Papers

In some multi-agent systems, the quantity to be optimized is not an externally specified reward but the information acquired about unknown properties of the environment as done in active sequential hypothesis testing (ASHT) problems. However, the ASHT literature tends to focus on finite single-agent problems with well-specified models, while there is currently a gap for practical multi-agent methods that can perform active sequential testing. We fill this gap with ICMAPE, a Bayesian learning-based framework for decentralized multi-agent pure-exploration driven by inference objectives. ICMAPE converts the fixed-confidence identification objective into a reward derived from inference confidence, so that standard reinforcement learning machinery can be applied to decentralized pure exploration. It jointly learns a centralized neural inference network that estimates a posterior distribution over hypotheses from global trajectory data, and decentralized policies that select actions from local observation histories and learn when to stop collecting data once the target confidence is reached. On two synthetic benchmarks and a Maryland nitrate concentration monitoring task based on real-world data, ICMAPE-TD3 achieves target accuracy with fewer exploration steps.

Supervised fine-tuning (SFT) is widely used to adapt large language models to downstream tasks. Crowdsourcing user conversations is an established approach to collecting SFT data at scale while reducing the need for costly manual annotation. However, it also allows untrusted users to contribute data to the fine-tuning pipeline. We investigate an underexplored privacy risk arising from this setting: can a malicious user poison a small fraction of the crowdsourced data to amplify extraction of previously unseen instructions contributed by other users? We show that this is possible using only black-box, output-only access to the deployed model. Experiments across four models and two datasets demonstrate substantial increases in training-data extraction: with only 50 poisoned examples, near-verbatim extraction reaches $3.71\times$ the rate without poisoning for Qwen2.5-14B on OpenMathInstruct and $3.08\times$ for Llama-3.1-8B on AceReason. Data filtering also proves largely ineffective in detecting poisoned samples: even the best-performing method achieves only 0.378 in F-1 score, leaving the majority of poisoned samples undetected. These findings demonstrate that seemingly benign crowdsourced contributions can amplify leakage of other records while remaining difficult to identify through data filtering.

Linear forecasters have shown competitive accuracy against Transformer-based models in long-term time series forecasting. We study how classical stationary prediction theory can guide parameter sharing for more compact linear forecasters. For centered second-order stationary processes with nonsingular history covariance, the minimum-MSE finite-window linear predictor factors into a Hankel cross-covariance matrix and an inverse Toeplitz covariance matrix. Shared lags and scale cancellation specify this predictor using $H+L-1$ autocorrelations for lookback $L$ and horizon $H$. Building on the innovations representation, our Hankel-Toeplitz Forecaster (HTF) learns one impulse response that defines both an inverse filter and a forecast map. We characterize the finite-history correction and, under summability assumptions, bound the excess risk of truncating the true filters. HTF uses $H+L-1$ trainable coefficients while allowing a full-rank forecasting matrix. Across seven benchmarks at $L=336$, its horizon-averaged MSE is within 1.2% of Dense Linear on each dataset with 75-229 times fewer trainable parameters.

Semantic Textual Similarity (STS) methods assume that a document's lexical content faithfully represents what it asserts. This assumption fails for discursive documents that discuss, compare, critique, and contextualize other positions in the process of articulating their own. The result is semantic diffusion: similarity scores between documents are inflated by vocabulary acquired through discursive engagement rather than substantive alignment. Standard Natural Language Processing (NLP) preprocessing (tokenization, stopword removal, stemming, lemmatization) cannot address this problem because it operates at the lexical level, treating all content identically regardless of its discursive function. This paper introduces high-level text preprocessing: a systematic, rule-based intervention applied before the standard preprocessing pipeline to isolate each document's actual claim from its discursive structure. We propose 12 rules, each with an explicit rationale, and demonstrate their effect on an encyclopedic philosophical corpus: three entries from the Stanford Encyclopedia of Philosophy (virtue ethics, deontological ethics, and consequentialism). A three-phase experiment using eight Transformer-based STS models shows that preprocessing reduces centroid cosine similarity scores across all three theory pairs, with 23 of 24 model-pair comparisons showing the expected decrease and cross-model agreement ranging from 7-1 to 8-0. We introduce the semantic diffusion index (SDI), a per-document metric for assessing the semantic reorientation between a document's raw and high-level preprocessed representations. Although the framework is demonstrated using philosophical texts, it potentially addresses a domain-agnostic problem applicable to legal texts, policy documents, academic articles, and any genre in which a discursive approach introduces vocabulary from positions the document does not endorse.

