeNet architectural families. Utilizing a unified experimental framework, the study isolates the impact of depth from confounding implementation variables. A formal distinction is introduced between nominal depth ($D_{\mathrm{nom}}$), representing the physical layer count, and effective depth ($D_{\mathrm{eff}}$), an operational metric quantifying the expected number of sequential transformations. Empirical results demonstrate that architectures utilizing identity shortcuts or branching modules maintain optimization stability by decoupling $D_{\mathrm{eff}}$ from $D_{\mathrm{nom}}$. These findings suggest that effective depth serves as a superior framework for predicting scaling potential and practical trainability, ultimately indicating that architectural topology - rather than sheer layer volume - is the primary determinant of gradient health in deep learning models.

Humanoid robots show promise for complex whole-body tasks in unstructured environments. Although Human-Object Interaction (HOI) has advanced, most methods focus on fully actuated objects rigidly coupled to the robot, ignoring underactuated objects with independent dynamics and non-holonomic constraints. These introduce control challenges from coupling forces and occlusions. We present HAIC, a unified framework for robust interaction across diverse object dynamics without external state estimation. Our key contribution is a dynamics predictor that estimates high-order object states (velocity, acceleration) solely from proprioceptive history. These predictions are projected onto static geometric priors to form a spatially grounded dynamic occupancy map, enabling the policy to infer collision boundaries and contact affordances in blind spots. We use asymmetric fine-tuning, where a world model continuously adapts to the student policy's exploration, ensuring robust state estimation under distribution shifts. Experiments on a humanoid robot show HAIC achieves high success rates in agile tasks (skateboarding, cart pushing/pulling under various loads) by proactively compensating for inertial perturbations, and also masters multi-object long-horizon tasks like carrying a box across varied terrain by predicting the dynamics of multiple objects.

Off-policy updates are inevitable in reinforcement learning (RL) for large language models (LLMs) due to rollout staleness from asynchronous training and mismatches between training and inference engines. Naive importance sampling gives an unbiased correction but suffers from high variance, which is amplified by unbounded ratios and autoregressive generation. Prior remedies either rely on scenario-specific engineering, or trade bias for variance via token-level clipping or sequence-level normalization, yet these approaches remain largely heuristic. We propose Variational sEquence-level Soft Policy Optimization (VESPO). By explicitly incorporating variance reduction into a variational formulation, we derive a principled closed-form reshaping kernel that operates directly on sequence-level importance weights, avoids token-level approximation and length normalization, and admits an explicit variance bound for the deployed kernel. Experiments on math reasoning and code generation show that VESPO maintains stable training under severe off-policy conditions (staleness up to 64x) and delivers consistent gains across both dense and Mixture-of-Experts (MoE) models, outperforming recent reshaping baselines under matched setup. Code is available at https://github.com/FloyedShen/VESPO.

While adaptive gradient methods are the workhorse of modern machine learning, sign-based optimization algorithms such as Lion and Muon have recently demonstrated superior empirical performance over AdamW in training large language models (LLM). However, a theoretical understanding of why sign-based updates outperform variance-adapted methods remains elusive. In this paper, we aim to bridge the gap between theory and practice through the lens of heavy-tailed gradient noise, a phenomenon frequently observed in language modeling tasks. Theoretically, we introduce a novel generalized heavy-tailed noise condition that captures the behavior of LLMs more accurately than standard finite variance assumptions. Under this noise model, we establish sharp convergence rates of SignSGD and Lion for generalized smooth function classes, matching or surpassing previous best-known bounds. Furthermore, we extend our analysis to Muon and Muonlight, providing what is, to our knowledge, the first rigorous analysis of matrix optimization under heavy-tailed stochasticity. These results offer a strong theoretical justification for the empirical superiority of sign-based optimizers, showcasing that they are naturally suited to handle the noisy gradients associated with heavy tails. Empirically, LLM pretraining experiments validate our theoretical insights and confirm that our proposed noise models are well-aligned with practice.

