We provide a counterexample to the minimal unimodal conjecture for polynomial neural networks (PNNs) with power activation functions. Fixing the input and output widths, the conjecture states that any minimal filling architecture has unimodal widths for the hidden layers. We found a counterexample via a frontier search and certified it using recursive dimension bounds and symbolic computation. Notably, several subarchitectures of this example exhibit large defect, in contrast with the predominantly small-defect behavior observed in prior examples.

Continual post-training aims to extend large language models (LLMs) with new knowledge, skills, and behaviors, yet it remains unclear when sequential updates enable capability transfer and when they cause catastrophic forgetting. Existing methods mitigate forgetting through sequential fine-tuning, replay, regularization, or model merging, but offer limited criteria for determining when incorporating new updates is beneficial or harmful. In this work, we study LLM continual post-training through three questions: What drives forgetting? When do sequentially acquired capabilities transfer or interfere? How can compatibility be used to control update integration? We address these questions through task geometry: we represent each post-training task by its parameter update and study the covariance geometry induced by the update. Our central finding is that: forgetting can be considered as a state-relative update-integration failure, it arises when the covariance geometries induced by tasks misalign with the geometry of the evolving model state. Sequential updates transfer when they remain compatible with the model state shaped by previous updates, and interfere when state-relative geometry conflict becomes high. Motivated by this finding, we propose Geometry-Conflict Wasserstein Merging (GCWM), a data-free update-integration method that constructs a shared Wasserstein metric via Gaussian Wasserstein barycenters and uses geometry conflict to gate geometry-aware correction. Across Qwen3 0.6B--14B on domain-continual and capability-continual settings, GCWM consistently outperforms data-free baselines, improving retention and final performance without replay data. These results identify geometry conflict as both an explanatory signal for forgetting and a practical control signal for LLM continual post-training.

Millimeter-wave (mmWave) radar provides privacy-preserving sensing and is valuable for human action recognition (HAR). Existing mmWave point cloud datasets are limited in scale and mostly collected under homogeneous single-source settings, preventing current methods from handling real-world distribution shifts caused by heterogeneous radar sources, such as different devices and frequency bands. To address this, we introduce UniMM-HAR, the largest and first mmWave point cloud HAR dataset for heterogeneous multi-source scenarios, standardizing three distinct radar configurations to realistically evaluate cross-source generalization. We further propose the Doppler-aware Point Cloud Network (DAP-Net) to tackle heterogeneity challenges. DAP-Net enhances intra-modal representations and performs cross-modal alignment to learn source-invariant action semantics. Leveraging action-consistent spatio-temporal Doppler patterns as anchors, the Dual-space Doppler Reparameterization (D2R) module performs sample-adaptive geometric densification and Doppler-guided feature recalibration, while the Text Alignment Module (TAM) provides stable semantic anchors via a pretrained textual space. Experiments show that DAP-Net significantly outperforms existing methods under heterogeneous radar settings, achieving state-of-the-art accuracy and strong cross-source robustness.

Masked diffusion language models enable parallel token generation and offer improved decoding efficiency over autoregressive models. However, their performance degrades significantly when generating multiple tokens simultaneously, due to a mismatch between token-level training objectives and joint sequence consistency. In this paper, we propose ME-DLM, an edit-based refinement framework that augments diffusion generation with lightweight post-editing steps. After producing an initial complete response, the model refines it through minimal edit operations, including replacement, deletion, and insertion, conditioned on the full sequence. Training supervision is derived from edit distance, providing a deterministic signal under a fixed canonicalization scheme for learning minimal corrections. This approach encourages sequence-level consistency through globally conditioned edits while preserving the efficiency benefits of parallel diffusion decoding. Extensive experiments demonstrate that ME-DLM improves the quality and robustness of multi-token parallel generation. In particular, when built upon LLaDA, our method achieves consistent gains of 11.6 points on HumanEval and 33.6 points on GSM8K while using one-eighth of the total diffusion steps. Code is available at https://github.com/renhouxing/ME-DLM.

