While numerous works have assessed the generative performance of language models (LMs) on tasks requiring Theory of Mind reasoning, research into the models' internal representation of mental states remains limited. Recent work has used probing to demonstrate that LMs can represent beliefs of themselves and others. However, these claims are accompanied by limited evaluation, making it difficult to assess how mental state representations are affected by model design and training choices. We report an extensive benchmark with various LM types with different model sizes, fine-tuning approaches, and prompt designs to study the robustness of mental state representations and memorisation issues within the probes. Our results show that the quality of models' internal representations of the beliefs of others increases with model size and, more crucially, with fine-tuning. We are the first to study how prompt variations impact probing performance on theory of mind tasks. We demonstrate that models' representations are sensitive to prompt variations, even when such variations should be beneficial. Finally, we complement previous activation editing experiments on Theory of Mind tasks and show that it is possible to improve models' reasoning performance by steering their activations without the need to train any probe.

With the rapid advancement of autonomous driving technology, self-driving cars have become a central focus in the development of future transportation systems. Scenario generation technology has emerged as a crucial tool for testing and verifying the safety performance of autonomous driving systems. Current research in scenario generation primarily focuses on open roads such as highways, with relatively limited studies on underground parking garages. The unique structural constraints, insufficient lighting, and high-density obstacles in underground parking garages impose greater demands on the perception systems, which are critical to autonomous driving technology. This study proposes an accelerated generation method for perception failure scenarios tailored to the underground parking garage environment, aimed at testing and improving the safety performance of autonomous vehicle (AV) perception algorithms in such settings. The method presented in this paper generates an intelligent testing environment with a high density of perception failure scenarios by learning the interactions between background vehicles (BVs) and autonomous vehicles (AVs) within perception failure scenarios. Furthermore, this method edits the Markov process within the perception failure scenario data to increase the density of critical information in the training data, thereby optimizing the learning and generation of perception failure scenarios. A simulation environment for an underground parking garage was developed using the Carla and Vissim platforms, with Bevfusion employed as the perception algorithm for testing. The study demonstrates that this method can generate an intelligent testing environment with a high density of perception failure scenarios and enhance the safety performance of perception algorithms within this experimental setup.

Gaussian Processes (GPs) provide a principled Bayesian framework for function approximation, making them particularly useful in many applications requiring uncertainty calibration [Rasmussen and Williams, 2006], such as Bayesian optimisation [Snoek et al., 2012] and time-series analysis [Roberts et al., 2013]. Despite offering reasonable uncertainty estimation, shallow GPs often struggle to model complex, non-stationary processes present in practical applications. To overcome this limitation, Deep Gaussian Processes (DGPs) employ a compositional architecture by stacking multiple GP layers, thereby enhancing representational power while preserving the model's intrinsic capability to quantify uncertainty [Damianou and Lawrence, 2013]. However, the conventional variational formulation of DGPs heavily depends on local inducing point approximations across intermediate GP layers [Titsias, 2009, Salimbeni and Deisenroth, 2017], which hinder the model from capturing the global structures commonly found in real-world scenarios. Incorporating Fourier features into GP models has shown promise in addressing this challenge in GP inference due to the periodic nature of these features. A line of research uses Random Fourier Features (RFFs, [Rahimi and Recht, 2007]) of stationary kernels to convert the original (deep) GPs into Bayesian networks in weight space [Lázaro-Gredilla et al., 2010, Gal and Turner, 2015, Cutajar et al., 2017]. Building on this concept within a sparse variational GP framework, recent advancements in inter-domain GPs [Lázaro-Gredilla and Figueiras-Vidal, 2009a, Van der Wilk et al., 2020] directly approximate the posterior of the original GPs by introducing fixed Variational Fourier Features (VFFs) through process projection onto a Reproducing Kernel Hilbert Space (RKHS)[Hensman et al., 2018, Rudner et al., 2020]. VFFs are derived by projecting GPs onto a different domain.

Capturing users' engagement is crucial for gathering feedback about the features of a software product. In a market-driven context, current approaches to collect and analyze users' feedback are based on techniques leveraging information extracted from product reviews and social media. These approaches are hardly applicable in bespoke software development, or in contexts in which one needs to gather information from specific users. In such cases, companies need to resort to face-to-face interviews to get feedback on their products. In this paper, we propose to utilize biometric data, in terms of physiological and voice features, to complement interviews with information about the engagement of the user on the discussed product-relevant topics. We evaluate our approach by interviewing users while gathering their physiological data (i.e., biofeedback) using an Empatica E4 wristband, and capturing their voice through the default audio-recorder of a common laptop. Our results show that we can predict users' engagement by training supervised machine learning algorithms on biometric data (F1=0.72), and that voice features alone are sufficiently effective (F1=0.71). Our work contributes with one the first studies in requirements engineering in which biometrics are used to identify emotions. This is also the first study in software engineering that considers voice analysis. The usage of voice features could be particularly helpful for emotion-aware requirements elicitation in remote communication, either performed by human analysts or voice-based chatbots, and can also be exploited to support the analysis of meetings in software engineering research.

We introduce NCP (Neural Conditional Probability), a novel operator-theoretic approach for learning conditional distributions with a particular focus on inference tasks. NCP can be used to build conditional confidence regions and extract important statistics like conditional quantiles, mean, and covariance. It offers streamlined learning through a single unconditional training phase, facilitating efficient inference without the need for retraining even when conditioning changes. By tapping into the powerful approximation capabilities of neural networks, our method efficiently handles a wide variety of complex probability distributions, effectively dealing with nonlinear relationships between input and output variables. Theoretical guarantees ensure both optimization consistency and statistical accuracy of the NCP method. Our experiments show that our approach matches or beats leading methods using a simple Multi-Layer Perceptron (MLP) with two hidden layers and GELU activations. This demonstrates that a minimalistic architecture with a theoretically grounded loss function can achieve competitive results without sacrificing performance, even in the face of more complex architectures.

