The application of formulas is a fundamental ability of humans when addressing numerical reasoning problems. However, existing numerical reasoning datasets seldom explicitly indicate the formulas employed during the reasoning steps. To bridge this gap, we construct a dataset for formula-based numerical reasoning called FormulaReasoning, which consists of 5,420 reasoning-based questions. We employ it to conduct evaluations of LLMs with size ranging from 7B to over 100B parameters utilizing zero-shot and few-shot chain-of-thought methods, and we further explore using retrieval-augmented LLMs provided with an external formula database associated with our dataset. We also experiment with supervised methods where we divide the reasoning process into formula generation, parameter extraction, and numerical calculation, and perform data augmentation. Our empirical findings underscore the significant potential for improvement in existing models when applied to our complex, formula-driven FormulaReasoning.

Personalised discount codes provide a powerful mechanism for managing customer relationships and operational spend in e-commerce. Bandits are well suited for this product area, given the partial information nature of the problem, as well as the need for adaptation to the changing business environment. Here, we introduce DISCO, an end-to-end contextual bandit framework for personalised discount code allocation at ASOS. DISCO adapts the traditional Thompson Sampling algorithm by integrating it within an integer program, thereby allowing for operational cost control. Because bandit learning is often worse with high dimensional actions, we focused on building low dimensional action and context representations that were nonetheless capable of good accuracy. Additionally, we sought to build a model that preserved the relationship between price and sales, in which customers increasing their purchasing in response to lower prices ("negative price elasticity"). These aims were achieved by using radial basis functions to represent the continuous (i.e. infinite armed) action space, in combination with context embeddings extracted from a neural network. These feature representations were used within a Thompson Sampling framework to facilitate exploration, and further integrated with an integer program to allocate discount codes across ASOS's customer base. These modelling decisions result in a reward model that (a) enables pooled learning across similar actions, (b) is highly accurate, including in extrapolation, and (c) preserves the expected negative price elasticity. Through offline analysis, we show that DISCO is able to effectively enact exploration and improves its performance over time, despite the global constraint. Finally, we subjected DISCO to a rigorous online A/B test, and find that it achieves a significant improvement of >1% in average basket value, relative to the legacy systems.

Training a deep neural network often involves stochastic optimization, meaning each run will produce a different model. The seed used to initialize random elements of the optimization procedure heavily influences the quality of a trained model, which may be obscure from many commonly reported summary statistics, like accuracy. However, random seed is often not included in hyper-parameter optimization, perhaps because the relationship between seed and model quality is hard to describe. This work attempts to describe the relationship between deep net models trained with different random seeds and the behavior of the expected model. We adopt robust hypothesis testing to propose a novel summary statistic for network similarity, referred to as the $\alpha$-trimming level. We use the $\alpha$-trimming level to show that the empirical cumulative distribution function of an ensemble model created from a collection of trained models with different random seeds approximates the average of these functions as the number of models in the collection grows large. This insight provides guidance for how many random seeds should be sampled to ensure that an ensemble of these trained models is a reliable representative. We also show that the $\alpha$-trimming level is more expressive than different performance metrics like validation accuracy, churn, or expected calibration error when taken alone and may help with random seed selection in a more principled fashion. We demonstrate the value of the proposed statistic in real experiments and illustrate the advantage of fine-tuning over random seed with an experiment in transfer learning.

On the morning of April 3, Taiwan was hit by a 7.4 magnitude earthquake. Seconds later, hundreds of battery-swap stations in Taiwan sensed something else: the power frequency of the electric grid took a sudden drop, a signal that some power plants had been disconnected in the disaster. The grid was now struggling to meet energy demand. These stations, built by the Taiwanese company Gogoro for electric-powered two-wheeled vehicles like scooters, mopeds, and bikes, reacted immediately. According to numbers provided by the company, 590 Gogoro battery-swap locations (some of which have more than one swap station) stopped drawing electricity from the grid, lowering local demand by a total six megawatts--enough to power thousands of homes. It took 12 minutes for the grid to recover, and the battery-swap stations then resumed normal operation.

Recent years have seen immense progress in 3D computer vision and computer graphics, with emerging tools that can virtualize real-world 3D environments for numerous Mixed Reality (XR) applications. However, alongside immersive visual experiences, immersive auditory experiences are equally vital to our holistic perception of an environment. In this paper, we aim to reconstruct the spatial acoustic characteristics of an arbitrary environment given only a sparse set of (roughly 12) room impulse response (RIR) recordings and a planar reconstruction of the scene, a setup that is easily achievable by ordinary users. To this end, we introduce DiffRIR, a differentiable RIR rendering framework with interpretable parametric models of salient acoustic features of the scene, including sound source directivity and surface reflectivity. This allows us to synthesize novel auditory experiences through the space with any source audio. To evaluate our method, we collect a dataset of RIR recordings and music in four diverse, real environments. We show that our model outperforms state-ofthe-art baselines on rendering monaural and binaural RIRs and music at unseen locations, and learns physically interpretable parameters characterizing acoustic properties of the sound source and surfaces in the scene.