Segmentation is a fundamental vision task underlying numerous downstream applications. Recent promptable segmentation models, such as Segment Anything Model 3 (SAM3), extend segmentation from category-agnostic mask prediction to concept-guided localization conditioned on high-level textual prompts. However, existing benchmarks primarily evaluate mask accuracy or object presence, leaving unclear whether these models faithfully ground the queried concept or instead rely on visually salient but semantically misleading cues. We introduce CAFE: \textbf{C}ounterfactual \textbf{A}ttribute \textbf{F}actuality \textbf{E}valuation, a novel benchmark for evaluating concept-faithful segmentation in promptable segmentation models. Our \textbf{CAFE} is built on attribute-level counterfactual manipulation: the target region and ground-truth mask are preserved, while attributes such as surface appearance, context, or material composition are modified to introduce misleading semantic cues. The benchmark contains 2,146 paired test samples, each consisting of a target image, a ground-truth mask, a positive prompt, and a misleading negative prompt. These samples cover three counterfactual categories: Superficial Mimicry (\textbf{SM}), Context Conflict (\textbf{CC}), and Ontological Conflict (\textbf{OC}). We evaluate various model types and sizes on our CAFE. Experiments reveal a systematic gap between localization quality and concept discrimination: models often generate accurate masks even for misleading prompts, suggesting that strong mask prediction does not necessarily imply faithful semantic grounding. Our CAFE provides a controlled benchmark for diagnosing whether promptable segmentation models perform concept-faithful grounding rather than shortcut-driven mask retrieval.

Inpatient clinical reasoning is a sequential decision under partial observability: the clinician sees the admission so far and must choose the next action whose downstream consequences are not yet visible. Existing clinical-LLM evaluations and RL rewards signals collapse this into closed-form retrieval, clinical journey leakage, or unanchored LLM-as-judge scoring. We introduce CLR-voyance, a framework that reformulates inpatient reasoning as a Partially Observable Markov Decision Process (POMDP) and supervises it with rewards that are simultaneously outcome-grounded and clinician-validated. We instantiate the formulation as CLR-POMDP, which partitions successful patient journeys into a policy-visible past and an oracle-only future. Using the past information, an oracle LLM generates a case-specific query-answer pair, and the first adaptive rubric for clinical reasoning which is verifiable in the future of the patient journey. These rubrics are used for both post-training and evaluation of models for inpatient clinical reasoning. We post-train Qwen3-8B and MedGemma-4B with GRPO followed by model merging, yielding state-of-the-art inpatient clinical reasoning while retaining generalist capabilities. CLR-voyance-8B achieves 84.91% on CLR-POMDP, ahead of frontier medical reasoning models like GPT-5 (77.83%) and MedGemma-27B (66.66%) and has comparable or better performance on existing medical benchmarks. To ensure a clinically meaningful setting, we conduct a large-scale clinician alignment study, where physicians curate per-case rubrics, grade candidate responses, and provide blinded pairwise preferences of model reasoning. This study provides insights on clinical LLM-as-a-judge and clinical preference-model selection, which can inform the community at large. CLR-voyance has been deployed for 6+ months at a partner public hospital, drafting thousands of reasoning-heavy inpatient notes.

This paper presents a hardware architecture that implements the Contrast Maximization (CM) algorithm in Field-Programmable Gate Array (FPGA) resources for event-based vision systems. CM estimates motion parameters by maximizing the contrast of an Image of Warped Events (IWE) reconstructed from asynchronous event streams. Event-based vision sensors generate sparse data with high temporal resolution and low spatial redundancy, which makes them well suited for hardware processing. The deterministic, massively parallel structure of the FPGA is leveraged to design a deeply pipelined architecture capable of high-throughput, energy-efficient processing suitable for real-time embedded applications. This paper details the hardware modules responsible for event warping, contrast computation, and iterative optimization, discusses key implementation decisions, and presents the hardware-aware optimization method used in the design. Experimental results demonstrate a substantial speed and efficiency improvement over CPU- and GPU-based implementations, with motion parameter estimation executing over 200 times faster. To the best of our knowledge, this is the first hardware architecture enabling acceleration of CM algorithm computations. Its performance is evaluated in terms of processing speed, energy efficiency, and hardware resource utilization. The proposed design is validated using an event-based object tracking application. The results confirm that the architecture provides a solid foundation for real-time motion estimation in high-speed, low-power embedded systems.

