Fig. S1: The proposed framework as a probabilistic graphical model. In this section we derive the variational lower-bound introduced in Sec.2.3 of the main article. W e firstly introduce Lemmas 1 and 2 as they appear in our derivations. As illustrated in Fig.S1, the ANN's input In Fig.S1 the lower boxes are the inducing points and other variables that determine the GPs' posterior. S1.1 Deriving the Lower-bound With Respect to the Kernel-mappings In the right-hand-side of Eq.S6 only the following terms are dependant on the kernel-mappings The first term is the expected log-likelihood of a Gaussian distribution (i.e. the conditional log-likelihood of Therefore, we can use Lemma.2 to simplify the first term: E According to Lemma.1 we have that Therefore, the KL-term of Eq.S8 is a constant with respect to the kernel mappings All in all, the lower-bound for optimizing the kernel-mappings is equal to the right-hand-side of Eq.S9 which was introduced and discussed in Sec.2.3. of the main article. S1.2 Deriving the Lower-bound With Respect to the ANN Parameters According to Eq.4 of the main article, in our formulation the ANN's parameters appear as some variational parameters. Therefore, the likelihood of all variables (Eq.S6) does not generally depend on the ANN's parameters. This likelihood turns out to be equivalent to commonly-used losses like the cross-entropy loss or the mean-squared loss. Here we elaborate upon how this happens. This conclusion was introduced and discussed in Eq.6 of the main article. W e can draw similar conclusions when the pipeline is for other tasks like regression, or even a combination of tasks.

Fig. S1: The proposed framework as a probabilistic graphical model. In this section we derive the variational lower-bound introduced in Sec.2.3 of the main article. W e firstly introduce Lemmas 1 and 2 as they appear in our derivations. As illustrated in Fig.S1, the ANN's input In Fig.S1 the lower boxes are the inducing points and other variables that determine the GPs' posterior. S1.1 Deriving the Lower-bound With Respect to the Kernel-mappings In the right-hand-side of Eq.S6 only the following terms are dependant on the kernel-mappings The first term is the expected log-likelihood of a Gaussian distribution (i.e. the conditional log-likelihood of Therefore, we can use Lemma.2 to simplify the first term: E According to Lemma.1 we have that Therefore, the KL-term of Eq.S8 is a constant with respect to the kernel mappings All in all, the lower-bound for optimizing the kernel-mappings is equal to the right-hand-side of Eq.S9 which was introduced and discussed in Sec.2.3. of the main article. S1.2 Deriving the Lower-bound With Respect to the ANN Parameters According to Eq.4 of the main article, in our formulation the ANN's parameters appear as some variational parameters. Therefore, the likelihood of all variables (Eq.S6) does not generally depend on the ANN's parameters. This likelihood turns out to be equivalent to commonly-used losses like the cross-entropy loss or the mean-squared loss. Here we elaborate upon how this happens. This conclusion was introduced and discussed in Eq.6 of the main article. W e can draw similar conclusions when the pipeline is for other tasks like regression, or even a combination of tasks.

Financial news plays a critical role in the information diffusion process in financial markets and is a known driver of stock prices. However, the information in each news article is not necessarily self-contained, often requiring a broader understanding of the historical news coverage for accurate interpretation. Further, identifying and incorporating the most relevant contextual information presents significant challenges. In this work, we explore the value of historical context in the ability of large language models to understand the market impact of financial news. We find that historical context provides a consistent and significant improvement in performance across methods and time horizons. To this end, we propose an efficient and effective contextualization method that uses a large LM to process the main article, while a small LM encodes the historical context into concise summary embeddings that are then aligned with the large model's representation space. We explore the behavior of the model through multiple qualitative and quantitative interpretability tests and reveal insights into the value of contextualization. Finally, we demonstrate that the value of historical context in model predictions has real-world applications, translating to substantial improvements in simulated investment performance.

We present RPGBench, the first benchmark designed to evaluate large language models (LLMs) as text-based role-playing game (RPG) engines. RPGBench comprises two core tasks: Game Creation (GC) and Game Simulation (GS). In GC, an LLM must craft a valid and playable RPG world using a structured event-state representation, ensuring logical coherence and proper termination conditions. In GS, the LLM simulates interactive gameplay across multiple rounds while consistently updating states and enforcing game rules. To comprehensively assess performance, RPGBench integrates objective and subjective evaluation methodologies. Objective measures verify adherence to event mechanics and check variable updates without requiring human intervention. Subjective measures, such as content interestingness, action quality, and role-playing capability, are evaluated via an LLM-as-a-judge framework, where a strong LLM grades each candidate's outputs. Empirical results demonstrate that state-of-the-art LLMs can produce engaging stories but often struggle to implement consistent, verifiable game mechanics, particularly in long or complex scenarios. By combining structured, rule-based assessments with LLM-based judgments, RPGBench provides a new standard for evaluating how well LLMs can balance creativity, coherence, and complexity in text-based RPGs, opening avenues for more immersive and controllable interactive storytelling.