Spatial reasoning is fundamental to general robot intelligence, as it enables robots to complete long-horizon tasks involving multi-object interaction. We introduce Simify, a training-free, test-time framework that performs explicit spatial reasoning via massively parallel physics simulation. From a single RGB-D image of a scene, Simify reconstructs simulation-ready assets leveraging 3D generative models and vision-language models. Then given a task specified by a reward function (e.g., build the tallest tower), Simify launches thousands of parallel rollouts in simulation and performs an evolutionary search to optimize object arrangements, typically converging within seconds. We conduct quantitative experiments on real-robot hardware to demonstrate the ability of our framework to execute complex object rearrangement tasks end-to-end with previously unseen objects. Results show that our framework outperforms prior work on foundation models for spatial reasoning by effectively exploiting large-scale parallel simulation during inference, and also highlight the importance of complete and accurate geometry for successful sim-to-real transfer.

Exploration–exploitation is a central trade-off in bandit learning. While classical algorithms such as upper confidence bound methods and Thompson Sampling effectively balance this trade-off in stationary environments, their exploration strategies mainly reduce uncertainty about the current optimal arm, which can be insufficient in nonstationary settings where future optimal arms may differ substantially from current ones. In this paper, we propose Future Information-Directed Sampling (FIDS), a new algorithm for Bayesian nonstationary bandits that explicitly explores to gather information about future optimal arms. We show that FIDS achieves regret comparable to Thompson Sampling up to a small constant factor, while being able to exploit predictive information structures that conventional exploration objectives fail to capture. To address the practical difficulty of posterior inference, we further propose a supervised-learning-based approximation framework that learns the FIDS policy from offline data, and demonstrate its effectiveness on synthetic benchmarks.

Dynamic graph anomaly detection requires repeated decisions as graph structure and class prevalence drift, yet detector benchmarks usually score a fixed pipeline after current labels are known. We introduce DynGraphAgentBench, an executable benchmark for agentic lifecycle control under delayed feedback. It comprises seven temporal graph datasets with node- and edge-level anomaly tasks, eleven selectable detectors, and eight chronological deployment windows per dataset. In each window, a controller sees only time-causal aggregate context, registered model cards, and its own matured history. It must choose a detector before current-window training or candidate scores exist. A sandboxed executor trains the chosen architecture on mature data, scores a hidden deployment window, and releases the outcome after a one-window delay. A deterministic verifier checks decision timing, leakage guards, legal actions, training scope, and persisted artifacts. We measure detection utility with average precision and capture at fixed review depth, and characterize adaptation through model switches and compute. Complete eight-window trajectories from two primary controllers and a no-memory reference on four datasets, together with three additional controllers on three datasets, expose useful, costly, and ineffective reactions to delayed evidence without granting an exhaustive current-window oracle.

In this paper, we study the higher-order ranking, by spanning-tree count, of graphs obtained from a complete graph by deleting a fixed number of edges. Using the edge-defect matrix determined by the deleted edges and the interaction number measuring the local overlap among them, we derive a stability inequality that quantitatively estimates the decrease in the number of spanning trees from the matching-deletion case. Combining this stability estimate with a classification of deletion graphs having small interaction number, we determine, up to isomorphism, the nine deletion graphs with the largest spanning-tree counts for $p\geq6$ and $n\geq2p$. We also clarify the relation between the interaction number, the local structure of the deletion graph, and the decrease in the number of spanning trees through a logarithmic expansion of the normalized spanning-tree count.

