This article looks at how reasoning works in current Large Language Models (LLMs) that function using the token-completion method. It examines their stochastic nature and their similarity to human abductive reasoning. The argument is that these LLMs create text based on learned patterns rather than performing actual abductive reasoning. When their output seems abductive, this is largely because they are trained on human-generated texts that include reasoning structures. Examples are used to show how LLMs can produce plausible ideas, mimic commonsense reasoning, and give explanatory answers without being grounded in truth, semantics, verification, or understanding, and without performing any real abductive reasoning. This dual nature, where the models have a stochastic base but appear abductive in use, has important consequences for how LLMs are evaluated and applied. They can assist with generating ideas and supporting human thinking, but their outputs must be critically assessed because they cannot identify truth or verify their explanations. The article concludes by addressing five objections to these points, noting some limitations in the analysis, and offering an overall evaluation.

This paper analyzes a fuzzy multiplex from a logical perspective in a way that has not been formalized so far. A fuzzy multiplex is a nested structure with inner nodes representing sub-system level agent traits and with outer nodes representing system agents; all while the ensemble is the system under consideration. Moreover, a mathematical framework is necessary to describe that structure which is formulated and then utilized. The system is firstly initialized using fuzzy set theory [2], inspired by Fuzzy Cognitive Maps [1]. Then a criterion that describes the structure is devised to implement a multiplex instead of a map [7] [8], and lastly system optimization is achieved. Furthermore, the theoretical context behind the multiplex is expounded in an attempt to establish a formal way of handling implications within a closed system using human intelligence. The paper is organized in sections following the reasoning process behind this unique idea. 1

The proliferation of probabilistic AI has prompted proposals for specialized stochastic computers. Despite promising efficiency gains, these proposals have failed to gain traction because they rely on fundamentally limited modeling techniques and exotic, unscalable hardware. In this work, we address these shortcomings by proposing an all-transistor probabilistic computer that implements powerful denoising models at the hardware level. A system-level analysis indicates that devices based on our architecture could achieve performance parity with GPUs on a simple image benchmark using approximately 10,000 times less energy.

Reproducibility is a cornerstone of scientific validation and of the authority it confers on its results. Reproducibility in machine learning evaluations leads to greater trust, confidence, and value. However, the ground truth responses used in machine learning often necessarily come from humans, among whom disagreement is prevalent, and surprisingly little research has studied the impact of effectively ignoring disagreement in these responses, as is typically the case. One reason for the lack of research is that budgets for collecting human-annotated evaluation data are limited, and obtaining more samples from multiple raters for each example greatly increases the per-item annotation costs. We investigate the trade-off between the number of items ($N$) and the number of responses per item ($K$) needed for reliable machine learning evaluation. We analyze a diverse collection of categorical datasets for which multiple annotations per item exist, and simulated distributions fit to these datasets, to determine the optimal $(N, K)$ configuration, given a fixed budget ($N \times K$), for collecting evaluation data and reliably comparing the performance of machine learning models. Our findings show, first, that accounting for human disagreement may come with $N \times K$ at no more than 1000 (and often much lower) for every dataset tested on at least one metric. Moreover, this minimal $N \times K$ almost always occurred for $K > 10$. Furthermore, the nature of the tradeoff between $K$ and $N$, or if one even existed, depends on the evaluation metric, with metrics that are more sensitive to the full distribution of responses performing better at higher levels of $K$. Our methods can be used to help ML practitioners get more effective test data by finding the optimal metrics and number of items and annotations per item to collect to get the most reliability for their budget.

Motion Transfer is a technique that synthesizes videos by transferring motion dynamics from a driving video to a source image. In this work we propose a deep learning-based framework to enable real-time video motion transfer which is critical for enabling bandwidth-efficient applications such as video conferencing, remote health monitoring, virtual reality interaction, and vision-based anomaly detection. This is done using keypoints which serve as semantically meaningful, compact representations of motion across time. To enable bandwidth savings during video transmission we perform forecasting of keypoints using two generative time series models VRNN and GRU-NF. The predicted keypoints are transformed into realistic video frames using an optical flow-based module paired with a generator network, thereby enabling efficient, low-frame-rate video transmission. Based on the application this allows the framework to either generate a deterministic future sequence or sample a diverse set of plausible futures. Experimental results demonstrate that VRNN achieves the best point-forecast fidelity (lowest MAE) in applications requiring stable and accurate multi-step forecasting and is particularly competitive in higher-uncertainty, multi-modal settings. This is achieved by introducing recurrently conditioned stochastic latent variables that carry past contexts to capture uncertainty and temporal variation. On the other hand the GRU-NF model enables richer diversity of generated videos while maintaining high visual quality. This is realized by learning an invertible, exact-likelihood mapping between the keypoints and their latent representations which supports rich and controllable sampling of diverse yet coherent keypoint sequences. Our work lays the foundation for next-generation AI systems that require real-time, bandwidth-efficient, and semantically controllable video generation.