Modern T2V/I2V generators synthesize people increasingly hard to distinguish from authentic footage, while current evaluation suites lag: legacy benchmarks target manipulation-based forgeries, and recent synthetic-video benchmarks prioritize scale over realistic human depiction. We introduce SynthForensics, a people-centric benchmark of $20{,}445$ videos from 8 T2V and 7 I2V open-source generators, paired-source from FF++/DFD reals, two-stage human-validated, in four compression versions with full metadata. In our paired-comparison human study, raters prefer SynthForensics in $71$--$77\%$ of head-to-head comparisons against each of nine existing synthetic-video benchmarks, while facial-quality metrics fall within the FF++/DFD baseline range. Across 15 detectors and three protocols, face-based methods drop $13$--$55$ AUC points (mean $27$) from FF++ to SynthForensics and a further $23$ under aggressive compression; fine-tuning closes the gap at a backward cost on legacy benchmarks; training from scratch shows synthetic and manipulation features largely disjoint for most detectors. We release dataset, pipeline, and code.

Adaptive cognition requires structured internal models of objects and their relations. Predictive neural networks are often proposed to learn such world models, but how these are instantiated and how they support prediction remain unclear. We investigate this in a minimal in-silico setting. A recurrent neural network samples tokens sequentially from 2D continuous token scenes and is trained to predict the upcoming token from the current input and a saccade-like displacement. On novel scenes, prediction accuracy improves across the sequence, indicating in-context learning. Decoding analyses reveal path integration and dynamic binding of token identity to position. Interventional analyses show that new bindings can be learned late in sequence and that out-of-distribution bindings can be learned as well. Together, these findings show how structured representations relying on flexible binding emerge to support prediction, offering a mechanistic account of sequential world modeling relevant to cognitive science.

Continual learning, especially class-incremental learning (CIL), on the basis of a pre-trained model (PTM) has garnered substantial research interest in recent years. However, how to effectively learn both discriminative and comprehensive feature representations while maintaining stability and plasticity over very long task sequences remains an open problem. We propose CaRE, a scalable {C}ontinual Le{a}rner with efficient Bi-Level {R}outing Mixture-of-{E}xperts (BR-MoE). The core idea of BR-MoE is a bi-level routing mechanism: a router selection stage that dynamically activates relevant task-specific routers, followed by an expert routing phase that dynamically activates and aggregates experts, aiming to inject discriminative and comprehensive representations into every intermediate network layer. On the other hand, we introduce a challenging dataset, OmniBenchmark-1K, for CIL performance evaluation on very long task sequences with hundreds of tasks. Extensive experiments show that CaRE demonstrates leading performance across a variety of datasets and task settings, including commonly used CIL datasets with classical CIL settings (e.g., 5-20 tasks). To the best of our knowledge, CaRE is the first continual learner that scales to very long task sequences (ranging from 100 to over 300 non-overlapping tasks), while outperforming all baselines by a large margin on such task sequences. We hope that this work will inspire further research into continual learning over extremely long task sequences. Code and dataset are publicly released at https://github.com/LMMMEng/CaRE.

Forecasting physical systems over long horizons from irregularly sampled observations demands models that are stable, computationally efficient, and free of fixed-timestep assumptions. We address this with a continuous-time Koopman autoencoder whose latent dynamics obey $dz/dt = \mathbf{K}_{\mathrm{cont}} z$, yielding closed-form inference via $z(τ) = \exp(\mathbf{K}_{\mathrm{cont}} τ) z(0)$ at any horizon $τ$ in a single step. This decouples forecast cost from forecast length at inference time and supports data assimilation as gradient-based optimization with cost independent of the assimilation window. However, scaling continuous-time Koopman dynamics to high-dimensional chaotic systems causes severe latent instability, including spectral collapse and trajectory divergence over long horizons. In contrast, discrete Koopman methods train an operator $\mathbf{A}$ such that $z_{t+Δt} = \mathbf{A} z_t$; recovering the continuous generator could be theoretically done through matrix logarithm but requires conditions not guaranteed by training, and approximation errors grow with the $Δt$ imposed by the training data. These methods also require fixed, regular timesteps. We identify an empirically effective set of structural constraints -- rollout training, forward-backward consistency, latent regularization, and physics-conditioned LoRA -- sufficient for stable long-horizon latent dynamics. On challenging fluid benchmarks, our method outperforms strong diffusion and operator-learning baselines on long-horizon forecasting while achieving a 110$\times$ inference speedup.