Neural operators can accelerate repeated nonlinear mechanics calculations, but their accuracy can deteriorate as operating conditions move beyond the training range. This work studies whether high-fidelity solutions acquired during use can be reused to adapt a neural operator and improve subsequent mechanics-based command selection. Two hard-magnetic soft-material systems are simulated using high-fidelity finite-element (FE) models, providing reference solutions for evaluating surrogate predictions and selected commands. A neural operator predicts deformation from known material, loading, and magnetic-field inputs, while an empirical error estimator determines which predictions may be used for command selection. Selected FE evaluations supplement these predictions, and their complete loading paths are retained for periodic updates of the neural operator and estimator. In both examples, the fixed operator loses substantial accuracy when stiffness and loading move outside the training range. Updates using 16 acquired paths recover much of the lost accuracy while preserving accuracy in the nominal regime. Under the same FE evaluation budget, the updated operators also improve command selection, although the benefit varies with the operating condition. Error estimation is less consistent, with inaccurate predictions sometimes accepted and accurate predictions rejected. These results demonstrate that reusing high-fidelity loading paths can extend the useful operating range of a neural operator. However, improved forward accuracy alone does not guarantee reliable prediction acceptance, highlighting prediction-specific error assessment as a separate requirement for trustworthy decision making.

Semi-structured pruning compresses large language models (LLMs) while keeping a regular sparse structure, but the prevailing N:M pattern fixes the same local sparsity ratio in every layer. Layer-adaptive sparsity allocation improves unstructured pruning, yet it has been reported to be less effective under N:M sparsity, leaving open whether adaptive allocation is of limited value for semi-structured pruning in general or only under the fine-grained N:M pattern. We examine this question with group-level sparsity, which partitions each weight matrix into regular groups, retains or prunes each group as a whole, and allows each layer's sparsity ratio to vary under a global budget. We propose GroupMask, which generates the group selectors of all layers with a lightweight hypernetwork, relaxes them with a Gumbel-Sigmoid parameterization and a straight-through estimator, and learns them through sparsity-budget regularization and self-distillation while keeping the pretrained weights frozen. On LLaMA-2-7B at 50% sparsity with the same $1\times256$ group size, learned layer-adaptive allocation reduces WikiText-2 perplexity from 10.02 to 8.30 and raises the average zero-shot accuracy from 0.455 to 0.496 relative to a uniform per-layer ratio. GroupMask obtains the lowest WikiText-2 perplexity on LLaMA-2-7B and the highest average zero-shot accuracy with Alpaca calibration among the evaluated baselines on five LLaMA and Qwen models. Our code is available at https://github.com/ZhengaoLi/GroupMask.

We study the trade-off between squared-error accuracy and incentive compatibility in linear regression. Agents report private labels associated with publicly known features and prefer predictions close to their true labels. Ordinary least squares (OLS) need not elicit truthful reports. For regression with $d$ parameters, we design a deterministic group-strategyproof mechanism achieving a $(d+1)$-approximation to the least-squares optimum and prove optimality even among universally strategyproof randomized mechanisms, answering an open question of Chen et al. (EC 2018). Relaxing universal strategyproofness to strategyproofness in expectation reveals a sharp separation: squared individual loss retains the factor $d+1$, while absolute individual loss admits the tight ratio $2-1/(\lceil d/2\rceil+1)$.

Quantum annealing is a promising form of quantum computation, but it slows down at a small energy gap $\Delta$ during the anneal, and the errors it makes there remain undetected. We introduce cavity quantum annealing, in which a cavity mode of frequency $O(1)\gg\Delta$, coupled mid-schedule, swaps these errors into photons. In the $p$-spin model, this reduces the annealing time to nearly the square root of that required without the cavity. Moreover, counting the photons certifies the result: high-photon runs, with an $O(1)$ yield, reach a ground-state fidelity above $99.99\%$ orders of magnitude sooner, a gain that grows exponentially with system size. A pre-loaded photon instead runs the swap in reverse, preparing an excited state. More broadly, our work shows that cavities can enhance computations performed with qubits, paving the way toward high-fidelity quantum state preparation by quantum annealing.