In domains with interdependent data, such as graphs, quantifying the epistemic uncertainty of a Graph Neural Network (GNN) is challenging as uncertainty can arise at different structural scales. Existing techniques neglect this issue or only distinguish between structure-aware and structure-agnostic uncertainty without combining them into a single measure. We propose GEBM, an energy-based model (EBM) that provides high-quality uncertainty estimates by aggregating energy at different structural levels that naturally arise from graph diffusion. In contrast to logit-based EBMs, we provably induce an integrable density in the data space by regularizing the energy function. We introduce an evidential interpretation of our EBM that significantly improves the predictive robustness of the GNN. Our framework is a simple and effective post hoc method applicable to any pre-trained GNN that is sensitive to various distribution shifts. It consistently achieves the best separation of in-distribution and out-of-distribution data on 6 out of 7 anomaly types while having the best average rank over shifts on \emph{all} datasets.

We study how abstract representations emerge in a Deep Belief Network (DBN) trained on benchmark datasets. Our analysis targets the principles of learning in the early stages of information processing, starting from the "primordial soup" of the under-sampling regime. As the data is processed by deeper and deeper layers, features are detected and removed, transferring more and more "context-invariant" information to deeper layers. We show that the representation approaches an universal model -- the Hierarchical Feature Model (HFM) -- determined by the principle of maximal relevance. Relevance quantifies the uncertainty on the model of the data, thus suggesting that "meaning" -- i.e. syntactic information -- is that part of the data which is not yet captured by a model. Our analysis shows that shallow layers are well described by pairwise Ising models, which provide a representation of the data in terms of generic, low order features. We also show that plasticity increases with depth, in a similar way as it does in the brain. These findings suggest that DBNs are capable of extracting a hierarchy of features from the data which is consistent with the principle of maximal relevance.

This paper addresses the need for deep learning models to integrate well-defined constraints into their outputs, driven by their application in surrogate models, learning with limited data and partial information, and scenarios requiring flexible model behavior to incorporate non-data sample information. We introduce Bayesian Entropy Neural Networks (BENN), a framework grounded in Maximum Entropy (MaxEnt) principles, designed to impose constraints on Bayesian Neural Network (BNN) predictions. BENN is capable of constraining not only the predicted values but also their derivatives and variances, ensuring a more robust and reliable model output. To achieve simultaneous uncertainty quantification and constraint satisfaction, we employ the method of multipliers approach. This allows for the concurrent estimation of neural network parameters and the Lagrangian multipliers associated with the constraints. Our experiments, spanning diverse applications such as beam deflection modeling and microstructure generation, demonstrate the effectiveness of BENN. The results highlight significant improvements over traditional BNNs and showcase competitive performance relative to contemporary constrained deep learning methods.

In this paper we describe a new conceptual framework that connects approximate Dynamic Programming (DP), Model Predictive Control (MPC), and Reinforcement Learning (RL). This framework centers around two algorithms, which are designed largely independently of each other and operate in synergy through the powerful mechanism of Newton's method. We call them the off-line training and the on-line play algorithms. The names are borrowed from some of the major successes of RL involving games; primary examples are the recent (2017) AlphaZero program (which plays chess, [SHS17], [SSS17]), and the similarly structured and earlier (1990s) TD-Gammon program (which plays backgammon, [Tes94], [Tes95], [TeG96]). In these game contexts, the off-line training algorithm is the method used to teach the program how to evaluate positions and to generate good moves at any given position, while the on-line play algorithm is the method used to play in real time against human or computer opponents. Significantly, the synergy between off-line training and on-line play also underlies MPC (as well as other major classes of sequential decision problems), and indeed the MPC design architecture is very similar to the one of AlphaZero and TD-Gammon. This conceptual insight provides a vehicle for bridging the cultural gap between RL and MPC, and sheds new light on some fundamental issues in MPC. These include the enhancement of stability properties through rollout, the treatment of uncertainty through the use of certainty equivalence, the resilience of MPC in adaptive control settings that involve changing system parameters, and the insights provided by the superlinear performance bounds implied by Newton's method.

Black-box optimization (BBO) aims to optimize an objective function by iteratively querying a black-box oracle. This process demands sample-efficient optimization due to the high computational cost of function evaluations. While prior studies focus on forward approaches to learn surrogates for the unknown objective function, they struggle with high-dimensional inputs where valid inputs form a small subspace (e.g., valid protein sequences), which is common in real-world tasks. Recently, diffusion models have demonstrated impressive capability in learning the high-dimensional data manifold. They have shown promising performance in black-box optimization tasks but only in offline settings. In this work, we propose diffusion-based inverse modeling for black-box optimization (Diff-BBO), the first inverse approach leveraging diffusion models for online BBO problem. Diff-BBO distinguishes itself from forward approaches through the design of acquisition function. Instead of proposing candidates in the design space, Diff-BBO employs a novel acquisition function Uncertainty-aware Exploration (UaE) to propose objective function values, which leverages the uncertainty of a conditional diffusion model to generate samples in the design space. Theoretically, we prove that using UaE leads to optimal optimization outcomes. Empirically, we redesign experiments on the Design-Bench benchmark for online settings and show that Diff-BBO achieves state-of-the-art performance.