Monte Carlo methods, Variational Inference, and their combinations play a pivotal role in sampling from intractable probability distributions. However, current studies lack a unified evaluation framework, relying on disparate performance measures and limited method comparisons across diverse tasks, complicating the assessment of progress and hindering the decision-making of practitioners. In response to these challenges, our work introduces a benchmark that evaluates sampling methods using a standardized task suite and a broad range of performance criteria. Moreover, we study existing metrics for quantifying mode collapse and introduce novel metrics for this purpose. Our findings provide insights into strengths and weaknesses of existing sampling methods, serving as a valuable reference for future developments. The code is publicly available here.

In this paper, we study cascading failures in power grids through the lens of information diffusion models. Similar to the spread of rumors or influence in an online social network, it has been observed that failures (outages) in a power grid can spread contagiously, driven by viral spread mechanisms. We employ a stochastic diffusion model that is Markovian (memoryless) and local (the activation of one node, i.e., transmission line, can only be caused by its neighbors). Our model integrates viral diffusion principles with physics-based concepts, by correlating the diffusion weights (contagion probabilities between transmission lines) with the hyperparametric Information Cascades (IC) model. We show that this diffusion model can be learned from traces of cascading failures, enabling accurate modeling and prediction of failure propagation. This approach facilitates actionable information through well-understood and efficient graph analysis methods and graph diffusion simulations. Furthermore, by leveraging the hyperparametric model, we can predict diffusion and mitigate the risks of cascading failures even in unseen grid configurations, whereas existing methods falter due to a lack of training data. Extensive experiments based on a benchmark power grid and simulations therein show that our approach effectively captures the failure diffusion phenomena and guides decisions to strengthen the grid, reducing the risk of large-scale cascading failures. Additionally, we characterize our model's sample complexity, improving upon the existing bound.

Electromagnetic (EM) simulation plays a crucial role in analyzing and designing devices with sub-wavelength scale structures such as solar cells, semiconductor devices, image sensors, future displays and integrated photonic devices. Specifically, optics problems such as estimating semiconductor device structures and designing nanophotonic devices provide intriguing research topics with far-reaching real world impact. Traditional algorithms for such tasks require iteratively refining parameters through simulations, which often yield sub-optimal results due to the high computational cost of both the algorithms and EM simulations. Machine learning (ML) emerged as a promising candidate to mitigate these challenges, and optics research community has increasingly adopted ML algorithms to obtain results surpassing classical methods across various tasks. To foster a synergistic collaboration between the optics and ML communities, it is essential to have an EM simulation software that is user-friendly for both research communities. To this end, we present Meent, an EM simulation software that employs rigorous coupled-wave analysis (RCWA). Developed in Python and equipped with automatic differentiation (AD) capabilities, Meent serves as a versatile platform for integrating ML into optics research and vice versa. To demonstrate its utility as a research platform, we present three applications of Meent: 1) generating a dataset for training neural operator, 2) serving as an environment for the reinforcement learning of nanophotonic device optimization, and 3) providing a solution for inverse problems with gradient-based optimizers. These applications highlight Meent's potential to advance both EM simulation and ML methodologies. The code is available at https://github.com/kc-ml2/meent with the MIT license to promote the cross-polinations of ideas among academic researchers and industry practitioners.

Sustainable artificial intelligence focuses on data, hardware, and algorithms to make machine learning models more environmentally responsible. In particular, machine learning models for speech representations are computationally expensive, generating environmental concerns because of their high energy consumption. Thus, we propose a sustainable self-supervised model to learn speech representation, combining optimizations in neural layers and training to reduce computing costs. The proposed model improves over a resource-efficient baseline, reducing both memory usage and computing cost estimations. It pretrains using a single GPU in less than a day. On top of that, it improves the error rate performance of the baseline in downstream task evaluations. When comparing it to large speech representation approaches, there is an order of magnitude reduction in memory usage, while computing cost reductions represent almost three orders of magnitude improvement.

In an era marked by the rapid scaling of foundation models, autonomous driving technologies are approaching a transformative threshold where end-to-end autonomous driving (E2E-AD) emerges due to its potential of scaling up in the data-driven manner. However, existing E2E-AD methods are mostly evaluated under the open-loop log-replay manner with L2 errors and collision rate as metrics (e.g., in nuScenes), which could not fully reflect the driving performance of algorithms as recently acknowledged in the community. For those E2E-AD methods evaluated under the closed-loop protocol, they are tested in fixed routes (e.g., Town05Long and Longest6 in CARLA) with the driving score as metrics, which is known for high variance due to the unsmoothed metric function and large randomness in the long route. Besides, these methods usually collect their own data for training, which makes algorithm-level fair comparison infeasible. To fulfill the paramount need of comprehensive, realistic, and fair testing environments for Full Self-Driving (FSD), we present Bench2Drive, the first benchmark for evaluating E2E-AD systems' multiple abilities in a closed-loop manner. Bench2Drive's official training data consists of 2 million fully annotated frames, collected from 10000 short clips uniformly distributed under 44 interactive scenarios (cut-in, overtaking, detour, etc), 23 weathers (sunny, foggy, rainy, etc), and 12 towns (urban, village, university, etc) in CARLA v2. Its evaluation protocol requires E2E-AD models to pass 44 interactive scenarios under different locations and weathers which sums up to 220 routes and thus provides a comprehensive and disentangled assessment about their driving capability under different situations. We implement state-of-the-art E2E-AD models and evaluate them in Bench2Drive, providing insights regarding current status and future directions.