Large Language Model (LLM) based Multi-Agent Debate (MAD) is one of the most effective test time scaling techniques. Through multi-round communication, agents complement each other in knowledge and reasoning and solve tasks that no single member can solve. However, existing MAD frameworks fail to beat strong Single Agent and Consistency-based baselines under the same strict cost limit, which shakes the foundation of the MAD field. We propose Conditional Progressive Pruning (CPP), a lightweight pruning framework that fully exploits multi-round MAD. CPP outperforms all existing MAD frameworks on multiple dominated benchmarks. It is also the first to fully outperform consistency methods. Our code, detailed agent interaction records will be released soon.

Manipulating a Rubik's Cube with a single dexterous hand is a challenging test of sustained, contact-rich control: the hand must execute successive layer turns while keeping the cube secure. Each turn requires some fingers to support the cube while others push a moving layer, release contact, and reset for the next move. To learn this coordination, we introduce FINGR (Future-supervised Interaction Network with Geometric Representations), a policy that combines finger-relative geometry with future interaction prediction. A shared point encoder expresses the cube relative to each fingertip and aggregates its points without depending on cubie indexing. Learned future tokens share the observation encoder and receive supervision for contact-force changes, layer-turn progress, and finger joint displacement at multiple time scales. The resulting representation conditions a flow policy that directly generates finger actions. On a real dexterous hand, our policy achieves 99.0% success over 300 turn attempts, compared with 79.7% for the base flow policy. Integrated with grasping and table-assisted regrasping, the policy solves all ten scrambled $2\times2\times2$ cubes in a mean complete-system time of approximately 137 seconds. The project website is available at https://www.lyt0112.com/projects/FINGR

Existing interpretable graph additive models still face limitations in either computational scalability or modeling flexibility. In terms of structural modeling, previous approaches either face quadratic scaling costs or sacrifice explicit source-to-target contribution decomposition. In terms of feature components, they rely either on per-feature neural networks or on single shared bases with limited feature specialization. We address both problems by introducing HARMONIA: Interpretable Graph Learning through Mixtures of Neural Bases, an interpretable-by-design framework. For feature modeling, HARMONIA introduces a Mixture of Neural Bases (MoNB), which routes features to specialized basis experts, enabling parameter sharing without sacrificing feature-specific specialization. For structural modeling, HARMONIA uses Relative Random Walk Probabilities (RRWP) to capture multi-hop and multi-path relationships, and proposes Sparse RRWP Aggregation (SRA) to compute these interactions through sparse graph propagation without quadratic pairwise complexity. HARMONIA retains a simple additive form in which predictions decompose into feature responses modulated by structural influence. Empirically, HARMONIA achieves stronger explanation recovery than existing interpretable graph baselines while maintaining competitive predictive performance and scaling to graphs with millions of nodes. These results show that interpretable graph learning can remain both faithful and scalable without sacrificing predictive effectiveness.

A decision model can give probabilities that sum to one for every question yet disagree with itself when the same decision is broken into smaller steps. We study this form of probabilistic coherence in Jev and the English Laya checkpoint, using 2,500 matched examples per system across TREC, CLINC150, and MASSIVE. Across 72,000 classification questions, we compare direct fine-label predictions with broad-category probabilities and predictions reconstructed through those categories. Both systems show substantial disagreement: mean category-level total variation ranges from 0.219 to 0.349 for Jev and from 0.424 to 0.689 for Laya, on a scale where zero means exact agreement. The consequences differ sharply. On CLINC150, reconstruction reduces Jev's accuracy by 22.9 percentage points (paired 95% bootstrap interval: [-24.9, -20.9]) and improves Laya's by 21.3 points ([18.0, 24.5]). The same directions hold across all three datasets, with all six unadjusted accuracy-change intervals excluding zero. Improved accuracy can also accompany less reliable confidence: on MASSIVE, Laya gains 9.2 accuracy points while its expected calibration error rises from 0.046 to 0.124. Error analysis identifies both broad-category mistakes and within-category confusions. These findings show why decision systems need joint evaluation of accuracy, confidence calibration, and probability coherence in the workflow used by an application.

