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Our syntax affords a novel topological semantics which, following Kelly 1996's approach in The Logic of Reliable Inquiry, takes as primitives agents' information bases. Our language has a rather rich syntax in order to capture equally rich notions central to Lewis' account of common knowledge; for instance, we speak of an agent 'having some reason to believe' a proposition and one proposition 'indicating' to an agent that another proposition holds. This paper attempts to draw from insights in learning theory to provide a formal account of common inductive knowledge and how it can be generated by a witness. The scaling of Large Language Models (LLMs) drives interest in matrix-based optimizers (e.g., Shampoo, Muon, SOAP) for their convergence efficiency; yet their requirement for holistic updates conflicts with the tensor fragmentation in distributed frameworks like Megatron. We provide theoretical guarantees for BlockPerm-SJLT under the oblivious subspace embedding (OSE) framework, and also analyze the effect of the tunable parameter on sketching quality. This paper evaluates the consensus-based C-colME framework, which relies on doubly stochastic averaging matrices to ensure convergence to the oracle solution. This pruning is strictly conditional, enforcing an adherence to a maximum permissible accuracy drop (Delta ax) before the model proceeds to 8-bit post-training quantization. By integrating data from OpenAlex and Crossref, we analyze open science indicators such as the presence of a pre-print, data sharing, and software sharing in 576,537 publications in the FOSM dataset. This study investigates the correlation of citation impact with various open science indicators (OSI) within the French Open Science Monitor (FOSM), a dataset comprising approximately 900,000 publications authored by French authors from 2020 to 2022. 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The fused point cloud is voxelized and encoded using sparse convolutions to form a BEV representation, from which a compact set of high-confidence object queries is initialised and refined through a transformer-based context aggregation module. LiDAR-based 3D object detectors often struggle to detect far-field objects due to the sparsity of point clouds at long ranges, which limits the availability of reliable geometric cues. This demonstrates that intelligent multi-agent reasoning can elevate open-source models beyond proprietary alternatives. Implicit SDF-based methods for single-view 3D reconstruction achieve high-quality surfaces but require large labeled datasets, limiting their scalability. Parallel diffusion decoding can accelerate diffusion language model inference by unmasking multiple tokens per step, but aggressive parallelism often harms quality. Collagen Complex Our evaluation on 12 real-world Java projects shows that NullRepair resolves 63% of the 1,119 nullability errors that remain after applying a state-of-the-art annotation inference technique. It leverages static analysis to identify safe and unsafe usage regions of symbols, using error-free usage examples to contextualize model prompts. While annotation inference can eliminate many errors automatically, a subset of residual errors -- typically a mix of real bugs and false positives -- often persist and can only be resolved via code changes. Cognitive maps are learned in the model by disentangling structural relationships in the inputs from their specific content, a property that can be achieved naturally by updating the positional encoding in Transformers with input-dependent matrices. CLaRa then trains the reranker and generator end-to-end via a single language modeling loss, with gradients flowing through both modules using a differentiable top-k estimator. 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We show that this noise-driven pre-training significantly improves convergence speed in subsequent tasks, without requiring additional data or changes to the network architecture. By decomposing attribution to individual operations within computation graphs and introducing a novel mechanism for deferred activation resolution, named the Promise System, our approach achieves true architecture agnosticity while maintaining LRP's theoretical guarantees. Across electromechanical, electrochemical, and physiological domains, we show that real-world processes consistently generate compact perceptual manifolds with the same geometric characteristics. Experiments on CIFAR-10, CelebA-64, and ImageNet-256 show that ReflexFlow outperforms prior approaches in mitigating exposure bias, achieving a 35.65% reduction in FID on CelebA-64. 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SRPP preserves PP/RPP semantics (customizable secrets with probability-aware secret-dataset relationships) while replacing high-dimensional Renyi divergence with projection-based quantification via two sliced measures, Average SRPP and Joint SRPP. Specifically, motivated by the curse of dimensionality and lack of practical composition tools for iterative learning in the recent Renyi Pufferfish Privacy (RPP) framework, we propose Sliced Renyi Pufferfish Privacy (SRPP). We validate ChronoRAN on two open-sourced 5G RAN testbeds (srsRAN and OAI) and a public commercial 5G network, demonstrating that it can closely match empirical latency distributions and significantly outperform prior analytical models and widely used simulators (MATLAB 5G Toolbox, 5G-LENA). For complex parameters, TAFC automatically triggers granular reasoning based on complexity scoring, ensuring appropriate justification for critical decisions. To address these limitations, we propose Think-Augmented Function Calling (TAFC), a novel framework that enhances function calling accuracy through explicit reasoning at both function and parameter levels. Finally, we propose a novel metric to monitor evolution convergence, serving as a function analogous to training loss in conventional optimization. Within this framework, we develop Yunjue Agent, a system that iteratively synthesizes, optimizes, and reuses tools to navigate emerging challenges. However, current strategies for mapping these representations are inherently pairwise, scaling quadratically with the number of models and failing to yield a consistent global reference. Experiments across