Cardiovascular disease remains the leading cause of global mortality, yet scalable cardiac monitoring is hindered by the gap between diagnostic-rich ECG and ubiquitous wearable PPG. Bridging this gap requires representations that are compact, transferable across modalities and devices, and deployable without task-specific retraining. Here we introduce biosignal fingerprints: compact latent representations of cardiovascular state derived from a cross-modal foundation model, the Multi-modal Masked Autoencoder (M2AE), trained on over 3.4 million paired ECG and PPG signals. M2AE integrates modality-specific encoders with a shared bottleneck and dual decoders, jointly optimized using reconstruction and cross-modal contrastive objectives, yielding generalizable fingerprints that retain intra- and inter-modality features. Like a biometric fingerprint, these representations uniquely encode an individual's cardiovascular state in a modality-agnostic, privacy-preserving form reusable across clinical tasks without exposing raw waveform data or requiring model retraining. Across 7 downstream tasks, spanning cross-modal reconstruction, cardiovascular disease classification, hypertension detection, mortality prediction, and demographic inference, biosignal fingerprints achieve competitive or superior performance compared to leading domain-specialist foundation models in frozen settings, including an AUROC of 0.974 for five-class CVD classification and 0.877 for hypertension detection, with a maximum improvement of 27.7% in AUROC across 5 classification tasks. Critically, strong performance is maintained with only a single modality, enabling deployment in resource-constrained, single-sensor environments typical of real-world wearable monitoring, with direct implications for continuous cardiovascular monitoring across clinical and consumer health settings.

Sign language production from symbolic notation offers a scalable route to accessible sign animation. We present KANMultiSign, a multi-scale sequence generator that translates HamNoSys notation into two-dimensional human pose sequences. Our framework makes two complementary contributions. First, we introduce a coarse-to-fine generation strategy with multi-scale supervision: the model is first guided by an intermediate body--hand--face scaffold to encourage global structural coherence, and then refines fine-grained hand articulation to improve finger-level detail. Second, we investigate integrating Kolmogorov--Arnold Network modules into a Transformer backbone, using learnable univariate function primitives to model the highly non-linear mapping from discrete phonological symbols to continuous body kinematics with a compact parameterization. Experiments on multiple public corpora spanning Polish, German, Greek, and French sign languages show consistent reductions in dynamic time warping based joint error compared with a strong notation-to-pose baseline, while using substantially fewer parameters. Controlled ablations further indicate that KAN-based variants substantially reduce parameter count while maintaining competitive performance when coupled with multi-scale supervision, rather than serving as the main driver of accuracy gains. These findings position multi-scale supervision as the key mechanism for improving notation-conditioned pose generation, with KAN offering a compact alternative for efficient modeling. Our code will be publicly available.

With the rapid growth of mobile robotics and embedded intelligence, there is an increasing demand for efficient on-device data processing on edge platforms. A promising research direction is the use of neuromorphic sensors inspired by human sensory systems, which generate sparse, event-based data encoding changes in the environment. In this work, we present the first end-to-end FPGA implementation of a keyword spotting system that integrates a Neuromorphic Auditory Sensor (NAS) and a graph neural network (GNN) on a single FPGA device, enabling real-time processing of raw audio data. The proposed architecture eliminates conventional signal preprocessing and operates directly on event-based audio streams. Leveraging a compute-near-memory network architecture, the system achieves efficient inference with low latency and low power consumption. Experimental results demonstrate an accuracy of 87.43% after quantization on the Google Speech Commands v2 dataset processed through the neuromorphic sensor, with end-to-end latency below 35 us and average power consumption of 1.12 W. The processed datasets, software models, and hardware modules are available at https://github.com/vision-agh/NAS-GNN-KWS.