Chain-of-Thought reasoning has enabled large language models to achieve substantial performance gains on complex tasks. However, these gains come at the cost of dramatically increased token consumption. This raises a fundamental question: is every token in the reasoning trace equally valuable? We present a diagnostic and optimization framework grounded in a key empirical finding: the value of tokens within a CoT reasoning sequence is highly non-uniform, and this non-uniformity can be effectively characterized by token-level log probability signals. We show that normalized log probability helps distinguish core tokens, which carry structural and decisive reasoning content, from redundant tokens, which are exploratory, low-confidence filler that contributes less directly to the final answer. Building on these findings, we formulate the TokenProbe framework around two empirical findings and one claim: findings identify token value inequality first and then establish TokenProbe as a core-token proxy, and the claim introduces an efficient GRPO objective positing that selectively compressing redundant tokens can yield Pareto improvements in the accuracy-token efficiency space. Empirically, our method preserves reasoning quality while reducing the token usage by 76% of the baseline. Under matched reasoning-length budgets, we show that it can even outperform strong flagship baselines like Gemini-3.1-Pro. Homepage: https://runjia.tech/tokenprobe/.

Immersive video communication requires photorealistic, compact dynamic scene representations that support efficient rendering. 3D Gaussian Splatting (3DGS) is a promising approach, but dynamic 3DGS remains difficult to compress due to its dense primitives and spatiotemporal redundancy. Anchor-based formulations improve compactness through sparse scaffolds that share geometry and appearance across primitives. However, existing designs typically deform a single canonical scaffold and condition each primitive solely on its associated anchor, limiting their ability to model non-local dynamics and disocclusions and exploit inter-anchor correlations. To address these limitations, we propose SAGA, a volumetric video codec built on Sparse Anchor-assisted GAussian splatting representations. SAGA represents a dynamic scene using hierarchical sparse anchors in 4D space-time. Coordinate-based INR decoders generate fine anchors and Gaussian primitives from features obtained through kernel interpolation among nearby anchors, enabling parameter sharing across spatiotemporal structures. A fixed-size memory with a novel orthogonality-informed slot-update strategy further captures long-range dependencies among unstructured anchors for entropy coding. Empirically, \name achieves PSNR-based BD-rate reductions of 90.88%, 64.30% and 65.14% relative to GIFStream, TED-4DGS, and OMG4, respectively, on the Neu3D testset.

Testing whether two populations of networks share the same edge probabilities is a basic problem in network inference. How hard it is depends on the norm used to measure the difference. For the inhomogeneous Erdős–Rényi (IER) model, the optimal sample complexity is known for every integer $L_r$ norm and for $1\le r<2$. For non-integral $r>2$, however, the known upper and lower bounds do not match, and the lower bound was conjectured to be tight. We study this gap for two-sample testing on aligned vertices. We propose a test that runs two published statistics, of orders $2$ and $\lceil r\rceil$, on the same data and rejects if either one rejects. Its thresholds come from Hölder interpolation, so that both statistics have the same sample cost. We prove that this test attains the conjectured rate. Combined with earlier results, this shows that for every fixed $r\ge1$ the minimax sample complexity is of order $n^{\max\{4/r-1,\,2/r\}}/\epsilon^2$, even when the separation changes with $n$. In simulations with $n$ between 32 and 256, the number of graphs needed for 80% power at level $0.05$ grows with $n$ at a rate consistent with the theory. For $r=2.5$, for example, the fitted exponent is $0.78$, against the theoretical value $0.8$. Interestingly, the two statistics split the work as the interpolation argument suggests: the higher-order statistic is more powerful when only a few edges change, and the $L_2$ statistic when many edges change.

