Papers

In this paper, we derive optimal order a posteriori error estimates for the variable step-size explicit two-step exponential Adams (E-Adams2) method for parabolic problems. We begin by introducing an E-Adams2 approximation, deffned by the piecewise linear approximate solutions, which leads to suboptimal error estimates. To recover optimal order error estimates, we introducean appropriate reconstruction of the approximation with the second order residual for the explicit E-Adams2 method, which plays key roles in deriving optimal order a posteriori error estimates for the proposed explicit method for linear and semilinear parabolic equations. Various numerical experiments are carried out to verify the correct convergence rates of the a posteriori quantities, and the high efffciency of the adaptive algorithm.

Online users often release multiple texts under the same identity, giving attackers an author profile that can reveal more than any single text. Existing authorship obfuscation methods optimize privacy independently for each document, leaving them blind to cross-document correlations that make aggregation dangerous. We propose Aggregation-Aware Synthetic Text Generation (AAST), a framework that addresses this gap by jointly selecting synthetic texts at the bundle level rather than optimizing each text in isolation. AAST targets attribution and verification attacks, including cross-genre settings where attacker references come from a genre not observed during generation or selection. Experiments across same-genre, cross-genre, neural, and independent non-neural stylometric attacks show that AAST lowers account-level linkability as bundle size grows, while preserving semantic quality, linguistic acceptability, and sentiment alignment.

Physical automation is scaling toward fleets of embodied machines commanded by an AI brain. Early deployments already run factories and warehouses at production rates beyond any human line, and their adoption is accelerating. But when their joint decisions cause harm, everyone involved has reason to blame everyone else, the machine vendor, the algorithm provider, the factory operator, the insurer, and the regulator, and no method can divide the responsibility between them. Existing methods read logs whose origin they cannot verify and name a single culprit, misrepresenting outcomes that are overdetermined, preempted, or caused by an omission. We present AUDITA, an audit layer pairing a tamper-evident record of every inter-agent command with a certified, graded causal-attribution engine. We prove its verdict cannot be gamed: a rule-following agent can never be made to look guilty, an attempt to shift blame is itself caught and graded, and we establish the exact limit of what an evidence-based auditor can certify. On live language-model pipelines it reduces the standard judge baseline's responsibility error roughly threefold; on a benchmark of accident-grounded structures it recovers responsibility where single-culprit baselines fail, and stays invariant under forgery. AUDITA turns the question of who is to blame from an argument about logs into a calculation over evidence.

We prove that for every fixed inverse temperature $\beta < 1 / 2$, with high probability over the disorder, the single-site Glauber dynamics for the $n$-spin Sherrington-Kirkpatrick model mixes from every initial configuration to within total variation distance $\varepsilon$ in $O_{\beta}\left(n \log\left(n / \varepsilon\right)\right)$ steps. The bound holds uniformly over all external fields and is optimal up to constants depending only on $\beta$. The main ingredient is a deterministic criterion for optimal-order Poincaré inequalities in general Ising models, established via the integrated Bakry-Émery criterion together with a new two-spin estimate. A standard application of the localization-scheme framework of Chen and Eldan then upgrades the Poincaré inequality to a modified log-Sobolev inequality, yielding the optimal mixing-time bound. The main ideas underlying the proof of the Poincaré inequality were generated by GPT-5.6 Sol Ultra.

Stacked intelligent metasurfaces (SIMs) have recently emerged as a promising architecture for large-scale beamforming systems, including cell-free massive MIMO (CF-mMIMO), due to their cost-effective wave-domain signal processing capabilities. However, existing algorithms for the joint optimization of digital and SIM-enabled wave-domain beamforming typically incur prohibitive computational complexity. In this work, we propose an efficient alternating optimization (AO) algorithm for weighted sum-rate maximization in SIM-assisted CF-mMIMO systems employing hybrid digital-wave beamforming. Unlike prior approaches that rely on general-purpose optimization solvers or per-element gradient ascent methods, the proposed algorithm updates the digital and wave-domain beamforming variables on a per-access point (AP) or per-SIM-layer basis, enabling closed-form updates at each step. Numerical results demonstrate that the proposed algorithm reduces the computational complexity by more than 99% compared to existing algorithms while achieving nearly identical sum-rate performance.