Recent Deep Unfolding Networks (DUNs) have significantly advanced Compressive Sensing (CS) by integrating iterative optimization with deep networks. However, existing DUNs still suffer from two challenges: 1) Reliance on a single measurement stream, which limits effective information interaction across distinct measurement subsets. 2) Uniform processing of all image regions, which overlooks varying reconstruction difficulties induced by diverse textures. To address these limitations, a novel Dual-Path Hyperprior Informed Deep Unfolding Network (DPH-DUN) is proposed, which partitions measurements into double subsets to enable hyperprior-guided reconstruction via a dual-path architecture. In the Deep Hyperprior Learning branch, a series of lightweight neural modules are designed to efficiently generate hyperprior knowledge of different domains, enabling collaborative guidance for the CS reconstruction. In the Hyperprior Informed Reconstruction branch, a deep unfolding framework with hyperprior guidance is constructed to iteratively refine reconstruction. Specifically, i) in the gradient descent step, a Hyperprior Informed Step Size Generation network is designed to dynamically generate spatially varying step maps, enabling adaptive fine-grained gradient updates. ii) In the proximal mapping step, two well-designed hyperprior informed attention mechanisms are introduced to dynamically focus on challenging regions via gradient-based hard and soft attentions, facilitating CS reconstruction accuracy. Extensive experiments demonstrate that the proposed DPH-DUN outperforms existing CS methods.

We consider the problem of learning an unknown subset $N_\text{target}$ of a domain in an online setting. In each round $t$, the learner predicts a set of items ${N}_t$ and receives one of two types of feedback, each with equal probability: precision feedback, in which a randomly chosen item from the predicted set $N_t$ is revealed and the learner is told whether it belongs to $N_\text{target}$ (incurring a reward if it does), or recall feedback, in which a randomly chosen item from the target set $N_\text{target}$ is revealed and the learner is told whether it belongs to $N_t$ (incurring a reward if it does). The goal is to maximize the cumulative reward over time. This simple online set learning problem abstracts a variety of learning scenarios with precision- and recall-type feedback. We show that a hypothesis class (a family of subsets of the domain) is learnable in this setting if and only if it has finite Vapnik-Chervonenkis (VC) dimension, mirroring the classical PAC characterization. However, the resulting algorithmic structure is markedly more intricate: in contrast to standard Probably Approximately Correct (PAC) learning -- where the algorithmic landscape is governed by the simple principle of Empirical Risk Minimization (ERM) -- our partial feedback model can invalidate ERM and even all proper learning rules. We develop algorithms to address the dependencies induced by the feedback, obtaining regret guarantees in both the realizable and agnostic settings. Our results provide a qualitative characterization of learnability in this model, addressing its most basic question, while pointing to a range of natural and intriguing open questions, including the determination of optimal regret rates.

Sign Language Translation (SLT) converts sign language videos into spoken-language text, bridging communication between Deaf and hearing communities. Current gloss-free approaches rely on large encoder-decoder models, limiting deployment. We propose a compact 77M-parameter pipeline that couples MMPose skeletal pose extraction with a single linear projection into T5-small. By varying the input frame rate, we expose a practical efficiency trade-off: at 12 fps the model halves its sequence length, achieving a 75% reduction in encoder quadratic self-attention computational complexity while incurring only a modest BLEU-4 drop (9.53 vs. 10.06 at 24 fps on How2Sign). Our system is roughly 3x smaller than prior T5-base systems, demonstrating that a lightweight architecture can remain competitive without hierarchical encoders or large-scale models.

Adaptive prompting mechanisms have been proposed to enhance vision-language models by dynamically tailoring prompts to inputs. However, in frozen few-shot prompt learning with CLIP-style backbones, we systematically observe that adaptive gates and prompt-selection modules often collapse: they produce nearly constant outputs, contribute negligible gradient signals, and frequently fail to outperform fixed prompts. To further explore this issue, we present a systematic diagnostic study to uncover the underlying causes and conditions of adaptation failure. Through controlled experiments across datasets and multiple prompt learning architectures, we identify two recurring failure modes: gradient magnitude imbalance and gate degradation. Our findings invite a re-examination of indiscriminately adding architectural complexity in parameter-efficient learning and clarify when prompt-level adaptive gating is, and is not, effective in this regime.