Practical assistive and rehabilitative brain–computer interfaces require subject-independent motor-imagery EEG (MI-EEG) decoders that generalize to new users under limited target-user data and constrained compute. However, held-out-subject performance can be overstated when test-subject information influences preprocessing, model selection, or ensemble selection. We present ThinkNet, a validation-controlled framework that combines train-only normalization, validation-guided evolutionary search, and validation-gated inference to identify compact decoders and inference policies for held-out subjects. We evaluate four-class BCI Competition IV-2a (session T) decoding with nine Leave-One-Subject-Out (LOSO) folds, three seeds, seven fixed decoder entries, and a broader search over ten representative decoder families; the held-out subject is never used for normalization, hyperparameter, architecture, or ensemble-policy selection. In the fixed benchmark, the validation-selected compact decoder achieved 44.35$\pm$15.41% accuracy with 4.9K parameters, 19 KB FP32 weights, and 0.99 ms batch-1 Orin CUDA inference. Across the broader search, compact models ($\leq$25K parameters) achieved higher mean held-out accuracy than mid-size and large alternatives after selected retraining (40.10% vs. 35.09% and 34.78%). Validation-gated ensembling improved over validation-selected single-model inference, reaching 43.98$\pm$16.25% in the fixed benchmark and 43.31$\pm$15.88% for the compact six-family ensemble. A non-deployable oracle analysis revealed a 6.1-point family-selection gap and near-zero validation–test correlation, showing that validation reliability remains a key bottleneck under subject shift. Thus, ThinkNet is a validation-controlled framework for compact MI-EEG model and inference-policy selection, rather than a single-architecture benchmark.

A famous folklore result in list coloring demonstrating that the gap between the list chromatic number and chromatic number of a graph can be arbitrarily large is: $\chi_{\ell}(K_{l,t}) = 1+l$ if and only if $t \geq l^l$. DP-coloring (also called correspondence coloring) is a well-studied generalization of list coloring introduced in 2015. In 2018, Mudrock studied the DP analogue of the aforementioned folklore result. He proved that for $l \in\mathbb{N}$, if $\mu(l)$ is the smallest integer $t$ such that $\chi_{DP}(K_{l,t})=1+l$, then $\left\lceil l^l/l!\right\rceil \leq \mu(l) \leq 1+l^l(\log(l!)+1)/l!$. Recently, Kaul, Mudrock, and Sharma studied a more general version of this problem by studying the smallest $t$ for which $\chi_{DP}(G \square K_{l,t}) = k + l$, where $G$ satisfies certain criticality conditions and $G \square K_{l,t}$ denotes the Cartesian product of $G$ and $K_{l,t}$. In this paper, we introduce a notion we call covering families that gives a new perspective on these DP-coloring questions. In particular, if $\kappa(l)$ denotes the minimum size of a covering family of $[l]^l$, we show that $\mu(l)=\kappa(l)$. We use this equivalence to prove $\mu(4)=12$ and to obtain new general lower bounds on $\mu(l)$. We also prove a general upper bound on the minimum size of covering families which yields an improved general upper bound on $\mu(l)$ and gives improvements on known bounds for related DP-coloring questions involving Cartesian products with complete bipartite graphs.