The study of adversarial examples and their origins remains an open area of research. Mechanistic interpretability, and superposition in particular, offers new avenues for approaching this problem. Gorton & Lewis (2025) demonstrate that adversarial examples arise from superposition and show empirically that adversarial training reduces superposition, yet provide no mechanistic account of why this occurs. We present an empirical explanation inspired by the feature taxonomy of Ilyas et al. (2019), tracing the following chain of causalities: adversarial training abandons non-robust features, leading to fewer total features to represent, resulting in less superposition.

Researchers must often choose between Bayesian or neural network models of behavior, two paradigms with complementary strengths and weaknesses. An ideal paradigm would facilitate testing many kinds of representations and inductive biases; Bayesian models make this easy, while neural networks do not. Similarly, an ideal paradigm would avoid over-simplifications; neural networks make this easy, while Bayesian models do not. Here, we introduce Bayesian distillation with Behavioral Tuning (BBT) as an approach to getting the best of both traditions. BBT offers a simple recipe for model building: first, a neural network is trained to mimic a Bayesian model through synthetic data, and second, the network is fine-tuned on human behavior to capture additional structure and nuance. Across four case studies in human concept learning, we find that BBT outperforms traditional approaches at predicting human behavior while also revealing psychological insights, resulting in models that can both mimic Bayesian priors and capture heuristics and biases that violate simple modeling assumptions.

Multi-agent systems built from large language models are deployed widely, yet how much performance is lost when two LLMs must coordinate rather than act alone remains unclear. We formulate the collaboration tax as the team-decentralisation loss of a two-player cooperative game with private information, with two propositions characterising its sign and its equivalence to a max-superadditivity violation. We operationalise this definition on 32 solo-tractable tasks grouped by source of grounding friction and measure it on 11 models from 7 providers. The tax is structured along two no-exception axes: a category ordering across every model and a monotonic decrease with capability. The proximate mechanism is not a reasoning deficit but a four-stage conversational cascade in which agents make ungrounded claims, fail to query the partner, skip integrating both views, and accept the answer without re-derivation. The tax is mechanically predictable from conversation features and partly tractable: a prompt intervention targeting all four stages closes a substantial fraction of the gap, with the dominant bottleneck differing across categories. In heterogeneous pairs the tax is pulled toward the stronger partner rather than the additive midpoint, empirically realising the max-superadditivity violation predicted by our framework. Together these results recast collaboration in LLM systems as a measurable, predictable, and partly tractable cost.

Ten years ago, we surveyed software visualization research under the assumption that the challenge for adoption was matching developers' needs with techniques. Generative AI might have made that assumption obsolete by driving the cost of producing a visualization on demand toward zero. We argue that this mirrors a broader inversion already underway in software engineering: as AI devalues the production of artifacts, it elevates the human work of perceiving and directing them. Looking back at our 2016 research, we found that domains we flagged as neglected, such as rationale, are exactly the ones AI now makes tractable, and a tool-sustainability problem we diagnosed then is one generative AI may worsen before it helps solve. One finding shifted outright: the share of studies delivered through immersive environments grew roughly fifteen-fold, though it remains a small minority of the field. We argue that future research should focus on helping people understand large and complex software systems, including the reasoning processes generated by AI agents alongside the code itself. Humans have always been accountable for what they trust, but AI may lead them to trust without enough scrutiny. We confront the risks that follow, from the reliability of AI-generated visualization itself to the temptation of competing with machines on their own terrain, and conclude that actionable visualization is no longer a distant destination but a standard the field can now meet.