Large language models (LLMs) have achieved remarkable progress in mathematical reasoning, but this ability is not equally accessible across languages. Especially low-resource languages exhibit much lower reasoning performance. To address this, we propose Crosslingual On-Policy Self-Distillation (COPSD), which transfers a model's own high-resource reasoning behavior to low-resource languages. COPSD uses the same model as student and teacher: the student sees only the low-resource problem, while the teacher receives privileged crosslingual context, including the problem translation and reference solution in English. Training minimizes full-distribution token-level divergence on the student's own rollouts, providing dense supervision while avoiding the sparsity and instability of outcome-only reinforcement learning (RL). Experiments on 17 low-resource African languages show that COPSD consistently improves low-resource mathematical reasoning across model sizes and substantially outperforms Group Relative Policy Optimization (GRPO). Further analyses show that COPSD improves answer-format adherence, strengthens test-time scaling, and generalizes to harder multilingual reasoning benchmarks, with especially large gains for lower-resource languages. We make our code and data available at: https://github.com/cisnlp/COPSD.

Tool-integrated reasoning has emerged as a promising paradigm for enhancing large language models with external computation, retrieval, and execution capabilities. However, the field still lacks a high-quality and unified evaluation benchmark, and existing TIR evaluations remain limited in dataset quality, task diversity, diagnostic comprehensiveness, and evaluation efficiency. In this work, we introduce TIDE-Bench, a holistic and efficient benchmark for evaluating TIR methods, featuring three key advantages. First, it provides diverse task settings, combining widely used mathematical reasoning and knowledge-intensive QA tasks with two newly designed tasks, namely the tool-grounded experimental design task and the dynamic interactive task, to probe models' abilities in complex tool invocation and multi-tool coordination. Second, TIDE-Bench adopts a comprehensive yet task-aware evaluation protocol, jointly measuring final answer quality, process reliability, tool-use efficiency, and inference cost across heterogeneous task settings. Third, TIDE-Bench constructs high-quality and discriminative evaluation sets by filtering low-discrimination instances from existing datasets, substantially reducing evaluation cost while focusing on more challenging samples. Extensive experiments on multiple foundation models and TIR methods reveal persistent bottlenecks in tool grounding, offering insights for future TIR research.

Extracting multi-step explanations from knowledge graphs poses a combinatorial challenge requiring both heuristic guidance (as candidates proliferate with depth) and credit assignment (as path quality emerges over extended sequences). Frontier LLMs, strong on knowledge/reasoning benchmarks, offer a compelling source of such heuristics, yet their knowledge comes sans guarantees and compositional performance degrades as chains lengthen. We thus present TESSERA, a 3-part neuro-symbolic framework that uses LLMs in a circumscribed role: for local discriminative judgement rather than autonomous multi-step generation; the knowledge graph then defines the hypothesis space enforcing hard structural constraints, and MCTS coordinates the long-horizon search with principled credit assignment via backpropagation. LLMs perform dual roles as a prior policy biasing exploration and a comparative state evaluator supplying reward signals. Evaluation on drug mechanism elucidation across two complementary knowledge graphs demonstrates fidelity to curated biology while surfacing coherent alternative mechanisms, with ablations confirming discriminative contribution from both LLM components. Beyond its current application, our framework offers a general paradigm for compositional reasoning over structured knowledge.

Multi-agent systems (MAS) have emerged as a promising paradigm for solving complex tasks. Recent work has explored self-evolving MAS that automatically optimize agent capabilities or communication topologies. However, existing methods either learn a topology that remains fixed at inference time or adapt only the topology or capability during inference. We empirically and theoretically show that effective test-time evolution requires jointly adapting both axes, but on different time scales: capabilities should update rapidly to handle emerging subtasks, while the topology should evolve more slowly to preserve coordination stability. We then introduce TacoMAS, a test-time co-evolution framework for dynamic MAS. TacoMAS formulates MAS inference as a task of online graph adaptation, where nodes represent agents with role-specific capabilities and edges define their communication topology. During inference, a fast capability loop updates agent expertise using trajectory-level feedback, while a slow meta-LLM-driven topology loop performs agents' birth-death operations on MAS, including edge edit, agent addition, and agent removal. We further show that this fast-slow design drives MAS evolution toward a task-conditioned stable equilibrium. Experiments on four benchmarks demonstrate that TacoMAS outperforms nearly 20 multi-agent baselines, achieving an average improvement of 13.3% over the strongest baseline. The codes are released at https://github.com/chenxu2-gif/TacoMAS-MultiAgent.