We describe a methodology for estimating the per-token energy cost of cloud-hosted large language model (LLM) inference, separating between input (prefill) and output (decode) tokens. Graphics processing unit (GPU) energy usage is measured during inference benchmarking with open-weights models on a wide range of text-based tasks. The remaining server energy contribution from non-GPU hardware is estimated from the inference wall time. Bayesian linear regression is used to model the relationship between energy per token and LLM size, request traffic, and hardware deployment configuration. Proprietary frontier LLMs of unknown size and deployment are binned into size buckets based on naming conventions and performance priors, and the space of possible LLM configurations is sampled with Monte-Carlo methods to give a representative average energy per token and uncertainty. We also describe how these energy measurements can be used to estimate the carbon-dioxide equivalent ($\mathrm{CO_2\text{-}eq}$) emissions, both usage and embodied, and water consumed per token of AI inference. This methodology provides actionable data that enables reductions in cost, electricity usage, $\mathrm{CO_2\text{-}eq}$ emitted and water consumed in cloud and Software as a Service (SaaS).

Directional multi-transmitter localization from sparse received-power observations is difficult because the receiver observes only the source-unresolved aggregate field: multiple directional sources superpose, building blockage fragments their visible regions, and stronger sources can mask weaker ones. We present SymNetPro, which retains the dual-task radio-map reconstruction and localization backbone of SymNet and adds two targeted components. First, a sparse line-of-sight (LOS)-aware attention bias injects obstruction-aware spatial relations into selected token interactions. Second, transmitter-drop augmentation recomposes training scenes after removing one sample-supported transmitter, exposing the model to controlled source-cardinality variation. Experiments on directional ray-traced urban environments show substantially lower OSPA than representative localization baselines under extreme sparse sampling, with consistent gains under measurement noise and increasing transmitter count. A transmitter-specific evidence analysis further shows that remaining misses concentrate in regimes where the target contributes little distinguishable power to the aggregate observation.

We show that the natural tensor product multiplication of two Archimedean almost \(f\)-algebras does not, in general, extend to their Fremlin tensor product. The two algebras in the counterexample have the same underlying vector lattice \(C[0,1]\). Their multiplications are explicit, positive and nilpotent of index three. The obstruction is the fact that the function \((s,t)\mapsto e^{st}\) does not belong to \(C[0,1]\ftensor C[0,1]\). The same construction gives Banach almost \(f\)-algebras and has consequences for previously published assertions on Riesz and Fremlin projective tensor products of almost \(f\)-algebras.

Subject-independent motor-imagery (MI) EEG decoding can exhibit subject-level failures even when average performance appears acceptable: under subject shift, a decoder can become an overconfident near-one-class predictor. This is especially problematic in source-free deployment, where target-user labels are unavailable during adaptation and expert selection. We present EEG-Fusion, a failure-informed decision-level fusion framework that treats source-free MI decoding as label-free reliability estimation over heterogeneous experts. EEG-Fusion applies subject-wise Euclidean alignment and normalization-only test-time adaptation, then routes each target subject to a neural, covariance-based, or physiological-feature expert using a reliability gate trained on source-held-out folds to predict expert performance and collapse risk from label-free stream diagnostics. The gate uses confidence, entropy, prediction diversity, expert agreement, and predicted class balance; collapse is measured as the maximum predicted class fraction. In 9-fold leave-one-subject-out (LOSO) evaluation with three seeds, relative to a no-alignment raw EEGNet source-free anchor, EEG-Fusion improves subject macro-F1 from 0.417 to 0.529 on BCI IV-2a local protocol, from 0.314 to 0.482 on BNCI2014-001, and from 0.607 to 0.708 on BNCI2014-004; corresponding collapse-index reductions are 0.199, 0.227, and 0.169. In a 9-subject Cho2017 external subset, EEG-Fusion improves macro-F1 from 0.516 to 0.630. These results suggest that label-free reliability estimation can reduce subject-level failure modes in source-free MI-EEG deployment.

