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Recent work has demonstrated that the latent spaces of large language models (LLMs) contain directions predictive of the truth of sentences. Multiple methods recover such directions and build probes that are described as getting at a model's "knowledge" or "beliefs". We investigate this phenomenon, looking closely at the impact of context on the probes. Our experiments establish where in the LLM the probe's predictions can be described as being conditional on the preceding (related) sentences. Specifically, we quantify the responsiveness of the probes to the presence of (negated) supporting and contradicting sentences, and score the probes on their consistency. We also perform a causal intervention experiment, investigating whether moving the representation of a premise along these belief directions influences the position of the hypothesis along that same direction. We find that the probes we test are generally context sensitive, but that contexts which should not affect the truth often still impact the probe outputs. Our experiments show that the type of errors depend on the layer, the (type of) model, and the kind of data. Finally, our results suggest that belief directions are (one of the) causal mediators in the inference process that incorporates in-context information.

Modern regression applications can involve hundreds or thousands of variables which motivates the use of variable selection methods. Bayesian variable selection defines a posterior distribution on the possible subsets of the variables (which are usually termed models) to express uncertainty about which variables are strongly linked to the response. This can be used to provide Bayesian model averaged predictions or inference, and to understand the relative importance of different variables. However, there has been little work on meaningful representations of this uncertainty beyond first order summaries. We introduce Cartesian credible sets to address this gap. The elements of these sets are formed by concatenating sub-models defined on each block of a partition of the variables. Investigating these sub-models allow us to understand whether the models in the Cartesian credible set always/never/sometimes include a particular variable or group of variables and provide a useful summary of model uncertainty. We introduce methods to find these sets that emphasize ease of understanding. The potential of the method is illustrated on regression problems with both small and large numbers of variables.

Modern machine learning techniques in the natural language processing domain can be used to automatically generate scripts for goal-oriented dialogue systems. The current article presents a general framework for studying the automatic generation of scripts for goal-oriented dialogue systems. A method for preprocessing dialog data sets in JSON format is described. A comparison is made of two methods for extracting user intent based on BERTopic and latent Dirichlet allocation. A comparison has been made of two implemented algorithms for classifying statements of users of a goal-oriented dialogue system based on logistic regression and BERT transformer models. The BERT transformer approach using the bert-base-uncased model showed better results for the three metrics Precision (0.80), F1-score (0.78) and Matthews correlation coefficient (0.74) in comparison with other methods.

Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy a large number of interactive samples, and the communication between these samples is crucial in speeding up the convergence. To justify the validity of these sampling strategies, the concept of interacting particles naturally calls for the mean-field theory. The theory establishes a correspondence between particle interactions encoded in a set of coupled ODEs/SDEs and a PDE that characterizes the evolution of the underlying distribution. This bridges numerical algorithms with the PDE theory used to show convergence in time. Many mathematical machineries are developed to provide the mean-field analysis, and we showcase two such examples: The coupling method and the compactness argument built upon the martingale strategy. The former has been deployed to show the convergence of ensemble Kalman sampler and ensemble Kalman inversion, and the latter will be shown to be immensely powerful in proving the validity of the Vlasov-Boltzmann simulator.

All poetic forms come from somewhere. Prosodic templates can be copied for generations, altered by individuals, imported from foreign traditions, or fundamentally changed under the pressures of language evolution. Yet these relationships are notoriously difficult to trace across languages and times. This paper introduces an unsupervised method for detecting structural similarities in poems using local sequence alignment. The method relies on encoding poetic texts as strings of prosodic features using a four-letter alphabet; these sequences are then aligned to derive a distance measure based on weighted symbol (mis)matches. Local alignment allows poems to be clustered according to emergent properties of their underlying prosodic patterns. We evaluate method performance on a meter recognition tasks against strong baselines and show its potential for cross-lingual and historical research using three short case studies: 1) mutations in quantitative meter in classical Latin, 2) European diffusion of the Renaissance hendecasyllable, and 3) comparative alignment of modern meters in 18--19th century Czech, German and Russian. We release an implementation of the algorithm as a Python package with an open license.

We propose an interdisciplinary framework that combines Bayesian predictive inference, a well-established tool in Machine Learning, with Formal Methods rooted in the computer science community. Bayesian predictive inference allows for coherently incorporating uncertainty about unknown quantities by making use of methods or models that produce predictive distributions, which in turn inform decision problems. By formalizing these decision problems into properties with the help of spatio-temporal logic, we can formulate and predict how likely such properties are to be satisfied in the future at a certain location. Moreover, we can leverage our methodology to evaluate and compare models directly on their ability to predict the satisfaction of application-driven properties. The approach is illustrated in an urban mobility application, where the crowdedness in the center of Milan is proxied by aggregated mobile phone traffic data. We specify several desirable spatio-temporal properties related to city crowdedness such as a fault-tolerant network or the reachability of hospitals. After verifying these properties on draws from the posterior predictive distributions, we compare several spatio-temporal Bayesian models based on their overall and property-based predictive performance.