While existing methods for reconstructing hand-object interactions have made impressive progress, they either focus on rigid or part-wise rigid objects-limiting their ability to model real-world objects (e.g., cloth, stuffed animals) that exhibit highly non-rigid deformations-or model deformable objects without full 3D hand reconstruction. To bridge this gap, we present PhysHanDI (Physics-based Reconstruction of Hand and Deformable Object Interactions), a framework that enables full 3D reconstruction of both interacting hands and non-rigid objects. Our key idea is to physically simulate object deformations driven by forces induced from densely reconstructed 3D hand motions, ensuring that the reconstructed object dynamics are both physically plausible and coherent with the interacting hand movements. Furthermore, we demonstrate that such simulation of object deformations can, in turn, refine and improve hand reconstruction via inverse physics. In experiments, PhysHanDI outperforms the state-of-the-art baseline across reconstruction and future prediction.

Despite rapid progress in Vision-Language-Action (VLA) models for robotic control, instruction drift remains a persistent failure mode in long-horizon tasks. This paper reconceptualizes this phenomenon, positing that instruction drift is fundamentally a systematic sampling error: local greedy sampling is prone to collapsing into "Negative Pivotal Windows"--irreversible local optima with high local probability that sever global success pathways. To address this, we propose Context-Aware Power Sampling (CAPS), a training-free inference-time computation framework. CAPS leverages power distributions to sharpen global trajectory probabilities, enabling lookahead search over the model's conditional generative trajectory distribution. Furthermore, we introduce a metacognitive control mechanism based on Signal-to-Noise Ratio (SNR). This mechanism triggers adaptive MCMC search solely when drift risk is detected, enabling a dynamic transition from "intuitive fast thinking" to "rational slow search." Experiments on RoboTwin, Simpler-WindowX, and Libero-long benchmarks show that CAPS achieves substantial improvements over strong baselines, including OpenVLA and TACO, without parameter updates. These results support the effectiveness of adaptive inference-time computation for improving long-horizon robustness in embodied control.

Diffusion large language models (dLLMs) offer a promising paradigm for parallel text generation, but in practice they face an accuracy-parallelism trade-off, where increasing tokens per forward (TPF) often degrades generation quality. Existing acceleration methods often gain speed at the cost of accuracy. To address this limitation, we propose TAD, a Temporal-Aware trajectory self-Distillation framework. During data construction, we condition a teacher model on both the prompt and the ground-truth response to generate decoding trajectories, recording the intermediate masked states throughout the process. Based on how many decoding steps remain before each masked token is revealed, we partition masked positions into near and distant subsets. For near tokens, we train the student with a hard cross-entropy loss using the teacher trajectory tokens as labels, encouraging confident predictions for tokens that are about to be decoded. For distant tokens, we apply a soft KL divergence loss between the teacher and student token distributions, providing softer supervision and preserving future planning knowledge. This temporal-aware partition naturally gives rise to two deployment configurations: a Quality model that prioritizes accuracy and a Speed model that favors more aggressive acceleration. Experiments show that TAD consistently improves the accuracy-parallelism trade-off. On LLaDA, it raises average accuracy from 46.2\% to 51.6\% with the Quality model and average AUP from 46.2 to 257.1 with the Speed model. Our code is available at: https://github.com/BHmingyang/TAD