Motivated by a class of three-component Fourier ODE systems consisting of a conserved mode coupled to a pair of oscillatory modes, we develop a "potential-vorticity-wave" (PV-Wave) decomposition strategy for constructing adapted energy variables in the stability analysis of Couette flows. The strategy separates the conserved potential-vorticity component, symmetrizes the remaining wave subsystem, and introduces an additional correction to control the couplings generated by time-dependent Fourier coefficients. We apply this framework to study the linearized dynamics of 3D Boussinesq MHD system and Rotating Boussinesq system for Couette flows and quantify the inviscid damping and parameter-dependent amplification arising from the interaction of Alfvén-gravity waves and inertial-gravity waves.

Since the pioneering work of Taylor and Goldstein in 1931 laid the foundation for the study of parallel stratified shear flows, non-parallel configurations have received comparatively little attention. We study the stability of the 3D Boussinesq system near the plane Couette flow $V^*=(y,0,0)$ under the vertically stratified background $\eta^*=\alpha z$. The shear and stratification directions are perpendicular. This geometry produces two structural effects that are absent in the parallel configuration: an additional nonlocal coupling in the non-zero-mode system, which obstructs a directly useful symmetrization, and a wave-shear coupled lift-up mechanism for the zero modes. The $L^p$ transient growth due to the lift-up effect can be suppressed either by sufficiently strong stratification (for $p>2$) or under suitable assumptions on the initial data (for $p\geq 2$). To study the nonzero-mode system, we introduce a reformulation based on the linearized potential vorticity (PV), a fundamental quantity in geophysical fluid dynamics, to recover a better energy structure. We establish the inviscid damping of $u_{1,\neq}$ and $u_{2,\neq}$. We further apply the linearized PV formulation to study the linear stability of the tilted Couette flow. Finally, we use this formulation to prove the nonlinear stability for perturbations on $\mathbb{T}\times\mathbb{R}\times\mathbb{T}$.

We study logarithmic complete monotonicity of a power family built from the digamma function. An explicit Laplace representation of its negative logarithmic derivative reduces the question to positivity of a continuous kernel. We prove a strict kernel bound on an explicit parameter range and obtain uniform lower bounds for all alternating logarithmic derivatives. In particular, this gives an independent proof of the property conjectured by Guo, Zhang, and Qi on the entire positive half-line. We also characterize the exact admissible parameter threshold by a variational minimum and show that the explicit sufficient bound is not optimal. The argument combines monotonicity of an auxiliary digamma kernel with a regularized logarithmic convolution. An appendix identifies a false auxiliary inequality in an earlier proof, while the present argument independently establishes its stated conclusion.

We study whether systems with multiple concurrent proposers (MCP) incentivize the geographic decentralization of proposers. In our model, concurrent proposers strategically choose their locations to maximize their captured market share of users, who decide where to send transactions by comparing each proposer's time to inclusion. The time to inclusion between a user and a proposer consists of two terms: the distance between them, and the distance between the proposer and her nearest quorum of attesters, the latter of which we term the quorum radius. We formally prove that proposers' quorum radii are the determinant of their incentives: proposers optimally choose where to locate in order to minimize their quorum radii. We obtain as a result co-location when proposers also serve as attesters, but geographic diversity when these roles are separate. We also examine pre-confirmations and faster intervalidator connections, showing that they attenuate the influence of the quorum radius and further destabilize co-location incentives.

We study the growth of the spectral function of the Laplace-Beltrami operator on a Riemannian manifold $M$ of dimension $n$. For $n\geq 3$ we show that for any $x\in M$ there is a full measure subset $Z_x\subset M$ such that for all $y\in Z_x$ \[E_{\Lambda}(x,y) = O_{M,x,y,\varepsilon}(\Lambda^{n/2}(\log\Lambda)^{3/2}(\log\log\Lambda)^{1/2+\varepsilon}). \] For $n=2$ we prove a stronger statement. For any $x\in M$ there is a full measure subset $Z_x\subset M$ such that for all $y\in Z_x$ \[E_{\Lambda}(x,y) = O_{M,x,y,\varepsilon}(\Lambda^{5/6}(\log\Lambda)^{1/6}(\log\log\Lambda)^{1/6+\varepsilon}) .\]