Combinatorial Optimization (CO) problems are fundamentally crucial in numerous practical applications across diverse industries, characterized by entailing enormous solution space and demanding time-sensitive response. Despite significant advancements made by recent neural solvers, their limited expressiveness does not conform well to the multi-modal nature of CO landscapes. While some research has pivoted towards diffusion models, they require simulating a Markov chain with many steps to produce a sample, which is time-consuming and does not meet the efficiency requirement of real applications, especially at scale. We propose DISCO, an efficient DIffusion Solver for Combinatorial Optimization problems that excels in both solution quality and inference speed. DISCO's efficacy is two-pronged: Firstly, it achieves rapid denoising of solutions through an analytically solvable form, allowing for direct sampling from the solution space with very few reverse-time steps, thereby drastically reducing inference time. Secondly, DISCO enhances solution quality by restricting the sampling space to a more constrained, meaningful domain guided by solution residues, while still preserving the inherent multi-modality of the output probabilistic distributions. DISCO achieves state-of-the-art results on very large Traveling Salesman Problems with 10000 nodes and challenging Maximal Independent Set benchmarks, with its per-instance denoising time up to 44.8 times faster. Through further combining a divide-and-conquer strategy, DISCO can be generalized to solve arbitrary-scale problem instances off the shelf, even outperforming models trained specifically on corresponding scales.

Although the sequential tsunami scenario detection framework was validated in our previous work, several tasks remain to be resolved from a practical point of view. This study aims to evaluate the performance of the previous tsunami scenario detection framework using a diverse database consisting of complex fault rupture patterns with heterogeneous slip distributions. Specifically, we compare the effectiveness of scenario superposition to that of the previous most likely scenario detection method. Additionally, how the length of the observation time window influences the accuracy of both methods is analyzed. We utilize an existing database comprising 1771 tsunami scenarios targeting the city Westport (WA, U.S.), which includes synthetic wave height records and inundation distributions as the result of fault rupture in the Cascadia subduction zone. The heterogeneous patterns of slips used in the database increase the diversity of the scenarios and thus make it a proper database for evaluating the performance of scenario superposition. To assess the performance, we consider various observation time windows shorter than 15 minutes and divide the database into five testing and learning sets. The evaluation accuracy of the maximum offshore wave, inundation depth, and its distribution is analyzed to examine the advantages of the scenario superposition method over the previous method. We introduce the dynamic time warping (DTW) method as an additional benchmark and compare its results to that of the Bayesian scenario detection method.

Policy gradient (PG) is a reinforcement learning (RL) approach that optimizes a parameterized policy model for an expected return using gradient ascent. While PG can work well even in non-Markovian environments, it may encounter plateaus or peakiness issues. As another successful RL approach, algorithms based on Monte Carlo Tree Search (MCTS), which include AlphaZero, have obtained groundbreaking results, especially in the game-playing domain. They are also effective when applied to non-Markov decision processes. However, the standard MCTS is a method for decision-time planning, which differs from the online RL setting. In this work, we first introduce Monte Carlo Tree Learning (MCTL), an adaptation of MCTS for online RL setups. We then explore a combined policy approach of PG and MCTL to leverage their strengths. We derive conditions for asymptotic convergence with the results of a two-timescale stochastic approximation and propose an algorithm that satisfies these conditions and converges to a reasonable solution. Our numerical experiments validate the effectiveness of the proposed methods.

Neural networks surround us, in the form of large language models, speech transcription systems, molecular discovery algorithms, robotics, and much more. Stripped of anything else, neural networks are compositions of differentiable primitives, and studying them means learning how to program and how to interact with these models, a particular example of what is called differentiable programming. This primer is an introduction to this fascinating field imagined for someone, like Alice, who has just ventured into this strange differentiable wonderland. I overview the basics of optimizing a function via automatic differentiation, and a selection of the most common designs for handling sequences, graphs, texts, and audios. The focus is on a intuitive, self-contained introduction to the most important design techniques, including convolutional, attentional, and recurrent blocks, hoping to bridge the gap between theory and code (PyTorch and JAX) and leaving the reader capable of understanding some of the most advanced models out there, such as large language models (LLMs) and multimodal architectures.

Knowledge graph (KG) reasoning is a task that aims to predict unknown facts based on known factual samples. Reasoning methods can be divided into two categories: rule-based methods and KG-embedding based methods. The former possesses precise reasoning capabilities but finds it challenging to reason efficiently over large-scale knowledge graphs. While gaining the ability to reason over large-scale knowledge graphs, the latter sacrifices reasoning accuracy. This paper aims to design a reasoning framework called Neural Probabilistic Logic Learning(NPLL) that achieves accurate reasoning on knowledge graphs. Our approach introduces a scoring module that effectively enhances the expressive power of embedding networks, striking a balance between model simplicity and reasoning capabilities. We improve the interpretability of the model by incorporating a Markov Logic Network based on variational inference. We empirically evaluate our approach on several benchmark datasets, and the experimental results validate that our method substantially enhances the accuracy and quality of the reasoning results.