Large Language Models (LLMs) are increasingly employed in enterprise question-answering (QA) systems, requiring adaptation to domain-specific knowledge. Among the most prevalent methods for incorporating such knowledge are Retrieval-Augmented Generation (RAG) and fine-tuning (FT). Yet, from a cost-accuracy trade-off perspective, it remains unclear which approach best suits industry scenarios. This study examines the impact of RAG and FT on two closed datasets specific to the automotive industry, assessing answer quality and operational costs. We extend the Cost-of-Pass framework proposed by Erol et al. (arXiv:2504.13359) to jointly assess output quality, generation cost, and user interaction cost. Our findings reveal that while premium models perform best out of the box, open-source models can achieve comparable quality when enhanced with RAG. Overall, RAG emerges as the most effective and cost-efficient adaptation method for both closed- and open-source models.

We present Version 2 of system Cplus2ASP, which implements the definite fragment of action language C+. Its input language is fully compatible with the language of the Causal Calculator Version 2, but the new system is significantly faster thanks to modern answer set solving techniques. The translation implemented in the system is a composition of several recent theoretical results. The system orchestrates a tool chain, consisting of f2lp, clingo, iclingo, and as2transition. Under the incremental execution mode, the system translates a C+ description into the input language of iclingo, exploiting its incremental grounding mechanism. The correctness of this execution is justified by the module theorem extended to programs with nested expressions. In addition, the input language of the system has many useful features, such as external atoms by means of Lua calls and the user interactive mode. The system supports extensible multi-modal translations for other action languages, such as B and BC, as well.

Recently there has been an increasing interest in incorporating ``intensional'' functions in answer set programming. Intensional functions are those whose values can be described by other functions and predicates, rather than being pre-defined as in the standard answer set programming. We demonstrate that the functional stable model semantics plays an important role in the framework of ``Answer Set Programming Modulo Theories (ASPMT)'' -- a tight integration of answer set programming and satisfiability modulo theories, under which existing integration approaches can be viewed as special cases where the role of functions is limited. We show that ``tight'' ASPMT programs can be translated into SMT instances, which is similar to the known relationship between ASP and SAT.

We introduce the concept of weighted rules under the stable model semantics following the log-linear models of Markov Logic. This provides versatile methods to overcome the deterministic nature of the stable model semantics, such as resolving inconsistencies in answer set programs, ranking stable models, associating probability to stable models, and applying statistical inference to computing weighted stable models. We also present formal comparisons with related formalisms, such as answer set programs, Markov Logic, ProbLog, and P-log.

Meta-learning for algorithm selection relies on a meta-dataset in which each row corresponds to a supervised learning dataset described by meta-features and labelled with a target value that is associated with algorithm choice (typically, some function of algorithm performance). A persistent limitation is that the number of curated real-world datasets is small, resulting in sparse meta-datasets that constrain meta-learner generalisation. In this paper, we address this problem by augmenting the meta-dataset with synthetic regression datasets produced via a large language model (LLM), with generation steered toward target regions of a low-dimensionality performance space. In our experiments, we adopt a two-dimensional geometric setting defined by the cross-validated $R^2$ scores of two anchor algorithms, known as landmarkers. We compare two augmentation strategies: (1) uniform sampling, which distributes synthetic datasets across the performance space; and (2) margin-based sampling, which concentrates them near the decision boundary where landmarker preference is most ambiguous. Across 42 real-world UCI regression datasets and 730 synthetic datasets, both strategies substantially improve meta-learner performance over the unaugmented baseline under regression and multi-label evaluation formulations. However, uniform augmentation consistently outperforms margin-based augmentation, achieving a 17.47% relative reduction in Hamming loss, a 100.41% relative improvement in subset accuracy, and a +6.09% relative gain in pooled out-of-fold $R^2$. These results lead us to postulate a central thesis: the performance of algorithms resides on a low-dimensional performance manifold, whose reconstruction bias may be minimised by user-guided LLMs that seek to maximise uniform $ε$-cover, and consequently, lead to improved meta-learning for algorithm selection.