We propose geodesic-based optimization methods on dually flat spaces, where the geometric structure of the parameter manifold is closely related to the form of the objective function. A primary application is maximum likelihood estimation in statistical models, especially exponential families, whose model manifolds are dually flat. We show that an m-geodesic update, which directly optimizes the log-likelihood, can theoretically reach the maximum likelihood estimator in a single step. In contrast, an e-geodesic update has a practical advantage in cases where the parameter space is geodesically complete, allowing optimization without explicitly handling parameter constraints. We establish the theoretical properties of the proposed methods and validate their effectiveness through numerical experiments.

Applied researchers now routinely work with regression models that feature a large number of covariates. A primary inferential goal in econometrics is to estimate the ceteris paribus effect of a specific variable while controlling for other variables (Belloni et al., 2013a, 2018). The prevailing practice interprets the coefficient on a regressor as a causal effect, conditional on the included controls. As the plausibility of conditional unconfoundedness is often argued using a large set of covariates, practitioners have increasingly embraced high-dimensional regression models. This setting has been extensively studied, predominantly using frequentist methods. Bayesian inference, on the other hand, has long been valued for its coherent framework for handling uncertainty in statistical analysis. As highlighted by Rubin (1984), Bayesian methods provide direct answers to many empirical questions by quantifying uncertainty about unknown parameters conditional on the observed data.

Accurate and efficient surrogate modeling is essential for modern computational science, and there are a staggering number of emulation methods to choose from. With new methods being developed all the time, comparing the relative strengths and weaknesses of different methods remains a challenge due to inconsistent benchmarking practices and (sometimes) limited reproducibility and transparency. In this work, we present a large-scale, fully reproducible comparison of $29$ distinct emulators across $60$ canonical test functions and $40$ real emulation datasets. To facilitate rigorous, apples-to-apples comparisons, we introduce the R package \texttt{duqling}, which streamlines reproducible simulation studies using a consistent, simple syntax, and automatic internal scaling of inputs. This framework allows researchers to compare emulators in a unified environment and makes it possible to replicate or extend previous studies with minimal effort, even across different publications. Our results provide detailed empirical insight into the strengths and weaknesses of state-of-the-art emulators and offer guidance for both method developers and practitioners selecting a surrogate for new data. We discuss best practices for emulator comparison and highlight how \texttt{duqling} can accelerate research in emulator design and application.

Moralisation and Triangulation are transformations allowing to switch between different ways of factoring a probability distribution into a graphical model. Moralisation allows to view a Bayesian network (a directed model) as a Markov network (an undirected model), whereas triangulation addresses the opposite direction. We present a categorical framework where these transformations are modelled as functors between a category of Bayesian networks and one of Markov networks. The two kinds of network (the objects of these categories) are themselves represented as functors from a `syntax' domain to a `semantics' codomain. Notably, moralisation and triangulation can be defined inductively on such syntax via functor pre-composition. Moreover, while moralisation is fully syntactic, triangulation relies on semantics. This leads to a discussion of the variable elimination algorithm, reinterpreted here as a functor in its own right, that splits the triangulation procedure in two: one purely syntactic, the other purely semantic. This approach introduces a functorial perspective into the theory of probabilistic graphical models, which highlights the distinctions between syntactic and semantic modifications.

High-performance concrete requires complex mix design decisions involving interdependent variables and practical constraints. While data-driven methods have improved predictive modeling for forward design in concrete engineering, inverse design remains limited, especially when some variables are fixed and only the remaining ones must be inferred. This study proposes a cooperative neural network framework for the partial inverse design of high-performance concrete. The framework integrates an imputation model with a surrogate strength predictor and learns through cooperative training. Once trained, it generates valid and performance-consistent mix designs in a single forward pass without retraining for different constraint scenarios. Compared with baseline models, including autoencoder models and Bayesian inference with Gaussian process surrogates, the proposed method achieves R-squared values of 0.87 to 0.92 and substantially reduces mean squared error by approximately 50% and 70%, respectively. The results show that the framework provides an accurate and computationally efficient foundation for constraint-aware, data-driven mix proportioning.