Functional miRNA--mRNA targeting is a large-bag prediction problem where each transcript yields a heavy-tailed pool of candidate target sites (CTSs), yet only a pair-level label is observed. Prior methods use max-pooling over individual CTS scores, ignoring relational patterns among sites, but modeling these patterns is critical for accuracy. The challenge is that naive relational aggregation incurs $\mathcal{O}(n^2)$ cost, prohibitive when $n$ reaches thousands, yet a cheap scan alone discards the very interactions that drive functional repression. We formalize this tension as \emph{Budgeted Relational Multi-Instance Learning (BR-MIL)}, a new MIL problem where the compute budget $K$ is a first-class constraint such that at most $K$ instances per bag may receive expensive encoding and relational processing. We establish theoretical foundations for BR-MIL, proving that both approximation quality and generalization are governed by $K$ rather than the raw bag size $n$. Building on this theory, we propose \textbf{PAIR-Former}, which scans all candidates cheaply, selects $K$ diverse CTSs, and aggregates them via Set Transformer. PAIR-Former achieves state-of-the-art performance, outperforming all reproduced baselines with F1$=0.840$ on miRAW (10-fold balanced CV) and $0.839$ on deepTargetPro in transfer evaluation, while achieving $0.793$ on the large-scale MTI benchmark (420K pairs, $38\times$ larger), demonstrating that budgeted relational MIL scales where naive approaches fail. Additional results on CAMELYON16 and Musk2 further show that the proposed BR-MIL formulation extends beyond biological sequence modeling.

State-of-the-art vision-language models (VLMs) score impressively on video benchmarks yet stumble on basic visual reasoning tasks involving spatial relations, navigation, and object selection that a preschooler solves easily. We hypothesize that the explicit pedagogical structure, specifically the context-question-pause-answer cycles embedded in children's educational video, provides naturally co-aligned reasoning traces: temporally synchronized visual cues, questions, and answers that emerge only from deliberate pedagogical authoring and cannot be practically reconstructed through manual annotation at scale. To test this, we introduce SoSVQA (Structure over Scale Visual Question Answering), a unified benchmark of 10K question-answer pairs automatically extracted from Dora the Explorer (DoraVQA) and Mickey Mouse Clubhouse (ClubHVQA) with precise timestamp alignment, and fine-tune Qwen2-VL and Qwen3-VL using Group Relative Policy Optimization (GRPO) to leverage the clear correctness signals and structured reasoning traces inherent in educational content. Despite training on just 10K QA pairs from 78 hours of children's television, orders of magnitude less data than GPT and Gemini, our approach delivers generalizable performance gains for Qwen-based VLMs, yielding consistent improvements on NExT-QA (+19.7), Video-MME (+10.6), and MotionBench (+4.9), matching the performance of leading proprietary systems and demonstrating that content structure can compensate for content scale.

Recent work has revealed a link between self-attention mechanisms in transformers and test-time kernel regression via the Nadaraya-Watson estimator, with standard softmax attention corresponding to a Gaussian kernel. However, a kernel-theoretic understanding of sparse attention mechanisms is currently missing. In this paper, we establish a formal correspondence between sparse attention and compact (bounded support) kernels. We show that normalized ReLU and sparsemax attention arise from Epanechnikov kernel regression under fixed and adaptive normalizations, respectively. More generally, we demonstrate that widely used kernels in nonparametric density estimation -- including Epanechnikov, biweight, and triweight -- correspond to $α$-entmax attention with $α= 1 + \frac{1}{n}$ for $n \in \mathbb{N}$, while the softmax/Gaussian relationship emerges in the limit $n \to \infty$. This unified perspective explains how sparsity naturally emerges from kernel design and provides principled alternatives to heuristic top-$k$ attention and other associative memory mechanisms. Experiments with a kernel-regression-based variant of transformers -- Memory Mosaics -- show that kernel-based sparse attention achieves competitive performance on language modeling, in-context learning, and length generalization tasks, offering a principled framework for designing attention mechanisms.

