My Son's Math Homework Is Essentially Just Pokémon Education games are taking over American classrooms. One afternoon earlier this year, my 11-year-old son was sitting at his laptop and working quietly on his math homework. At least, that's what he was supposed to be doing. When I glanced at his screen, equations were nowhere to be seen. He was controlling a monster in the midst of battle, casting magic spells to outduel an opposing player.

Armed with some Python and a white-hot sense of injustice, one medical student spent six months trying to figure out whether an algorithm trashed his job application. It was mid-October, peak leaf-peeping season in Hanover, New Hampshire, and Chad Markey was on a rare break between clinical rotations during his last year of medical school. He should have been inhaling Green Mountain air and gossiping with his Dartmouth classmates about life after graduation. In a few months, they'd all be going their separate ways to start residency training at hospitals around the country. Instead, Markey was alone in his apartment, deep down a rabbit hole, preparing to go to war. He'd wake each morning, eat breakfast, open his laptop at the kitchen table or settle into the tan armchair with the good back support, and start coding . Some days, he wouldn't notice the sun had gone down until one of his roommates came home and asked why the lights weren't on. For days, Markey had been scrolling through a Discord group about medical residency, a font of crowdsourced knowledge where students report back to their peers on every stage of the application and selection process. He'd watched as other students, lots of them, posted about the interview invitations they'd received.

Quantum neural networks (QNNs) have emerged as a leading strategy to establish applications in machine learning, chemistry, and optimization. While the applications of QNN have been widely investigated, its theoretical foundation remains less understood. In this paper, we formulate a theoretical framework for the expressive ability of data re-uploading quantum neural networks that consist of interleaved encoding circuit blocks and trainable circuit blocks. First, we prove that single-qubit quantum neural networks can approximate any univariate function by mapping the model to a partial Fourier series. We in particular establish the exact correlations between the parameters of the trainable gates and the Fourier coefficients, resolving an open problem on the universal approximation property of QNN. Second, we discuss the limitations of single-qubit native QNNs on approximating multivariate functions by analyzing the frequency spectrum and the flexibility of Fourier coefficients. We further demonstrate the expressivity and limitations of single-qubit native QNNs via numerical experiments. We believe these results would improve our understanding of QNNs and provide a helpful guideline for designing powerful QNNs for machine learning tasks.

We consider the problem of teaching via demonstrations in sequential decisionmaking settings. In particular, we study how to design a personalized curriculum over demonstrations to speed up the learner's convergence. We provide a unified curriculum strategy for two popular learner models: Maximum Causal Entropy Inverse Reinforcement Learning (MaxEnt-IRL) and Cross-Entropy Behavioral Cloning (CrossEnt-BC). Our unified strategy induces a ranking over demonstrations based on a notion of difficulty scores computed w.r.t. the teacher's optimal policy and the learner's current policy. Compared to the state of the art, our strategy doesn't require access to the learner's internal dynamics and still enjoys similar convergence guarantees under mild technical conditions. Furthermore, we adapt our curriculum strategy to the setting where no teacher agent is present using task-specific difficulty scores. Experiments on a synthetic car driving environment and navigation-based environments demonstrate the effectiveness of our curriculum strategy.

We study social learning dynamics motivated by reviews on online platforms. The agents collectively follow a simple multi-armed bandit protocol, but each agent acts myopically, without regards to exploration. We allow a wide range of myopic behaviors that are consistent with (parameterized) confidence intervals for the arms' expected rewards. We derive stark exploration failures for any such behavior, and provide matching positive results. As a special case, we obtain the first general results on failure of the greedy algorithm in bandits, thus providing a theoretical foundation for why bandit algorithms should explore.1

Theorem proving in natural mathematical language - the mixture of symbolic and natural language used by humans - plays a central role in mathematical advances and education, and tests aspects of reasoning that are core to intelligence. Yet it has remained underexplored with modern generative models. We study largescale language models on two new generation tasks: suggesting the next step in a mathematical proof, and full proof generation. We develop NATURALPROVER,a language model that generates proofs by conditioning on background references (e.g.

When answering a question, humans utilize the information available across different modalities to synthesize a consistent and complete chain of thought (CoT). This process is normally a black box in the case of deep learning models like large-scale language models. Recently, science question benchmarks have been used to diagnose the multi-hop reasoning ability and interpretability of an AI system. However, existing datasets fail to provide annotations for the answers, or are restricted to the textual-only modality, small scales, and limited domain diversity. To this end, we present Science Question Answering (SCIENCEQA), a new benchmark that consists of 21k multimodal multiple choice questions with diverse science topics and annotations of their answers with corresponding lectures and explanations. We further design language models to learn to generate lectures and explanations as the chain of thought (CoT) to mimic the multi-hop reasoning process when answering SCIENCEQA questions. SCIENCEQA demonstrates the utility of CoT in language models, as CoT improves the question answering performance by 1.20% in fewshot GPT-3 and 3.99% in fine-tuned UnifiedQA. We also explore the upper bound for models to leverage explanations by feeding those in the input; we observe that it improves the few-shot performance of GPT-3 by 18.96%. Our analysis further shows that language models, similar to humans, benefit from explanations to learn from fewer data and achieve the same performance with just 40% of the data.1

We present a novel methodology aimed at optimizing the application of frozen large language models (LLMs) for resource-intensive vision-language (VL) pre-training. The current paradigm uses visual features as prompts to guide language models, with a focus on determining the most relevant visual features for corresponding text. Our approach diverges by concentrating on the language component, specifically identifying the optimal prompts to align with visual features. We introduce the Prompt-Transformer (P-Former), a model that predicts these ideal prompts, which is trained exclusively on linguistic data, bypassing the need for image-text pairings.