For centuries, women have been cast as the source of harm in public narratives, from witch hunts in early modern Europe to contemporary stereotypes about emotional instability. These cultural patterns reflect enduring biases in how people attribute causality and assign blame, often portraying women as agents of disruption and men as figures of rational authority. In this study, we examine how such gendered causal attributions appear in everyday language. Leveraging three complete 24-hour datasets of all English-language posts on Twitter, and using language models, we extract cause-and-effect relationship pairs and identify gendered attribution of causal agents. We then analyze how gender attribution relates to sentiment, the kinds of effects invoked, and the diffusion of posts through the social networks. Our findings reveal that female-attributed causes are more often associated with negative sentiment and emotional or relational outcomes, whereas male-attributed causes are more frequently linked to positive sentiment and abstract, structural effects. Moreover, male-attributed narratives spread more widely across communities. These results suggest that longstanding gender stereotypes continue to appear in how people express and amplify causal narratives in public discourse, in decentralized, high-velocity environments like social media.

LLMs generate fluent plans for robots but routinely violate the syntactic and se8mantic constraints they must satisfy to execute, and existing remedies trade formal guarantees against plan quality: soft methods (affordance scoring, grounded decoding) give no guarantee, while symbolic planners (LLM+P) discard the LM's commonsense. We propose Meta-Ctrl, a constrained-decoding framework that guarantees the encoded constraints while preserving the base LM's plan quality. Meta-Ctrl introduces meta-tokens—a compact vocabulary of grounded actions—enforcing syntax at the token level and semantics (preconditions, goals, ordering) at the action level, an exact factorization that cuts the memory of constrained decoding from over 107TB to under 2GB. With it, a small open-weight LM becomes competitive where it otherwise sits at the bottom of the leaderboard: on WAH-NL under the LoTa-Bench protocol it reaches the highest reported subgoal success rate, exceeding GPT-4's, with consistent gains across the Embodied Agent Interface. We further demonstrate it on a real tabletop robot, where every generated plan satisfies its preconditions and goals by construction. Project website: https://metactrlg.github.io

Causal reasoning is fundamental to human understanding and information organization. People prefer causal explanations because they offer coherence, predictability, and a sense of control. Conversational structures shape how knowledge and perspectives are shared, validated, and amplified in networked publics. Understanding the structural effects of causal language can reveal pathways to fostering deeper, more meaningful interactions online. In this work, we investigate how causal language influences the topology and temporal evolution of discussion threads in online conversations with a dataset of 17 million posts across 200 subreddits in 2023 on Reddit. Our results show that causal language is consistently associated with deeper, more sustained conversations, with effects emerging early in the lifecycle of a thread, as demonstrated through a counterfactual experiment. Importantly, emotional responses do not differ substantially between causal language and non-causal language, suggesting that structural depth arises from framing itself rather than affective escalation. A lightweight qualitative analysis shows that causal framing titles prompt users to elaborate more with reasoning and contribute personal experiences, supporting deeper multi-turn exchanges. These findings suggest that causal language acts not merely as a stylistic device, but as a cognitively grounded and structurally influential signal that shapes the topological structures of online conversations.

Across implicit-neural-representation (INR) architectures and analytic benchmarks we observe that a thoroughly tuned Adam (especially its learning rate (lr), e.g. in a hyperparameter sweep from $lr = 0.05$ to $10^{-8}$) can potentially reach a very low loss even on ill-conditioned loss landscape or converge at a plateau far above the loss attained by second-order methods. This report defines the measured metrics that help determine if Adam can mitigate the ill-conditioning on a given loss landscape. We provide the indicators by which each outcome is determined, that are: the condition number of the Hessian and of the Adam-preconditioned Hessian $D^{-1/2}HD^{-1/2}$ (with the derivation from Adam's update rule), the diagonal mass $\rho$ that distinguishes axis-aligned from cross-coupled ill-conditioning, the negative spectral mass estimated by stochastic Lanczos quadrature, and the gradient energy fractions over curvature bands, including the flat fraction that indicates the Adam stall. A worked out $2\times 2$ example and an illustration show the reasons why a diagonal preconditioning by Adam can remove axis-aligned ill-conditioning by rescaling and why it cannot do the same if the ill-conditioning is cross coupled. In addition, we present a case study of FINER image fitting architecture that goes over the whole loss landscape analysis framework: the fitting architecture description, reasons due to which its landscape stalls Adam at saddles, the measured PSNR values through our tuned baselines to the $120$–$134$\,dB results of the blockwise second order methods, the error maps behind those numbers, and description of the benefits such image fitting accuracy gives in practice.