We introduce \textsc{$k$-lazyGD}, an online learning algorithm that bridges the gap between greedy Online Gradient Descent (OGD, for $k{=}1$) and lazy GD/dual-averaging (for $k{=}T$), creating a spectrum between reactive and stable updates. We analyze this spectrum in Smoothed Online Convex Optimization (SOCO), where the learner incurs both hitting and movement costs. Our main contribution is establishing that laziness is possible without sacrificing hitting performance: we prove that \textsc{$k$-lazyGD} achieves the optimal dynamic regret $\mathcal{O}(\sqrt{(P_T{+}1)T})$ for any laziness slack $k$ up to $Θ(\sqrt{T/P_T})$, where $P_T$ is the comparator path length. This result formally connects the allowable laziness to the comparator's shifts, showing that \textsc{$k$-lazyGD} can retain the inherently small movements of lazy methods without compromising tracking ability. We base our analysis on the Follow the Regularized Leader (FTRL) framework, and derive a matching lower bound. Since the slack depends on $P_T$, an ensemble of learners with various slacks is used, yielding a method that is provably stable when it can be, and agile when it must be.

Deploying federated learning across heterogeneous IoT device fleets requires tailored neural network architectures for each device class, yet existing Federated Neural Architecture Search (FedNAS) methods suffer from unguided supernet training and prohibitively costly post-training search pipelines that demand over 20 GPU-hours per deployment target. We introduce DeepFedNAS, a two-phase framework built on a multi-objective fitness function that synthesizes information-theoretic network metrics with architectural heuristics. In the first phase, Federated Pareto Optimal Supernet Training replaces random subnet sampling with a pre-computed cache of elite, high-fitness architectures, yielding a superior supernet. In the second phase, a Predictor-Free Search uses this fitness function as a zero-cost accuracy proxy, discovering hardware-optimized subnets in ~20 seconds, a ~61x speedup over the baseline pipeline. Experiments on CIFAR-10, CIFAR-100, and CINIC-10 demonstrate state-of-the-art accuracy (up to +1.21% on CIFAR-100), a 2.8x reduction in per-round transmission size, and robust performance under extreme non-IID conditions (α = 0.1), making DeepFedNAS practical for scalable, communication-constrained IoT federations. Source code: https://github.com/bostankhan6/DeepFedNAS

Wildfire monitoring requires high-resolution atmospheric measurements, yet low-cost sensors on Unmanned Aerial Vehicles (UAVs) exhibit baseline drift, cross-sensitivity, and response lag that corrupt concentration estimates. Traditional deep learning denoising approaches demand large datasets impractical to obtain from limited UAV flight campaigns. We present PC$^2$DAE, a physics-informed denoising autoencoder that addresses data scarcity by embedding physical constraints directly into the network architecture. Non-negative concentration estimates are enforced via softplus activations and physically plausible temporal smoothing, ensuring outputs are physically admissible by construction rather than relying on loss function penalties. The architecture employs hierarchical decoder heads for Black Carbon, Gas, and CO$_2$ sensor families, with two variants: PC$^2$DAE-Lean (21k parameters) for edge deployment and PC$^2$DAE-Wide (204k parameters) for offline processing. We evaluate on 7,894 synchronized 1 Hz samples collected from UAV flights during prescribed burns in Saskatchewan, Canada (approximately 2.2 hours of flight data), two orders of magnitude below typical deep learning requirements. PC$^2$DAE-Lean achieves 67.3\% smoothness improvement and 90.7\% high-frequency noise reduction with zero physics violations. Five baselines (LSTM-AE, U-Net, Transformer, CBDAE, DeSpaWN) produce 15--23\% negative outputs. The lean variant outperforms wide (+5.6\% smoothness), suggesting reduced capacity with strong inductive bias prevents overfitting in data-scarce regimes. Training completes in under 65 seconds on consumer hardware.