language, vision, vision--language, image generation, and reinforcement learning tasks validate our scaling rules and show that learning rates tuned on LoRA transfer reliably to full finetuning. While it induces a small memory footprint, its training dynamics can be surprisingly complex as they depend on several hyperparameters such as initialization, adapter rank, and learning rate. To bridge the diversity gap of the existing RGB-Thermal datasets, we introduce the TartanRGBT platform, the first open-source data collection platform with synced RGB-Thermal image acquisition. We propose SDPED, a compact ED model built upon Cascaded Skipping Density Blocks (CSDB), motivated by a task-adaptive architectural transfer from image super-resolution. By performing eigen-decomposition on this operator, we can separate time-variant and time-invariant components of semantics, which allows us to explicitly separate the static and dynamic semantics in the video. Science-informed deep learning (ScIDL) has emerged as a promising paradigm to address these limitations by integrating scientific knowledge into deep learning pipelines. In wireless systems, DL has been applied to problems where analytical modeling or optimization is difficult to formulate, relies on oversimplified assumptions, or becomes computationally intractable. The codes developed and the data used in this study are provided as open source on a GitHub repository, with a link included in the paper for full access. Speculative decoding can significantly accelerate LLM serving, yet most deployments today disentangle speculator training from serving, treating speculator training as a standalone offline modeling problem. We study off-policy reinforcement learning for controlling continuous-time Markov diffusion processes with discrete-time observations and actions. To address this shortcoming, we propose a Learned Model Predictive Game (LMPG) approach that amortizes model predictive gameplay to reduce latency. The results obtained here provide a constructive argument showing the theoretical possibility of a neurocomputational realization of the core computational structure of syntax. The resulting set of functions is an algebra over an operad, where the operations in the operad model circuits that transform the input wave forms into a combined output that encodes the syntactic structure. The complete REACT framework's efficacy is validated in a pipe inspection scenario, demonstrating safe navigation and full coverage inspection. By integrating REACT into a coverage path planning framework, we achieve safe and entanglement-free inspection paths, previously challenging due to tether constraints. We also provide a generic framework to extend our results to empirical distributions of queries, and demonstrate its effectiveness for Gowalla dataset. However, despite their widespread use, traditional loss functions have significant drawbacks when dealing with high-dimensional and outlier-sensitive datasets, which frequently results in reduced performance and slower convergence during training. These tasks span diverse domains, including language modeling, mathematics, bioinformatics, and time series forecasting. Most federated learning (FL) methods use a client-server scheme, where clients communicate only with a central server. A case study on fifteen selected representative methods is presented, involved with runtime analysis, error analysis, and robustness analysis. Finding a circuit augmentation algorithm that matches this bound would yield a strongly polynomial time algorithm for linear programming, resolving Smale's 9th problem. Furthermore, existing methods frequently suffer from "prototype drift," where learned prototypes lack tangible grounding in the training distribution and change their activation under small perturbations.Specifically, motivated by the curse of dimensionality and lack of practical composition tools for iterative learning in the recent Renyi Pufferfish Privacy (RPP) framework, we propose Sliced Renyi Pufferfish Privacy (SRPP).Ultimately, the presented approach bridges the gap between high-dimensional GNN embeddings and human-understandable network behavior, offering new insights for network administrators and security analysts.We propose an arbitrarily higher (even) order implicit leapfrog scheme for time discretization of a three-field formulation of Maxwell's equations.We propose overlap geometry as an alternative trust region, constraining distributional overlap via the Bhattacharyya coefficient (closely related to the Hellinger/Renyi-1/2 geometry).Research indicates that Maca might improve sexual desire without significant hormonal changes.Demographic and clinical data were obtained through questionnaires and interviews with the participants, and the levels of serum hormones and enzymes were measured.We created simulated versions of student essays, and human raters assigned scores to them and rated the realism of the generated text.Although traditional methods, such as constrained decoding, alleviate this problem by externally rejecting untypable code, the model itself does not effectively learn type reasoning internally, which ultimately limits its overall performance.This may include individuals who experience challenges in libido, stamina, or confidence related to sexual performance. 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Self-confidence is a critical aspect of overall well-being, and KangaRise Alpha Max recognizes the importance of this trait in the context of male enhancement. Surprisingly, BM25 significantly outperforms LLM-based retrievers by approximately 30%, as existing agents generate keyword-oriented sub-queries. To alleviate lazy optimization, we incorporate mismatch correction for training stability and introduce Profiling-based Rewards (PR) and Profiling-based Rejection Sampling (PRS) to overcome the issue. Building on KernelGYM, we investigate effective multi-turn RL methods and identify a biased policy gradient issue caused by self-inclusion in GRPO. However, training LLMs for this task requires sufficient data, a robust environment, and the process is often vulnerable to reward hacking and lazy optimization. While Group Relative Policy Optimization (GRPO) has emerged as a scalable framework for critic-free policy learning, extending it to settings with explicit behavioral constraints remains underexplored.