Standard Mixture-of-Experts (MoE) transformers route tokens to expert subnetworks within each layer, but the layer structure itself remains monolithic. We introduce Mixture of Layers (MoL), which replaces full-width transformer blocks (d_model) with K parallel thin blocks at reduced dimensionality (d_thin << d_model), connected via learned down/up projections and composed via top-k block routing. Scaling sparse block routing to many blocks creates an attention coverage problem, as each block sees fewer tokens. We address this by introducing hybrid attention, which pairs one shared softmax block for global context with Gated DeltaNet linear attention in routed blocks.

Large language models rely on multihead attention, but interactions among heads remain poorly understood. We apply the Game Theoretic Free Energy Principle (GTFEP): a framework casting multiagent systems as distributed variational inference to analyze attention heads as bounded rational agents. According to GTFEP, each head minimizes its variational free energy, and collective behavior follows a Gibbs distribution over coalition structures whose energy is decomposed into Harsanyi dividends. Using a tractable approximation (uniform prior, deterministic dynamics), coalition free energy reduces to joint Shannon entropy of discretized head outputs (argmax key index). Pairwise dividends become mutual information (nonnegative), while triple dividends correspond to interaction information and can be negative. On BERT, GPT2, and Llama with GSM8K, triple dividends are consistently negative, revealing higher order redundancy. The Nash FEP correspondence guarantees that stationary points of collective free energy are epsilon Nash equilibria; thus, heads with negligible contribution can be pruned with minimal performance loss. Pruning heads with low marginal contribution reduces computational cost with minimal performance loss: for example, pruning 20% of heads in GPT2 reduces FLOPs by 18%, increases throughput by 22%, and raises perplexity only modestly (from 28.4 to 33.4 on GSM8K). Our work shows GTFEP provides a principled foundation for analyzing and optimizing transformer architectures.

Unobserved confounding prevents standard covariate adjustment from identifying causal response functions in observational studies. Proxy causal learning addresses this problem through bridge equations involving treatment- and outcome-inducing proxies, avoiding direct recovery of the latent confounder. Existing doubly robust proxy estimators combine outcome and treatment bridges, but typically rely on fixed kernels, sieves, or low-dimensional semiparametric models; existing neural proxy methods are more flexible, but are largely single-bridge estimators. We develop a neural doubly robust framework for proxy causal learning with continuous and structured treatments. Our method introduces a neural mean-embedding estimator for the treatment bridge, combines it with a neural outcome bridge, and estimates the doubly robust correction through a final regression stage. The framework covers population, heterogeneous, and conditional dose-response functions, yielding full response-curve estimators rather than binary-treatment effects. The algorithms use two stages for each bridge and history-aware updates of the final linear layers to stabilize stochastic multi-stage training. We prove consistency of the algorithms showing that the doubly robust error is controlled by the final averaging and regression errors together with the smaller of the outcome- and treatment-side weak-norm bridge errors. Across synthetic and image-valued benchmarks, the proposed estimators outperform existing baselines and single-bridge neural estimators, showing the benefit of combining learned outcome and treatment bridges in a doubly robust construction. Our implementation is available at https://github.com/BariscanBozkurt/DRPCL-Neural-Mean-Embedding.

Tracking points in videos is typically formulated as frame-to-frame correspondence, where each point is matched locally to the next frame. While this works over short horizons, errors accumulate under articulation, occlusion, and viewpoint change, leading to silent semantic drift that existing trackers cannot detect or correct. In this work, we revisit long-horizon tracking from a monitoring perspective and introduce QueST, a monitoring-by-design framework that treats interaction-relevant entities as persistent semantic queries rather than transient point tracks. Instead of local propagation, each query attends globally over spatio-temporal video features at every time-step, providing a stable semantic anchor across time. We further constrain query trajectories with lightweight 3D physical grounding, using geometric plausibility to suppress unbounded drift under occlusion. We evaluate QueST on long-horizon articulated sequences from PartNet-Mobility in SAPIEN and compare against RAFT-3D, CoTracker, and TAP-Net. QueST substantially reduces terminal drift achieving a 67.7% Absolute Point Error (APE) improvement over TAP-Net while better preserving identity over extended horizons. Our results show that embedding semantic monitoring directly into perception enables more reliable long-horizon tracking under distribution shift.