Qualitative mechanical problem-solving (QMPS) refers to solving qualitative problems from the mechanical domain. Qualitative problems can be solved with minimal discipline-specific information, without any robust quantitative calculation, generally by using qualitative reasoning and commonsense knowledge. QMPS is a vital aspect of human intelligence that allows us to tackle a wide range of tasks, from simple everyday ones such as turning on a tap to complex tasks in highly demanding and well-paying jobs in various fields, e.g., emergency medicine, plumbing, driving, etc. Employers often use the Bennett Mechanical Comprehension Test (BMCT) to evaluate job candidates' ability to solve such problems. In this work, we assess two state-of-the-art multimodal models, Gemma-3 and Qwen-VL, on their ability to interpret mechanical problem images by eliciting a step-by-step chain of thought (CoT) and a final answer. Each image inherently encodes ground-truth qualitative facts, such as contact points in gears, support relations, and relative weights, which we use to evaluate each model's spatial and commonsense reasoning capabilities. We assess each chain for coherence, completeness, and logical progression to assess each model's thought process, and final answers are compared to verified solutions to measure accuracy.

Proactively initiating a conversation is a fundamental social competence and a critical capability for social robots. However, determining how and when to start a conversation in a given situation remains an open challenge, primarily due to the lack of a principled definition of conversational context. While recent large language models (LLMs) demonstrate impressive conversational fluency, they are predominantly turn-reactive and often produce generic or monotonous openers when tasked with initiating interaction, even when contextual information is available. Such limitations are particularly problematic for embodied social robots, where inappropriate or poorly timed initiations can negatively affect user engagement and rapport. In this work, we propose a schema of contextual variables that jointly characterize situations relevant for proactive conversation initiation. The schema is designed to structure perceptual, situational, and interactional cues such that they can be effectively exploited by language models. Furthermore, motivated by the absence of suitable training data, we introduce a curated dataset of contextually-aligned conversation openers (CCO) covering diverse everyday scenarios. Using this dataset, we fine-tune small language models (SLMs) to generate proactive conversation initiations. Through a comparative evaluation involving zero-shot LLMs, off-the-shelf SLMs, and our fine-tuned models, we demonstrate that explicit contextual structuring and targeted data curation substantially improve the quality and contextual appropriateness of conversation openers. Our results highlight the importance of context modeling for proactive social interaction and provide actionable building blocks for conversational robots.

As social robots become increasingly present in everyday environments, establishing rapport with users is critical for enabling sustained and meaningful human-robot interaction. In human-human communication, self-disclosure is a well-established mechanism for building rapport; however, its role and impact in human-robot interaction (HRI) are not yet well understood. Although recent advances in large language models (LLMs) have improved the linguistic competence of conversational robots, such systems are typically deployed as reactive information providers, offering limited social reciprocity and relational depth. In this article, we investigate the role of robot self-disclosure in fostering rapport during face-to-face human-robot interaction. We propose a dialogue system, called RADIA that leverages retrieval-augmented generation (RAG) to enable a robot to retrieve and reference simulated autobiographical memories, allowing first-person self-disclosure to be incorporated naturally into ongoing conversations. We evaluate the proposed approach through an in-person user study, comparing interactions with a self-disclosing robot against a baseline non-self-disclosing robot. Our results show that robot self-disclosure significantly influences conversational dynamics and enhances users' perceived rapport with the robot, suggesting that self-disclosure is a valuable social behavior for long-term and socially engaging human-robot interaction.