Data valuation, which measures the contribution of individual data source on machine learning (ML) model performance, plays a crucial role in improving algorithmic transparency and creating incentive mechanisms for data sharing and monetization (Liu et al., 2023). Its importance is particularly evident in sectors like healthcare and finance, where explainable ML is increasingly being adopted for high-stake decision-making (Sahoh and Choksuriwong, 2023). The recent rise of data marketplaces further highlights the need for accurate data valuation (Ghorbani and Zou, 2019; Jia et al., 2019a). By integrating diverse data sources, these marketplaces enhance ML tasks and unlock significant business values (Agarwal et al., 2019). Fair compensation for data creators based on the value of their data is crucial in such contexts, making the equitable valuation of data a key issue (Altman, 2023). Data Shapley has recently gained widespread recognition for quantifying the contribution of individual data points to ML models (Ghorbani and Zou, 2019; Jia et al., 2019b). It is uniquely defined by four axioms (see Axiom 2.1-2.4 in Section 2).

The logit transform is arguably the most widely-employed link function beyond linear settings. This transformation routinely appears in regression models for binary data and provides, either explicitly or implicitly, a core building-block within state-of-the-art methodologies for both classification and regression. Its widespread use, combined with the lack of analytical solutions for the optimization of general losses involving the logit transform, still motivates active research in computational statistics. Among the directions explored, a central one has focused on the design of tangent lower bounds for logistic log-likelihoods that can be tractably optimized, while providing a tight approximation of these log-likelihoods. Although progress along these lines has led to the development of effective minorize-maximize (MM) algorithms for point estimation and coordinate ascent variational inference schemes for approximate Bayesian inference under several logit models, the overarching focus in the literature has been on tangent quadratic minorizers. In fact, it is still unclear whether tangent lower bounds sharper than quadratic ones can be derived without undermining the tractability of the resulting minorizer. This article addresses such a challenging question through the design and study of a novel piece-wise quadratic lower bound that uniformly improves any tangent quadratic minorizer, including the sharpest ones, while admitting a direct interpretation in terms of the classical generalized lasso problem. As illustrated in a ridge logistic regression, this unique connection facilitates more effective implementations than those provided by available piece-wise bounds, while improving the convergence speed of quadratic ones.

In this article, we propose and apply a method to compare adaptations of the same story across different media. We tackle this task by modelling such adaptations through character networks. We compare them by leveraging two concepts at the core of storytelling: the characters involved, and the dynamics of the story. We propose several methods to match characters between media and compare their position in the networks; and perform narrative matching, i.e. match the sequences of narrative units that constitute the plots. We apply these methods to the novel series \textit{A Song of Ice and Fire}, by G.R.R. Martin, and its comics and TV show adaptations. Our results show that interactions between characters are not sufficient to properly match individual characters between adaptations, but that using some additional information such as character affiliation or gender significantly improves the performance. On the contrary, character interactions convey enough information to perform narrative matching, and allow us to detect the divergence between the original novels and its TV show adaptation.

Deep learning[133] uses several layers of neurons between the network's inputs and outputs. The multiple layers can progressively extract higher-level features from the raw input. For example, in image processing, lower layers may identify edges, while higher layers may identify the concepts relevant to a human such as digits or letters or faces.[134] Deep learning has drastically improved the performance of programs in many important subfields of artificial intelligence, including computer vision, speech recognition, image classification[135] and others. Deep learning often uses convolutional neural networks for many or all of its layers.

Abstract--Machine learning researchers have long noted a trade-off between interpretability and prediction performance. On the one hand, traditional models are often interpretable to humans but they cannot achieve high prediction performances. At the opposite end of the spectrum, deep models can achieve state-of-the-art performances in many tasks. However, deep models' predictions are known to be uninterpretable to humans. In this paper we present a framework that shortens the gap between the two aforementioned groups of methods. Given an artificial neural network (ANN), our method finds a Gaussian process (GP) whose predictions almost match those of the ANN. As GPs are highly interpretable, we use the trained GP to explain the ANN's decisions. We use our method to explain ANNs' decisions on may datasets. The explanations provide intriguing insights about the ANNs' decisions. With the best of our knowledge, our inference formulation for GPs is the first one in which an ANN and a similarly behaving Gaussian process naturally appear. Furthermore, we examine some of the known theoretical conditions under which an ANN is interpretable by GPs. Some of those theoretical conditions are too restrictive for modern architectures. However, we hypothesize that only a subset of those theoretical conditions are sufficient. Finally, we implement our framework as a publicly available tool called GPEX. Given any pytorch feed-forward module, GPEX allows users to interpret any ANN subcomponent of the module effortlessly and without having to be involved in the inference algorithm.