This paper explores methods for verifying the properties of Binary Neural Networks (BNNs), focusing on robustness against adversarial attacks. Despite their lower computational and memory needs, BNNs, like their full-precision counterparts, are also sensitive to input perturbations. Established methods for solving this problem are predominantly based on Satisfiability Modulo Theories and Mixed-Integer Linear Programming techniques, which are characterized by NP complexity and often face scalability issues. We introduce an alternative approach using Semidefinite Programming relaxations derived from sparse Polynomial Optimization. Our approach, compatible with continuous input space, not only mitigates numerical issues associated with floating-point calculations but also enhances verification scalability through the strategic use of tighter first-order semidefinite relaxations. We demonstrate the effectiveness of our method in verifying robustness against both $\|.\|_\infty$ and $\|.\|_2$-based adversarial attacks.

Existing AI alignment approaches assume that preferences are static, which is unrealistic: our preferences change, and may even be influenced by our interactions with AI systems themselves. To clarify the consequences of incorrectly assuming static preferences, we introduce Dynamic Reward Markov Decision Processes (DR-MDPs), which explicitly model preference changes and the AI's influence on them. We show that despite its convenience, the static-preference assumption may undermine the soundness of existing alignment techniques, leading them to implicitly reward AI systems for influencing user preferences in ways users may not truly want. We then explore potential solutions. First, we offer a unifying perspective on how an agent's optimization horizon may partially help reduce undesirable AI influence. Then, we formalize different notions of AI alignment that account for preference change from the outset. Comparing the strengths and limitations of 8 such notions of alignment, we find that they all either err towards causing undesirable AI influence, or are overly risk-averse, suggesting that a straightforward solution to the problems of changing preferences may not exist. As there is no avoiding grappling with changing preferences in real-world settings, this makes it all the more important to handle these issues with care, balancing risks and capabilities. We hope our work can provide conceptual clarity and constitute a first step towards AI alignment practices which explicitly account for (and contend with) the changing and influenceable nature of human preferences.

Diffusion-based representation learning has achieved substantial attention due to its promising capabilities in latent representation and sample generation. Recent studies have employed an auxiliary encoder to identify a corresponding representation from a sample and to adjust the dimensionality of a latent variable z. Meanwhile, this auxiliary structure invokes information split problem because the diffusion and the auxiliary encoder would divide the information from the sample into two representations for each model. Particularly, the information modeled by the diffusion becomes over-regularized because of the static prior distribution on xT. To address this problem, we introduce Diffusion Bridge AuteEncoders (DBAE), which enable z-dependent endpoint xT inference through a feed-forward architecture. This structure creates an information bottleneck at z, so xT becomes dependent on z in its generation. This results in two consequences: 1) z holds the full information of samples, and 2) xT becomes a learnable distribution, not static any further. We propose an objective function for DBAE to enable both reconstruction and generative modeling, with their theoretical justification. Empirical evidence supports the effectiveness of the intended design in DBAE, which notably enhances downstream inference quality, reconstruction, and disentanglement. Additionally, DBAE generates high-fidelity samples in the unconditional generation.

We present an algorithm for skill discovery from expert demonstrations. The algorithm first utilizes Large Language Models (LLMs) to propose an initial segmentation of the trajectories. Following that, a hierarchical variational inference framework incorporates the LLM-generated segmentation information to discover reusable skills by merging trajectory segments. To further control the trade-off between compression and reusability, we introduce a novel auxiliary objective based on the Minimum Description Length principle that helps guide this skill discovery process. Our results demonstrate that agents equipped with our method are able to discover skills that help accelerate learning and outperform baseline skill learning approaches on new long-horizon tasks in BabyAI, a grid world navigation environment, as well as ALFRED, a household simulation environment.

Graph neural networks excel at modeling pairwise interactions, but they cannot flexibly accommodate higher-order interactions and features. Topological deep learning (TDL) has emerged recently as a promising tool for addressing this issue. TDL enables the principled modeling of arbitrary multi-way, hierarchical higher-order interactions by operating on combinatorial topological spaces, such as simplicial or cell complexes, instead of graphs. However, little is known about how to leverage geometric features such as positions and velocities for TDL. This paper introduces E(n)-Equivariant Topological Neural Networks (ETNNs), which are E(n)-equivariant message-passing networks operating on combinatorial complexes, formal objects unifying graphs, hypergraphs, simplicial, path, and cell complexes. ETNNs incorporate geometric node features while respecting rotation and translation equivariance. Moreover, ETNNs are natively ready for settings with heterogeneous interactions. We provide a theoretical analysis to show the improved expressiveness of ETNNs over architectures for geometric graphs. We also show how several E(n) equivariant variants of TDL models can be directly derived from our framework. The broad applicability of ETNNs is demonstrated through two tasks of vastly different nature: i) molecular property prediction on the QM9 benchmark and ii) land-use regression for hyper-local estimation of air pollution with multi-resolution irregular geospatial data. The experiment results indicate that ETNNs are an effective tool for learning from diverse types of richly structured data, highlighting the benefits of principled geometric inductive bias.