Accurate reconstruction of incomplete sensor fields is critical for state awareness in safety-critical digital twins (DTs). Thermocouples in high-temperature and radiation environments may drift, fail, or become intermittently unavailable, causing partial observability. This study develops a sparse-sensor reconstruction framework for Oregon State University's High Temperature Test Facility (HTTF) and evaluates six methods under intra- and inter-experiment protocols: three conditional generative models (i.e., a diffusion model [DM], variational autoencoder [VAE], and generative adversarial network [GAN]), two deterministic recurrent neural-network models, and ridge regression. For intra-experiment reconstruction within the PG{-}29 depressurized conduction cooldown (DCC) test, the models combine graph-based spatial encoding with gated recurrent units. The graph neural network (GNN)–gated recurrent unit (GRU) VAE achieves the lowest error, with a mean absolute error (MAE) of $11.73,^\circ$C, a root mean square error (RMSE) of $20.54,^\circ$C, and an $R^2$ of 0.98. The deterministic GNN–GRU and plain GRU obtain RMSE values of $25.26,^\circ$C and $35.22,^\circ$C, respectively, demonstrating the benefit of spatial modeling. All three generative models reduce RMSE by more than half compared with ridge regression. The DM maintains an $R^2$ of 0.94 when known sensors decrease from 91 to 45. For inter-experiment reconstruction, models trained on PG{-}27 pressurized conduction cooldown (PCC) are evaluated on PG{-}29 using section-context conditioning. The section-context DM achieves the best transfer performance, with an RMSE of $42.84,^\circ$C and an $R^2$ of 0.91. These results demonstrate the value of spatiotemporal generative modeling for missing-sensor reconstruction in safety-critical DT applications.

Social media bots are often portrayed as malicious automations to be detected and removed, but automation on social media platforms encompasses a wide spectrum of roles, behaviors, and rhetorical strategies that can shape online discourse in both constructive and destructive ways. This work conceptualizes these automated actors as Cyber Social Agents through a taxonomy of archetypes characterized by their operational tactics and rhetorical style. We integrate this taxonomy into an LLM-driven social simulation, where agents communicate and coordinate in a network environment. Using empirically grounded CSA personas, we simulate heterogeneous online societies to study how agent diversity shapes information diffusion and social influence. Our approach bridges the gap between rule-based agent models and LLM-powered simulations with generated agents that are parameterized from empirical data.

Accurate modeling of the daily evolution of sea ice concentration (SIC) is central to improving the credibility and operational forecasting capability of deep learning-based sea ice prediction. However, existing deep learning methods often couple the underlying sea ice evolution relationships and data errors within high-dimensional nonlinear mappings, making it difficult to construct a stable and verifiable evolution core and apply it reliably to practical forecasting. To address this issue, this study proposes a reanalysis-forecast dual-domain decoupled framework for learning sea ice evolution operators. The framework builds upon a lightweight physical baseline to generate daily evolution trajectories, employs a temporally constrained joint multi-lead compensation network to com?pensate for unresolved processes, and introduces an ice-mass?aware transport mechanism to suppress numerical dissipation. In the forecasting stage, the parameters of the base evolution core are fixed, while a lightweight variable-semantic adaptation mechanism calibrates inter-domain distributions and evolution responses, thereby separating forecast-domain errors from base evolution errors. Experiments show that the constructed base evolution core can accurately and stably simulate daily sea ice evolution at both short-term and annual scales under reanal?ysis forcing, and can be effectively transferred to the forecast domain through lightweight adaptation, achieving stable prac?tical forecasting capability while preserving the base evolution structure. The source code will be made publicly available at https://github.com/zhangmaqun65535/SNM upon acceptance of this manuscript.

