Learning to Prove Theorems via Interacting with Proof Assistants

Humans prove theorems by relying on substantial high-level reasoning and problem-specific insights. Proof assistants offer a formalism that resembles human mathematical reasoning, representing theorems in higher-order logic and proofs as high-level tactics. However, human experts have to construct proofs manually by entering tactics into the proof assistant. In this paper, we study the problem of using machine learning to automate the interaction with proof assistants. We construct CoqGym, a large-scale dataset and learning environment containing 71K human-written proofs from 123 projects developed with the Coq proof assistant. We develop ASTactic, a deep learning-based model that generates tactics as programs in the form of abstract syntax trees (ASTs). Experiments show that ASTactic trained on CoqGym can generate effective tactics and can be used to prove new theorems not previously provable by automated methods. Code is available at https://github.com/princeton-vl/CoqGym.Comment: Accepted to ICML 201

SpatialSense: An Adversarially Crowdsourced Benchmark for Spatial Relation Recognition

Understanding the spatial relations between objects in images is a surprisingly challenging task. A chair may be "behind" a person even if it appears to the left of the person in the image (depending on which way the person is facing). Two students that appear close to each other in the image may not in fact be "next to" each other if there is a third student between them. We introduce SpatialSense, a dataset specializing in spatial relation recognition which captures a broad spectrum of such challenges, allowing for proper benchmarking of computer vision techniques. SpatialSense is constructed through adversarial crowdsourcing, in which human annotators are tasked with finding spatial relations that are difficult to predict using simple cues such as 2D spatial configuration or language priors. Adversarial crowdsourcing significantly reduces dataset bias and samples more interesting relations in the long tail compared to existing datasets. On SpatialSense, state-of-the-art recognition models perform comparably to simple baselines, suggesting that they rely on straightforward cues instead of fully reasoning about this complex task. The SpatialSense benchmark provides a path forward to advancing the spatial reasoning capabilities of computer vision systems. The dataset and code are available at https://github.com/princeton-vl/SpatialSense.Comment: Accepted to ICCV 201

Rel3D: A Minimally Contrastive Benchmark for Grounding Spatial Relations in 3D

Understanding spatial relations (e.g., "laptop on table") in visual input is important for both humans and robots. Existing datasets are insufficient as they lack large-scale, high-quality 3D ground truth information, which is critical for learning spatial relations. In this paper, we fill this gap by constructing Rel3D: the first large-scale, human-annotated dataset for grounding spatial relations in 3D. Rel3D enables quantifying the effectiveness of 3D information in predicting spatial relations on large-scale human data. Moreover, we propose minimally contrastive data collection -- a novel crowdsourcing method for reducing dataset bias. The 3D scenes in our dataset come in minimally contrastive pairs: two scenes in a pair are almost identical, but a spatial relation holds in one and fails in the other. We empirically validate that minimally contrastive examples can diagnose issues with current relation detection models as well as lead to sample-efficient training. Code and data are available at https://github.com/princeton-vl/Rel3D.Comment: Accepted to NeurIPS 202

A Study of Face Obfuscation in ImageNet

Face obfuscation (blurring, mosaicing, etc.) has been shown to be effective for privacy protection; nevertheless, object recognition research typically assumes access to complete, unobfuscated images. In this paper, we explore the effects of face obfuscation on the popular ImageNet challenge visual recognition benchmark. Most categories in the ImageNet challenge are not people categories; however, many incidental people appear in the images, and their privacy is a concern. We first annotate faces in the dataset. Then we demonstrate that face obfuscation has minimal impact on the accuracy of recognition models. Concretely, we benchmark multiple deep neural networks on obfuscated images and observe that the overall recognition accuracy drops only slightly (<= 1.0%). Further, we experiment with transfer learning to 4 downstream tasks (object recognition, scene recognition, face attribute classification, and object detection) and show that features learned on obfuscated images are equally transferable. Our work demonstrates the feasibility of privacy-aware visual recognition, improves the highly-used ImageNet challenge benchmark, and suggests an important path for future visual datasets. Data and code are available at https://github.com/princetonvisualai/imagenet-face-obfuscation.Comment: Accepted to ICML 202

Strongly Incremental Constituency Parsing with Graph Neural Networks

Parsing sentences into syntax trees can benefit downstream applications in NLP. Transition-based parsers build trees by executing actions in a state transition system. They are computationally efficient, and can leverage machine learning to predict actions based on partial trees. However, existing transition-based parsers are predominantly based on the shift-reduce transition system, which does not align with how humans are known to parse sentences. Psycholinguistic research suggests that human parsing is strongly incremental—humans grow a single parse tree by adding exactly one token at each step. In this paper, we propose a novel transition system called attach-juxtapose. It is strongly incremental; it represents a partial sentence using a single tree; each action adds exactly one token into the partial tree. Based on our transition system, we develop a strongly incremental parser. At each step, it encodes the partial tree using a graph neural network and predicts an action. We evaluate our parser on Penn Treebank (PTB) and Chinese Treebank (CTB). On PTB, it outperforms existing parsers trained with only constituency trees; and it performs on par with state-of-the-art parsers that use dependency trees as additional training data. On CTB, our parser establishes a new state of the art. Code is available at https://github.com/princeton-vl/attach-juxtapose-parser

Generating Natural Language Proofs with Verifier-Guided Search

Deductive reasoning (drawing conclusions from assumptions) is a challenging problem in NLP. In this work, we focus on proof generation: given a hypothesis and a set of supporting facts in natural language, the model generates a proof tree indicating how to deduce the hypothesis from supporting facts. Instead of generating the entire proof in one shot, prior work has demonstrated the promise of stepwise generation but achieved limited success on real-world data. Existing stepwise methods struggle to generate proof steps that are both valid and relevant. In this paper, we present a novel stepwise method NLProofS (Natural Language Proof Search), which learns to generate relevant steps conditioning on the hypothesis. At the core of our approach, we train an independent verifier to check the validity of proof steps. Instead of generating steps greedily, we search for proofs maximizing a global proof score judged by the verifier. NLProofS achieves state-of-the-art performance on EntailmentBank and RuleTaker. For example, it improves the percentage of correctly predicted proofs from 20.9% to 33.3% in the distractor setting of EntailmentBank. This is the first time stepwise methods have led to better generation of challenging human-authored proofs

Systematical Characterization of the <i>AT-Hook</i> Gene Family in <i>Juglans regia</i> L. and the Functional Analysis of the <i>JrAHL2</i> in Flower Induction and Hypocotyl Elongation

AT-hook motif nuclear localization (AHL) proteins play essential roles in various plant biological processes. Yet, a comprehensive understanding of AHL transcription factors in walnut (Juglans regia L.) is missing. In this study, 37 AHL gene family members were first identified in the walnut genome. Based on the evolutionary analysis, JrAHL genes were grouped into two clades, and their expansion may occur due to segmental duplication. The stress-responsive nature and driving of developmental activities of JrAHL genes were revealed by cis-acting elements and transcriptomic data, respectively. Tissue-specific expression analysis showed that JrAHLs had a profound transcription in flower and shoot tip, JrAHL2 in particular. Subcellular localization showed that JrAHL2 is anchored to the nucleus. Overexpression of JrAHL2 in Arabidopsis adversely affected hypocotyl elongation and delayed flowering. Our study, for the first time, presented a detailed analysis of JrAHL genes in walnut and provided theoretical knowledge for future genetic breeding programs