Cardinality Estimation (CE) for query is to estimate the number of results without execution, which is an effective index in query optimization. Recently, CE over has achieved great success in knowledge graphs (KGs) that consist of triple facts. To more precisely represent facts, current researchers propose hyper-relational KGs (HKGs) to represent a triple fact with qualifiers, where qualifiers provide additional context to the fact. However, existing CE methods over KGs achieve unsatisfying performance on HKGs due to the complexity of qualifiers in HKGs. Also, there is only one dataset for HKG query cardinality estimation, i.e., WD50K-QE, which is not comprehensive and only covers limited patterns. The lack of querysets over HKG also becomes a bottleneck to comprehensively investigate CE problems on HKGs. In this work, we first construct diverse and unbiased hyper-relational querysets over three popular HKGs for investigating CE. Besides, we also propose a novel qualifier-attached graph neural network (GNN) model that effectively incorporates qualifier information and adaptively combines outputs from multiple GNN layers, to accurately predict the cardinality. Our experiments illustrate that the proposed hyper-relational query encoder outperforms all state-of-the-art CE methods over three popular HKGs on the diverse and unbiased benchmark.

This work studies discrete-time discounted Markov decision processes with continuous state and action spaces and addresses the inverse problem of inferring a cost function from observed optimal behavior. We first consider the case in which we have access to the entire expert policy and characterize the set of solutions to the inverse problem by using occupation measures, linear duality, and complementary slackness conditions. To avoid trivial solutions and ill-posedness, we introduce a natural linear normalization constraint. This results in an infinite-dimensional linear feasibility problem, prompting a thorough analysis of its properties. Next, we use linear function approximators and adopt a randomized approach, namely the scenario approach and related probabilistic feasibility guarantees, to derive epsilon-optimal solutions for the inverse problem. We further discuss the sample complexity for a desired approximation accuracy. Finally, we deal with the more realistic case where we only have access to a finite set of expert demonstrations and a generative model and provide bounds on the error made when working with samples.

In noisy and low-data regimes prevalent in real-world applications, a key challenge of machine learning lies in effectively incorporating inductive biases that promote data efficiency and robustness. Meta-learning and informed ML stand out as two approaches for incorporating prior knowledge into ML pipelines. While the former relies on a purely data-driven source of priors, the latter is guided by prior domain knowledge. In this paper, we formalise a hybrid paradigm, informed meta-learning, facilitating the incorporation of priors from unstructured knowledge representations, such as natural language; thus, unlocking complementarity in cross-task knowledge sharing of humans and machines. We establish the foundational components of informed meta-learning and present a concrete instantiation of this framework--the Informed Neural Process. Through a series of experiments, we demonstrate the potential benefits of informed meta-learning in improving data efficiency, robustness to observational noise and task distribution shifts.

Adversarial examples pose a security threat to many critical systems built on neural networks. Given that deterministic robustness often comes with significantly reduced accuracy, probabilistic robustness (i.e., the probability of having the same label with a vicinity is $\ge 1-\kappa$) has been proposed as a promising way of achieving robustness whilst maintaining accuracy. However, existing training methods for probabilistic robustness still experience non-trivial accuracy loss. It is unclear whether there is an upper bound on the accuracy when optimising towards probabilistic robustness, and whether there is a certain relationship between $\kappa$ and this bound. This work studies these problems from a Bayes error perspective. We find that while Bayes uncertainty does affect probabilistic robustness, its impact is smaller than that on deterministic robustness. This reduced Bayes uncertainty allows a higher upper bound on probabilistic robust accuracy than that on deterministic robust accuracy. Further, we prove that with optimal probabilistic robustness, each probabilistically robust input is also deterministically robust in a smaller vicinity. We also show that voting within the vicinity always improves probabilistic robust accuracy and the upper bound of probabilistic robust accuracy monotonically increases as $\kappa$ grows. Our empirical findings also align with our results.

Previous unsupervised anomaly detection (UAD) methods often struggle with significant intra-class diversity; i.e., a class in a dataset contains multiple subclasses, which we categorize as Feature-Rich Anomaly Detection Datasets (FRADs). This challenge is evident in applications such as unified setting and unmanned supermarket scenarios. To address this challenge, we developed MiniMaxAD, a lightweight autoencoder designed to efficiently compress and memorize extensive information from normal images. Our model employs a technique that enhances feature diversity, thereby increasing the effective capacity limit of the network. It also utilizes large kernel convolution to extract highly abstract patterns, which contribute to efficient and compact feature embedding. Moreover, we introduce an Adaptive Contraction Loss (ADCLoss), specifically tailored to FRADs, to address the limitations of the global cosine distance loss. In our methodology, any dataset can be unified under the framework of feature-rich anomaly detection, in a way that the benefits far outweigh the drawbacks. MiniMaxAD underwent comprehensive testing across six challenging UAD benchmarks, achieving state-of-the-art results in four and highly competitive outcomes in the remaining two. Notably, our model not only achieved state-of-the-art performance in unmanned supermarket tasks but also exhibited an inference speed 37 times faster than the previous best method, demonstrating its effectiveness in complex UAD tasks.