Kuszmaul, Liang, and Zhou (SODA 2026) ask whether succinct constant-time dynamic fusion nodes exist when the number of stored keys is polylogarithmic in the universe size. We give a negative answer for always-correct structures. For n^8 <= U, log_2 U >= 2^70, and redundancy 0 <= R < n, a dynamic dictionary requires at least 2^-26 log_2(1+n/(R+1)) expected-amortized cell probes per operation. The model permits fixed layouts of packed cells of at most one word each, including the short-spill convention used by succinct word-RAM structures, and covers zero-error Las Vegas algorithms with fresh per-invocation randomness and almost-sure termination. The proof repairs a conditioning defect in the inherited communication argument by placing pointwise probe caps inside the consistency event, then extends the lower bound to large universes through a scale-adaptive entropy parameter. Consequently, when U=2^w and n=ceil(w^c) for any fixed c>0, no always-correct predecessor structure can use log_2 binom(U,n)+o(n) persistent mutable bits and support constant-time operations. Constant expected-amortized time requires Omega(n) redundant bits. Lean 4 checks the complete packed-memory and fresh-random indexed models, hard distribution, communication bounds, separator, nested-forest accounting, deterministic and Las Vegas lower bounds, strict-predecessor reduction, and redundancy corollaries.

Enabling operators to perceive and interact with remote environments naturally is a fundamental challenge in robotic teleoperation. This is especially critical in tasks involving physical interaction, where real-time haptic awareness improves operational safety and effectiveness. Existing kinesthetic haptic feedback methods suffer from instability during rigid surface contacts and remain sensitive to communication delays, while visual cue-based force feedback imposes additional cognitive load and limits sustained situational awareness. This work presents a teleoperation interface that conveys remote surface interactions to the operator through electrovibration-based tactile feedback, enabling naturally mapped force reflection while avoiding the stability issues associated with kinesthetic feedback and the latency limitations of mechanical actuators. A user study (N=21) evaluated interface usability, sense of presence, and operator workload under two force reflection conditions: visual feedback and electrovibration-based tactile feedback. Characterisation experiments further assessed path-following accuracy and response time across both conditions. Results show that tactile feedback significantly reduced response time by 15.35% (p=0.002, d=0.96) and increased the sense of presence by 31% (p<0.001, d=0.90) compared to visual feedback, while imposing comparable workload and usability across both conditions. These findings demonstrate that electrovibration-based tactile feedback is a viable and effective modality for robot teleoperation, improving operator responsiveness and sense of presence in contact-rich manipulation tasks, with direct applicability to safety-critical domains such as nuclear maintenance.

Detecting illicit cryptocurrency transactions is hampered by extreme class imbalance, adversarial obfuscation, and a scarcity of reliable labels. While semi-supervised learning (SSL) offers a promising solution by leveraging unlabeled data, we show that its success is not guaranteed by data volume alone but is contingent on data quality. We introduce an SSL framework for detecting illicit Bitcoin flows in Shared Send Mixers (SSM) transactions, built on a comprehensive historical dataset comprising 163 million transactions. Our main conclusion is that the success of SSL depends on data quality rather than volume: high-fidelity features such as KeyLinker address clustering and Shared Send Untangling (SSU) complexity metrics achieve an F1 score of 0.84 on unlabeled data. Finally, we empirically show that common heuristics like One-Time Change (OTC), though abundant, introduce noise, while strategic reliance on higher-fidelity features like KeyLinker is essential. Our work establishes that in blockchain forensics, the path to better performance lies in smarter feature engineering for data quality, not just larger datasets.

