Large language models (LLMs) have demonstrated remarkable progress in leveraging diverse knowledge sources. This study investigates how nine widely used LLMs allocate knowledge between local context and global parameters when answering open-ended questions in knowledge-consistent scenarios. We introduce a novel dataset, WikiAtomic, and systematically vary context sizes to analyze how LLMs prioritize and utilize the provided information and their parametric knowledge in knowledge-consistent scenarios. Additionally, we also study their tendency to hallucinate under varying context sizes. Our findings reveal consistent patterns across models, including a consistent reliance on both contextual (around 70%) and parametric (around 30%) knowledge, and a decrease in hallucinations with increasing context. These insights highlight the importance of more effective context organization and developing models that use input more deterministically for robust performance.

Conversational search facilitates complex information retrieval by enabling multi-turn interactions between users and the system. Supporting such interactions requires a comprehensive understanding of the conversational inputs to formulate a good search query based on historical information. In particular, the search query should include the relevant information from the previous conversation turns. However, current approaches for conversational dense retrieval primarily rely on fine-tuning a pre-trained ad-hoc retriever using the whole conversational search session, which can be lengthy and noisy. Moreover, existing approaches are limited by the amount of manual supervision signals in the existing datasets. To address the aforementioned issues, we propose a History-Aware Conversational Dense Retrieval (HAConvDR) system, which incorporates two ideas: context-denoised query reformulation and automatic mining of supervision signals based on the actual impact of historical turns. Experiments on two public conversational search datasets demonstrate the improved history modeling capability of HAConvDR, in particular for long conversations with topic shifts.

Theoretical background is provided towards the mathematical foundation of the minimum enclosing ball problem. This problem concerns the determination of the unique spherical surface of smallest radius enclosing a given bounded set in the d-dimensional Euclidean space. The study of several problems that are similar or related to the minimum enclosing ball problem has received a considerable impetus from the large amount of applications of these problems in various fields of science and technology. The proposed theoretical framework is based on several enclosing (covering) and partitioning (clustering) theorems and provides among others bounds and relations between the circumradius, inradius, diameter and width of a set. These enclosing and partitioning theorems are considered as cornerstones in the field that strongly influencing developments and generalizations to other spaces and non-Euclidean geometries.

Many machine learning approaches for decision making, such as reinforcement learning, rely on simulators or predictive models to forecast the time-evolution of quantities of interest, e.g., the state of an agent or the reward of a policy. Forecasts of such complex phenomena are commonly described by highly nonlinear dynamical systems, making their use in optimization-based decision-making challenging. Koopman operator theory offers a beneficial paradigm for addressing this problem by characterizing forecasts via linear time-invariant (LTI) ODEs -- turning multi-step forecasting into sparse matrix multiplications. Though there exists a variety of learning approaches, they usually lack crucial learning-theoretic guarantees, making the behavior of the obtained models with increasing data and dimensionality unclear. We address the aforementioned by deriving a novel reproducing kernel Hilbert space (RKHS) over trajectories that solely spans transformations into LTI dynamical systems. The resulting Koopman Kernel Regression (KKR) framework enables the use of statistical learning tools from function approximation for novel convergence results and generalization error bounds under weaker assumptions than existing work. Our experiments demonstrate superior forecasting performance compared to Koopman operator and sequential data predictors in RKHS.

In this paper I discuss both syntax and semantics of subjective probability. The semantics determines ways of testing probability statements. Among important varieties of subjective probabilities are intersubjective probabilities and impersonal probabilities, and I will argue that well-tested impersonal probabilities acquire features of objective probabilities. Jeffreys's law, my next topic, states that two successful probability forecasters must issue forecasts that are close to each other, thus supporting the idea of objective probabilities. Finally, I will discuss connections between subjective and frequentist probability.

One of the most popular methods of the machine learning prediction explanation is the SHapley Additive exPlanations method (SHAP). An imprecise SHAP as a modification of the original SHAP is proposed for cases when the class probability distributions are imprecise and represented by sets of distributions. The first idea behind the imprecise SHAP is a new approach for computing the marginal contribution of a feature, which fulfils the important efficiency property of Shapley values. The second idea is an attempt to consider a general approach to calculating and reducing interval-valued Shapley values, which is similar to the idea of reachable probability intervals in the imprecise probability theory. A simple special implementation of the general approach in the form of linear optimization problems is proposed, which is based on using the Kolmogorov-Smirnov distance and imprecise contamination models. Numerical examples with synthetic and real data illustrate the imprecise SHAP.

A research report on "Global Automotive Artificial Intelligence (AI) Market 2019 Industry Research Report" is being published by researchunt.com. This is a key document as far as the clients and industries are concerned to not only understand the Global competitive market status that exists currently but also what future holds for it in the upcoming period, i.e., between 2018 and 2025. It has taken the previous market status of 2013 – 2018 to project the future status. The report has categorized in terms of region, type, key industries, and application. Global Automotive Artificial Intelligence (AI) revenue was xx.xx Million USD in 2013, grew to xx.xx Million USD in 2017, and will reach xx.xx Million USD in 2023, with a CAGR of x.x% during 2018-2023.

Because preferences naturally arise and play an important role in many real-life decisions, they are at the backbone of various fields. In particular preferences are increasingly used in almost all matching procedures-based applications. In this work we highlight the benefit of using AI insights on preferences in a large scale application, namely the French Admission Post-Baccalaureat Platform (APB). Each year APB allocates hundreds of thousands first year applicants to universities. This is done automatically by matching applicants preferences to university seats. In practice, APB can be unable to distinguish between applicants which leads to the introduction of random selection. This has created frustration in the French public since randomness, even used as a last mean does not fare well with the republican egalitarian principle. In this work, we provide a solution to this problem. We take advantage of recent AI Preferences Theory results to show how to enhance APB in order to improve expressiveness of applicants preferences and reduce their exposure to random decisions.

We present a computable algorithm that assigns probabilities to every logical statement in a given formal language, and refines those probabilities over time. For instance, if the language is Peano arithmetic, it assigns probabilities to all arithmetical statements, including claims about the twin prime conjecture, the outputs of long-running computations, and its own probabilities. We show that our algorithm, an instance of what we call a logical inductor, satisfies a number of intuitive desiderata, including: (1) it learns to predict patterns of truth and falsehood in logical statements, often long before having the resources to evaluate the statements, so long as the patterns can be written down in polynomial time; (2) it learns to use appropriate statistical summaries to predict sequences of statements whose truth values appear pseudorandom; and (3) it learns to have accurate beliefs about its own current beliefs, in a manner that avoids the standard paradoxes of self-reference. For example, if a given computer program only ever produces outputs in a certain range, a logical inductor learns this fact in a timely manner; and if late digits in the decimal expansion of $\pi$ are difficult to predict, then a logical inductor learns to assign $\approx 10\%$ probability to "the $n$th digit of $\pi$ is a 7" for large $n$. Logical inductors also learn to trust their future beliefs more than their current beliefs, and their beliefs are coherent in the limit (whenever $\phi \implies \psi$, $\mathbb{P}_\infty(\phi) \le \mathbb{P}_\infty(\psi)$, and so on); and logical inductors strictly dominate the universal semimeasure in the limit. These properties and many others all follow from a single logical induction criterion, which is motivated by a series of stock trading analogies. Roughly speaking, each logical sentence $\phi$ is associated with a stock that is worth \$1 per share if [...]