Discovering governing equations from data is important to many scientific and engineering applications. Despite promising successes, existing methods are still challenged by data sparsity as well as noise issues, both of which are ubiquitous in practice. Moreover, state-of-the-art methods lack uncertainty quantification and/or are costly in training. To overcome these limitations, we propose a novel equation discovery method based on Kernel learning and BAyesian Spike-and-Slab priors (KBASS). We use kernel regression to estimate the target function, which is flexible, expressive, and more robust to data sparsity and noises. We combine it with a Bayesian spike-and-slab prior -- an ideal Bayesian sparse distribution -- for effective operator selection and uncertainty quantification. We develop an expectation propagation expectation-maximization (EP-EM) algorithm for efficient posterior inference and function estimation. To overcome the computational challenge of kernel regression, we place the function values on a mesh and induce a Kronecker product construction, and we use tensor algebra methods to enable efficient computation and optimization. We show the significant advantages of KBASS on a list of benchmark ODE and PDE discovery tasks.

Over the past two decades, the availability of high-performance computing and the development of neural networks of larger capacity have conspired to fuel a revolution in the way we think at the optimisation of complex systems. When the dimensionality of the space of relevant design parameters exceeds a few units, and brute-force scans cease be a viable option for its exploration. We nowadays, have the option of letting automated systems find their way to configurations that correspond to advantageous extrema of carefully specified objective functions. The engine under the hood of these optimisation searches is automatic differentiation, which allows computer programs to keep track of the gradient of the objective function, through the chain rule of differential calculus, as computer code performs arbitrarily complex successions of operations to model the behaviour of the system. Crucial to a successful optimisation of the system is the inclusion in the model of all relevant effects that have an impact on the precision of the inference that the data generated by the system may produce. An incomplete description of the inference itself, or a mock up of the reconstruction techniques performing the dimensionality reduction step which translates raw data into high-level features informing the objective function, are likely to prevent the identification of designs that maximise the true objective, as they introduce a misalignment.

Wordle is a popular, online word game offered by the New York Times (nytimes.com). Currently there are some 2 million players of the English version worldwide. Players have 6 attempts to guess the daily word (target word) and after each attempt, the player receives color-coded information about the correctness and position of each letter in the guess. After either a successful completion of the puzzle or the final unsuccessful attempt, software can assess the player's luck and skill using Information Theory and can display data for the first, second, ..., sixth guesses of a random sample of all players. Recently, I discovered that the latter data is presented in a format that can easily be copied and pasted into a spreadsheet. I compiled data on Wordle players' first guesses from May 2023 - August 2023 and inferred some interesting information about Wordle players. A) Every day, about 0.2-0.5% of players solve the puzzle in one attempt. Because the odds of guessing the one of 2,315 possible target words at random is 0.043%, this implies that 4,000 - 10,000 players cheat by obtaining the target word outside of playing the game! B) At least 1/3 of the players have a favorite starting word, or cycle through several. And even though players should be aware that target words are never repeated, most players appear to remain loyal to their starting word even after its appearance as a target word. C) On August 15, 2023, about 30,000 players abruptly changed their starting word, presumably based on a crossword puzzle clue! Wordle players can be influenced! This study goes beyond social media postings, surveys, and Google Trends to provide solid, quantitative evidence about cheating in Wordle.

Chain-of-thought (CoT) prompting, which offers step-by-step problem-solving rationales, has impressively unlocked the reasoning potential of large language models (LLMs). Yet, the standard CoT is less effective in problems demanding multiple reasoning steps. This limitation arises from the complex reasoning process in multi-step problems: later stages often depend on the results of several steps earlier, not just the results of the immediately preceding step. Such complexities suggest the reasoning process is naturally represented as a graph. The almost linear and straightforward structure of CoT prompting, however, struggles to capture this complex reasoning graph. To address this challenge, we propose Residual Connection Prompting (RESPROMPT), a new prompting strategy that advances multi-step reasoning in LLMs. Our key idea is to reconstruct the reasoning graph within prompts. We achieve this by integrating necessary connections-links present in the reasoning graph but missing in the linear CoT flow-into the prompts. Termed "residual connections", these links are pivotal in morphing the linear CoT structure into a graph representation, effectively capturing the complex reasoning graphs inherent in multi-step problems. We evaluate RESPROMPT on six benchmarks across three diverse domains: math, sequential, and commonsense reasoning. For the open-sourced LLaMA family of models, RESPROMPT yields a significant average reasoning accuracy improvement of 12.5% on LLaMA-65B and 6.8% on LLaMA2-70B. Breakdown analysis further highlights RESPROMPT particularly excels in complex multi-step reasoning: for questions demanding at least five reasoning steps, RESPROMPT outperforms the best CoT based benchmarks by a remarkable average improvement of 21.1% on LLaMA-65B and 14.3% on LLaMA2-70B. Through extensive ablation studies and analyses, we pinpoint how to most effectively build residual connections.

Developing machine intelligence abilities in robots and autonomous systems is an expensive and time consuming process. Existing solutions are tailored to specific applications and are harder to generalize. Furthermore, scarcity of training data adds a layer of complexity in deploying deep machine learning models. We present a new platform for General Robot Intelligence Development (GRID) to address both of these issues. The platform enables robots to learn, compose and adapt skills to their physical capabilities, environmental constraints and goals. The platform addresses AI problems in robotics via foundation models that know the physical world. GRID is designed from the ground up to be extensible to accommodate new types of robots, vehicles, hardware platforms and software protocols. In addition, the modular design enables various deep ML components and existing foundation models to be easily usable in a wider variety of robot-centric problems. We demonstrate the platform in various aerial robotics scenarios and demonstrate how the platform dramatically accelerates development of machine intelligent robots.