In this work, a new two-grid method presented for the elliptic partial differential equations is generalized to the time-dependent linear parabolic partial differential equations. The new two-grid waveform relaxation method uses the numerical method of lines, replacing any spatial derivative by a discrete formula, obtained here by the finite element method. A convergence analysis in terms of the spectral radius of the corresponding two-grid waveform relaxation operator is also developed. Moreover, the efficiency of the presented method and its analysis are tested, applying the two-dimensional heat equation.

In this work, a semialgebraic mode analysis (SAMA) is proposed for investigating the convergence of a multigrid waveform relaxation method applied to the Finite Element (FE) discretization of the heat equation in two and three dimensions. This analysis for finite element methods is more involved and more general than that for Finite Difference (FD) discretizations, since mass matrix must be considered. The proposed analysis results in a very useful tool to study the behaviour of the multigrid waveform relaxation method depending on the parameters of the problem.

Bitcoin's Unspent Transaction Output (UTXO) model enables public analysis of fund flows, but users often merge transactions into Shared Send Mixers (SSMs) to obscure these flows. Untangling SSMs to recover original subtransactions is an NP-complete problem. While a practical untangling algorithm exists, it fails to classify 1.4% of SSM transactions due to computational time limits. This paper introduces four novel heuristics that exploit structural weaknesses in real-world SSM transactions to resolve these timeout cases: preemptive grouping, connectable singleton, ambiguous pairing, and knapsack fallback. We provide theoretical proofs validating each heuristic and integrate them into an optimized pipeline. Applied to timeout transactions, our approach classifies 98.5% of previously unresolved cases, reducing the overall unclassified transaction rate from 1.4% to 0.021% of all SSM transactions. Our open-source implementation and comprehensive evaluation on the complete Bitcoin blockchain demonstrate that the heuristics effectively untangle previously intractable transactions, enabling more accurate flow analysis and deeper structural insights into cryptocurrency transaction patterns.

When the weights and biases of a neural network range over a fixed finite alphabet, training the network to fit a data set exactly becomes a finite combinatorial problem, and parameterized complexity asks which structural quantities of an instance make this problem tractable. Ganian, Sommer, and Sorge (ICLR 2026) showed that training quantized networks is fixed-parameter tractable when parameterized jointly by the input dimension $\alpha$, the output dimension $\omega$, and the treewidth of the architecture, and they asked whether $\alpha+\omega$ alone suffices. We show that it does not: training binary quantized networks is W[1]-hard parameterized by $\alpha+\omega$, so it admits no algorithm with running time $f(\alpha+\omega)\cdot|I|^{O(1)}$ for any computable $f$ unless FPT = W[1]. Hardness holds already for exact fitting of $k+1$ examples whose inputs equal their targets and form a coordinatewise prefix chain, and also when all biases are fixed to zero. The proof rests on a one-flip routing equivalence. On such data, nonnegative binary weights force every neuron to switch on at most once, and a network fits the data exactly if and only if the architecture contains vertex-disjoint paths that link each changing input to the corresponding output. Every neuron therefore has one of only $k+1$ activation profiles, yet deciding whether these profiles can be realized simultaneously is as hard as disjoint-path routing. Small input and output dimensions thus limit what each neuron can do locally, but not how the architecture forces neurons to share resources globally.

We propose a Bayesian nonparametric mixture of regression trees with a Dirichlet process prior over tree-parameter pairs, enabling data-driven selection of ensemble size and unifying CART, BART, random forests, and boosting. A novel splitting rule driven by the posterior predictive of a Gaussian process within each terminal node generates flexible, smooth decision boundaries; remarkably, the GP density cancels exactly in the Metropolis–Hastings ratio for GROW/PRUNE moves, ensuring computational feasibility. An exact Gibbs sampler for posterior predictive inference propagates uncertainty through random tree traversal. A parallel MPI implementation distributes independent tree updates across processors, achieving adequate speedups. We prove posterior consistency at rate $n^{-1/4}$ in Hellinger distance under only continuity of the true regression function, allowing misspecification, via the identity $h(\Theta)=0$. Simulations on Friedman benchmark show near-nominal coverage (0.94 Gaussian, 0.92 Cauchy), robust to high-dimensional noise and heavy tails, outperforming BART and bagged CART. Applications to QSAR toxicity, crime, riboflavin, wheat genomics, and air quality confirm reliable credible intervals and automatic sparsity. The DP mixture offers a principled, robust, theoretically justified alternative for challenging regression with honest uncertainty quantification.