Beam search is a standard tree search algorithm when it comes to finding sequences of maximum likelihood, for example, in the decoding processes of large language models. However, it is myopic since it does not take the whole path from the root to a leaf into account. Moreover, it is agnostic to prior knowledge available about the process: For example, it does not consider that the objective being maximized is a likelihood and thereby has specific properties, like being bound in the unit interval. Taking a probabilistic approach, we define a prior belief over the LLMs' transition probabilities and obtain a posterior belief over the most promising paths in each iteration. These beliefs are helpful to define a non-myopic Bayesian-optimization-like acquisition function that allows for a more data-efficient exploration scheme than standard beam search. We discuss how to select the prior and demonstrate in on- and off-model experiments with recent large language models, including Llama-2-7b, that our method achieves higher efficiency than beam search: Our method achieves the same or a higher likelihood while expanding fewer nodes than beam search.

Background: Machine learning (ML) model composition is a popular technique to mitigate shortcomings of a single ML model and to design more effective ML-enabled systems. While ensemble learning, i.e., forwarding the same request to several models and fusing their predictions, has been studied extensively for accuracy, we have insufficient knowledge about how to design energy-efficient ensembles. Objective: We therefore analyzed three types of design decisions for ensemble learning regarding a potential trade-off between accuracy and energy consumption: a) ensemble size, i.e., the number of models in the ensemble, b) fusion methods (majority voting vs. a meta-model), and c) partitioning methods (whole-dataset vs. subset-based training). Methods: By combining four popular ML algorithms for classification in different ensembles, we conducted a full factorial experiment with 11 ensembles x 4 datasets x 2 fusion methods x 2 partitioning methods (176 combinations). For each combination, we measured accuracy (F1-score) and energy consumption in J (for both training and inference). Results: While a larger ensemble size significantly increased energy consumption (size 2 ensembles consumed 37.49% less energy than size 3 ensembles, which in turn consumed 26.96% less energy than the size 4 ensembles), it did not significantly increase accuracy. Furthermore, majority voting outperformed meta-model fusion both in terms of accuracy (Cohen's d of 0.38) and energy consumption (Cohen's d of 0.92). Lastly, subset-based training led to significantly lower energy consumption (Cohen's d of 0.91), while training on the whole dataset did not increase accuracy significantly. Conclusions: From a Green AI perspective, we recommend designing ensembles of small size (2 or maximum 3 models), using subset-based training, majority voting, and energy-efficient ML algorithms like decision trees, Naive Bayes, or KNN.

The environments where individuals live can present diverse navigation challenges, resulting in varying navigation abilities and strategies. Inspired by differing urban layouts and the Dual Solutions Paradigm test used for human navigators, we developed a simulated navigation environment to train deep reinforcement learning agents in a shortcut usage task. We modulated the frequency of exposure to a shortcut and navigation cue, leading to the development of artificial agents with differing abilities. We examined the encoded representations in artificial neural networks driving these agents, revealing intricate dynamics in representation learning, and correlated them with shortcut use preferences. Furthermore, we demonstrated methods to analyze representations across a population of nodes, which proved effective in finding patterns in what would otherwise be noisy single-node data. These techniques may also have broader applications in studying neural activity. From our observations in representation learning dynamics, we propose insights for human navigation learning, emphasizing the importance of navigation challenges in developing strong landmark knowledge over repeated exposures to landmarks alone.

In recent times, large language models (LLMs) have made significant strides in generating computer code, blurring the lines between code created by humans and code produced by artificial intelligence (AI). As these technologies evolve rapidly, it is crucial to explore how they influence code generation, especially given the risk of misuse in areas like higher education. This paper explores this issue by using advanced classification techniques to differentiate between code written by humans and that generated by ChatGPT, a type of LLM. We employ a new approach that combines powerful embedding features (black-box) with supervised learning algorithms - including Deep Neural Networks, Random Forests, and Extreme Gradient Boosting - to achieve this differentiation with an impressive accuracy of 98%. For the successful combinations, we also examine their model calibration, showing that some of the models are extremely well calibrated. Additionally, we present white-box features and an interpretable Bayes classifier to elucidate critical differences between the code sources, enhancing the explainability and transparency of our approach. Both approaches work well but provide at most 85-88% accuracy. We also show that untrained humans solve the same task not better than random guessing. This study is crucial in understanding and mitigating the potential risks associated with using AI in code generation, particularly in the context of higher education, software development, and competitive programming.

This work starts with the intention of using mathematics to understand the intriguing vulnerability observed by ~\citet{szegedy2013} within artificial neural networks. Along the way, we will develop some novel tools with applications far outside of just the adversarial domain. We will do this while developing a rigorous mathematical framework to examine this problem. Our goal is to build out theory which can support increasingly sophisticated conjecture about adversarial attacks with a particular focus on the so called ``Dimpled Manifold Hypothesis'' by ~\citet{shamir2021dimpled}. Chapter one will cover the history and architecture of neural network architectures. Chapter two is focused on the background of adversarial vulnerability. Starting from the seminal paper by ~\citet{szegedy2013} we will develop the theory of adversarial perturbation and attack. Chapter three will build a theory of persistence that is related to Ricci Curvature, which can be used to measure properties of decision boundaries. We will use this foundation to make a conjecture relating adversarial attacks. Chapters four and five represent a sudden and wonderful digression that examines an intriguing related body of theory for spatial analysis of neural networks as approximations of kernel machines and becomes a novel theory for representing neural networks with bilinear maps. These heavily mathematical chapters will set up a framework and begin exploring applications of what may become a very important theoretical foundation for analyzing neural network learning with spatial and geometric information. We will conclude by setting up our new methods to address the conjecture from chapter 3 in continuing research.