Recent work, using the Biasing Features metric, labels a CoT as unfaithful if it omits a prompt-injected hint that affected the prediction. We argue this metric adopts a narrow notion of faithfulness and confuses unfaithfulness with incompleteness, the lossy compression needed to turn distributed transformer computation into a linear natural language narrative. On multi-hop reasoning tasks with instruct-tuned and reasoning models, many CoTs flagged as unfaithful by Biasing Features are judged faithful by other metrics, exceeding 50% in some models. With a new faithful@k metric, we show that larger inference-time budgets greatly increase hint verbalization (up to 90% in some settings), suggesting much apparent unfaithfulness is due to tight token limits. Using Causal Mediation Analysis, we further show that even non-verbalized hints can causally mediate prediction changes through the CoT. We therefore caution against relying solely on hint-based evaluations and advocate a broader interpretability toolkit, including causal mediation and corruption-based metrics. We do not claim all CoTs are faithful, only that the absence of hint words alone does not prove unfaithfulness.

Preferential Bayesian Optimization (PBO) aims to find a decision-maker's most preferred solution in as few pairwise comparisons as possible. Existing approaches rely on Gaussian Process (GP) surrogates, which provide strong performance but limited interpretability. This limits real-world usability in high-stakes domains, such as healthcare, where interpretability and trust are essential. We propose DT-PBO, a novel tree-based surrogate model for PBO that is inherently interpretable while capturing preference uncertainty. Specifically, we introduce a novel splitting heuristic that constructs interpretable shallow decision trees directly from pairwise comparison data, and use Laplace approximation to obtain probabilistic estimates for each leaf. This enables efficient preference modeling without sacrificing interpretability. Across eight benchmark functions, our method achieves competitive convergence to GP-based PBO, particularly on functions with rugged optimization landscapes. Additional experiments show robustness against noise and a fast computational running time. Experiments on real-world datasets further demonstrate that our model provides interpretable insights into decision-maker preferences that would remain opaque under GP-based approaches.

In this paper, we introduce Exact Flow Linear Attention~(EFLA), an exact-flow formulation of delta-rule linear attention. We show that the delta-rule update can be interpreted as an explicit Euler discretization of an underlying continuous-time system. EFLA replaces this first-order update with the exact closed-form flow. By exploiting the rank-1 structure of the dynamics matrix, both the matrix exponential and the input integral collapse to a simple update that preserves delta-rule linear attention's algebraic structure, parameter count, linear-time complexity, and chunkwise parallelism. This attention mechanism removes the Euler discretization error of the delta-rule dynamics without introducing additional parameters. Experiments on robustness tests, language modeling benchmarks, and the MAD synthetic benchmark show that EFLA improves stability under corrupted and high-energy inputs, reduces perplexity, and achieves stronger downstream performance compared to SSM and Euler-style baselines. These results establish exact-flow integration as a principled and scalable update mechanism for delta-rule linear attention.

We present an end-to-end framework for planning supported by verifiers. An orchestrator receives a human specification written in natural language and converts it into a PDDL (Planning Domain Definition Language) model, where the domain and problem are iteratively refined by sub-modules (agents) to address common planning requirements, such as time constraints and optimality, as well as ambiguities and contradictions that may exist in the human specification. We support two categories of agents: hardcoded, which are informed by logs and error traces and have a pre-defined goal (e.g., fix issues with PDDL syntax, check temporal constraints), and dynamic, which have no predefined goal but adapt to the specific domain and revise the latent planning abstraction. The validated domain and problem are then passed to an external planning engine to generate a plan. The orchestrator and agents are powered by Large Language Models (LLMs) and require no human intervention at any stage of the process. Finally, a module translates the final plan back into natural language to improve human readability while maintaining the correctness of each step. We demonstrate the flexibility and effectiveness of our framework on GPT-\{4o, 5-mini, 5.4\}, and Gemini-\{2.5, 3\}-flash across more than ten domains and tasks, including the Google NaturalPlan benchmark, Planbench, and classic planning problems like Sokoban, Blocksworld and the Tower of Hanoi, where LLMs are known to struggle even with small instances. Our framework can be integrated with any PDDL planning engine and validator (we successfully tested Fast Downward, LPG, POPF, VAL, and uVAL) and represents a significant step toward end-to-end planning aided by LLMs.