In this work, we present an efficient way to decouple the multicontinuum problems. To construct decoupled schemes, we propose Implicit-Explicit time approximation in general form and study them for the fine-scale and coarse-scale space approximations. We use a finite-volume method for fine-scale approximation, and the nonlocal multicontinuum (NLMC) method is used to construct an accurate and physically meaningful coarse-scale approximation. The NLMC method is an accurate technique to develop a physically meaningful coarse scale model based on defining the macroscale variables. The multiscale basis functions are constructed in local domains by solving constraint energy minimization problems and projecting the system to the coarse grid. The resulting basis functions have exponential decay properties and lead to the accurate approximation on a coarse grid. We construct a fully Implicit time approximation for semi-discrete systems arising after fine-scale and coarse-scale space approximations. We investigate the stability of the two and three-level schemes for fully Implicit and Implicit-Explicit time approximations schemes for multicontinuum problems in fractured porous media. We show that combining the decoupling technique with multiscale approximation leads to developing an accurate and efficient solver for multicontinuum problems.

Scale has opened new frontiers in natural language processing, but at a high cost. In response, by learning to only activate a subset of parameters in training and inference, Mixture-of-Experts (MoE) have been proposed as an energy efficient path to even larger and more capable language models and this shift towards a new generation of foundation models is gaining momentum, particularly within the field of Automatic Speech Recognition (ASR). Recent works that incorporating MoE into ASR models have complex designs such as routing frames via supplementary embedding network, improving multilingual ability for the experts, and utilizing dedicated auxiliary losses for either expert load balancing or specific language handling. We found that delicate designs are not necessary, while an embarrassingly simple substitution of MoE layers for all Feed-Forward Network (FFN) layers is competent for the ASR task. To be more specific, we benchmark our proposed model on a large scale inner-source dataset (160k hours), the results show that we can scale our baseline Conformer (Dense-225M) to its MoE counterparts (MoE-1B) and achieve Dense-1B level Word Error Rate (WER) while maintaining a Dense-225M level Real Time Factor (RTF). Furthermore, by applying Unified 2-pass framework with bidirectional attention decoders (U2++), we achieve the streaming and non-streaming decoding modes in a single MoE based model, which we call U2++ MoE. We hope that our study can facilitate the research on scaling speech foundation models without sacrificing deployment efficiency.

In mesh simplification, common requirements like accuracy, triangle quality, and feature alignment are often considered as a trade-off. Existing algorithms concentrate on just one or a few specific aspects of these requirements. For example, the well-known Quadric Error Metrics (QEM) approach prioritizes accuracy and can preserve strong feature lines/points as well but falls short in ensuring high triangle quality and may degrade weak features that are not as distinctive as strong ones. In this paper, we propose a smooth functional that simultaneously considers all of these requirements. The functional comprises a normal anisotropy term and a Centroidal Voronoi Tessellation (CVT) energy term, with the variables being a set of movable points lying on the surface. The former inherits the spirit of QEM but operates in a continuous setting, while the latter encourages even point distribution, allowing various surface metrics. We further introduce a decaying weight to automatically balance the two terms. We selected 100 CAD models from the ABC dataset, along with 21 organic models, to compare the existing mesh simplification algorithms with ours. Experimental results reveal an important observation: the introduction of a decaying weight effectively reduces the conflict between the two terms and enables the alignment of weak features. This distinctive feature sets our approach apart from most existing mesh simplification methods and demonstrates significant potential in shape understanding.

When writing high-performance code for numerical computation in a scripting language like MATLAB, it is crucial to have the operations in a large for-loop vectorized. If not, the code becomes too slow to use, even for a moderately large problem. However, in the process of vectorizing, the code often loses its original structure and becomes less readable. This is particularly true in the case of a finite element implementation, even though finite element methods are inherently structured. A basic remedy to this is the separation of the vectorization part from the mathematics part of the code, which is easily achieved through building the code on top of the basic linear algebra subprograms that are already vectorized codes, an idea that has been used in a series of papers over the last fifteen years, developing codes that are fast and still structured and readable. We discuss the vectorized basic linear algebra package and introduce a formalism using multi-linear algebra to explain and define formally the functions in the package, as well as MATLAB pagetime functions. We provide examples from computations of varying complexity, including the computation of normal vectors, volumes, and finite element methods. Benchmarking shows that we also get fast computations. Using the library, we can write codes that closely follow our mathematical thinking, making writing, following, reusing, and extending the code easier.