Language models can over-condition on irrelevant preceding text: predictions already supported by local context may still change when distant, unrelated prefix tokens are perturbed. This interference is especially consequential in long, packed, or distractor-heavy contexts, where useful evidence and irrelevant spans coexist. We propose Selective Prefix Anti-Interference Regularization (SPAR), a pretraining objective for selective anti-interference. SPAR runs the original sequence and a corrupt-prefix input in which only the far prefix is changed, then uses a short-context sufficiency gate and a gated KL objective to stabilize locally supported suffix predictions. The gate operationalizes a model-based estimate of whether the far prefix supplies additional information about the target token. Mechanism analyses show that the gate identifies locally sufficient tokens and sharply reduces prefix sensitivity on gate-selected suffix tokens. In continued training on pretrained base models, SPAR improves RULER across Qwen2.5-0.5B, Qwen2.5-3B, Llama-3.2-1B, Llama-3.1-8B, and GPT2-XL under equal counted training compute; pretraining experiments further show gains on both RULER and NoLiMa. These results show that selective anti-interference is an effective objective-level signal for robust context use.

3D Gaussian Splatting provides an efficient representation for 3D reconstruction, and recent extensions attach semantic attributes to Gaussians for open-vocabulary scene understanding. However, lifting view-dependent 2D foundation-model outputs into 3D space introduces cross-view inconsistencies and weak geometric grounding, leading to severe semantic drift and boundary leakage. We propose GaussianDS, a depth-supervised semantic 3DGS framework that treats semantic lifting as a supervision-alignment problem and jointly optimizes RGB appearance, rendered depth, and compact semantics from scratch. Specifically, GaussianDS organizes unordered multi-view images into a pose-aware pseudo-video trajectory to propagate view-consistent masks via SAM2. During joint optimization, scale-shift-aligned monocular depth supervision and depth total-variation regularization stabilize Gaussian geometry, while a depth-edge-aware refinement loss explicitly anchors semantic transitions onto physical geometric discontinuities. Extensive evaluations show that our end-to-end framework not only retains high-fidelity 3D reconstruction and real-time rendering, but also establishes superior semantic understanding. GaussianDS sets new state-of-the-art performance on LERF (60.5% mIoU) and 3D-OVS (97.79% mIoU, 90.28% mBIoU) by mitigating semantic leakage, while seamlessly facilitating downstream 3D object removal.

Large language models (LLMs) are increasingly used to draft contractual language, yet conventional accuracy or preference-based evaluations are poorly matched to legal drafting. A clause may be fluent and stylistically polished while still omitting an essential carve-out, allocating risk in an unenforceable way, assuming an inapplicable jurisdiction, or exposing a party to regulatory liability. This paper presents a empirical study design and framework for evaluating LLM-generated contract clauses. The study evaluates four models - Claude Haiku 4.5, Gemini 2.5 Flash Lite, GPT 5.4 Nano, and Qwen 3.5 Flash, across 22 contract clause categories and 34 legally-motivated failure modes. We combine two evaluation frameworks: CLAUSE, which classifies prompts by legal function and failure target, and LENS-CRAFT, which scores outputs across nine legal-quality dimensions. Instead of averaging dimension scores, the study applies a Max Severity Principle so that a single legally decisive defect remains visible. The paper provides the evaluation protocol, taxonomy, analysis plan, and a results structure for reporting empirical findings. We argue that legal AI evaluation should move beyond aggregate accuracy toward clause-specific, failure-mode-driven, and risk-sensitive assessment.