Despite recent theoretical progress on the non-convex optimization of two-layer neural networks, it is still an open question whether gradient descent on neural networks without unnatural modifications can achieve better sample complexity than kernel methods. This paper provides a clean mean-field analysis of projected gradient flow on polynomial-width two-layer neural networks. Different from prior works, our analysis does not require unnatural modifications of the optimization algorithm. We prove that with sample size $n = O(d^{3.1})$ where $d$ is the dimension of the inputs, the network trained with projected gradient flow converges in $\text{poly}(d)$ time to a non-trivial error that is not achievable by kernel methods using $n \ll d^4$ samples, hence demonstrating a clear separation between unmodified gradient descent and NTK. As a corollary, we show that projected gradient descent with a positive learning rate and a polynomial number of iterations converges to low error with the same sample complexity.

A recent focus of large language model (LLM) development, as exemplified by generative search engines, is to incorporate external references to generate and support its claims. However, evaluating the attribution, i.e., verifying whether the generated statement is fully supported by the cited reference, remains an open problem. Although human evaluation is common practice, it is costly and time-consuming. In this paper, we investigate the automatic evaluation of attribution given by LLMs. We begin by defining different types of attribution errors, and then explore two approaches for automatic evaluation: prompting LLMs and fine-tuning smaller LMs. The fine-tuning data is repurposed from related tasks such as question answering, fact-checking, natural language inference, and summarization. We manually curate a set of test examples covering 12 domains from a generative search engine, New Bing. Our results on this curated test set and simulated examples from existing benchmarks highlight both promising signals and challenges. We hope our problem formulation, testbeds, and findings will help lay the foundation for future studies on this important problem.

Despite the fact that large-scale Language Models (LLM) have achieved SOTA performances on a variety of NLP tasks, its performance on NER is still significantly below supervised baselines. This is due to the gap between the two tasks the NER and LLMs: the former is a sequence labeling task in nature while the latter is a text-generation model. In this paper, we propose GPT-NER to resolve this issue. GPT-NER bridges the gap by transforming the sequence labeling task to a generation task that can be easily adapted by LLMs e.g., the task of finding location entities in the input text "Columbus is a city" is transformed to generate the text sequence "@@Columbus## is a city", where special tokens @@## marks the entity to extract. To efficiently address the "hallucination" issue of LLMs, where LLMs have a strong inclination to over-confidently label NULL inputs as entities, we propose a self-verification strategy by prompting LLMs to ask itself whether the extracted entities belong to a labeled entity tag. We conduct experiments on five widely adopted NER datasets, and GPT-NER achieves comparable performances to fully supervised baselines, which is the first time as far as we are concerned. More importantly, we find that GPT-NER exhibits a greater ability in the low-resource and few-shot setups, when the amount of training data is extremely scarce, GPT-NER performs significantly better than supervised models. This demonstrates the capabilities of GPT-NER in real-world NER applications where the number of labeled examples is limited.

Dynamic sparsity, where the sparsity patterns are unknown until runtime, poses a significant challenge to deep learning. The state-of-the-art sparsity-aware deep learning solutions are restricted to pre-defined, static sparsity patterns due to significant overheads associated with preprocessing. Efficient execution of dynamic sparse computation often faces the misalignment between the GPU-friendly tile configuration for efficient execution and the sparsity-aware tile shape that minimizes coverage wastes (non-zero values in tensor). In this paper, we propose PIT, a deep-learning compiler for dynamic sparsity. PIT proposes a novel tiling mechanism that leverages Permutation Invariant Transformation (PIT), a mathematically proven property, to transform multiple sparsely located micro-tiles into a GPU-efficient dense tile without changing the computation results, thus achieving both high GPU utilization and low coverage waste. Given a model, PIT first finds feasible PIT rules for all its operators and generates efficient GPU kernels accordingly. At runtime, with the novel SRead and SWrite primitives, PIT rules can be executed extremely fast to support dynamic sparsity in an online manner. Extensive evaluation on diverse models shows that PIT can accelerate dynamic sparsity computation by up to 5.9x (average 2.43x) over state-of-the-art compilers.

Recent success of deep learning is largely attributed to the sheer amount of data used for training deep neural networks.Despite the unprecedented success, the massive data, unfortunately, significantly increases the burden on storage and transmission and further gives rise to a cumbersome model training process. Besides, relying on the raw data for training \emph{per se} yields concerns about privacy and copyright. To alleviate these shortcomings, dataset distillation~(DD), also known as dataset condensation (DC), was introduced and has recently attracted much research attention in the community. Given an original dataset, DD aims to derive a much smaller dataset containing synthetic samples, based on which the trained models yield performance comparable with those trained on the original dataset. In this paper, we give a comprehensive review and summary of recent advances in DD and its application. We first introduce the task formally and propose an overall algorithmic framework followed by all existing DD methods. Next, we provide a systematic taxonomy of current methodologies in this area, and discuss their theoretical interconnections. We also present current challenges in DD through extensive experiments and envision possible directions for future works.