Making Written Theorems Explorable by Grounding Them in Formal Representations

LLM-generated explanations can make technical content more accessible, but there is a ceiling on what they can support interactively. Because LLM outputs are static text, they cannot be executed or stepped through. We argue that grounding explanations in a formalized representation enables interactive affordances beyond what static text supports. We instantiate this idea for mathematical proof comprehension with explorable theorems, a system that uses LLMs to translate a theorem and its written proof into Lean, a programming language for machine-checked proofs, and links the written proof with the Lean code. Readers can work through the proof at a step-level granularity, test custom examples or counterexamples, and trace the logical dependencies bridging each step. Each worked-out step is produced by executing the Lean proof on that example and extracting its intermediate state. A user study ($n = 16$) shows potential advantages of this approach: in a proof-reading task, participants who had access to the provided explorability features gave better, more correct, and more detailed answers to comprehension questions, demonstrating a stronger overall understanding of the underlying mathematics.

Automating Program Structure Classification

When students write programs, their program structure provides insight into their learning process. However, analyzing program structure by hand is time-consuming, and teachers need better tools for computer-assisted exploration of student solutions. As a first step towards an education-oriented program analysis toolkit, we show how supervised machine learning methods can automatically classify student programs into a predetermined set of high-level structures. We evaluate two models on classifying student solutions to the Rainfall problem: a nearest-neighbors classifier using syntax tree edit distance and a recurrent neural network. We demonstrate that these models can achieve 91% classification accuracy when trained on 108 programs. We further explore the generality, trade-offs, and failure cases of each model.

Rekall: Specifying Video Events using Compositions of Spatiotemporal Labels

Many real-world video analysis applications require the ability to identify domain-specific events in video, such as interviews and commercials in TV news broadcasts, or action sequences in film. Unfortunately, pre-trained models to detect all the events of interest in video may not exist, and training new models from scratch can be costly and labor-intensive. In this paper, we explore the utility of specifying new events in video in a more traditional manner: by writing queries that compose outputs of existing, pre-trained models. To write these queries, we have developed Rekall, a library that exposes a data model and programming model for compositional video event specification. Rekall represents video annotations from different sources (object detectors, transcripts, etc.) as spatiotemporal labels associated with continuous volumes of spacetime in a video, and provides operators for composing labels into queries that model new video events. We demonstrate the use of Rekall in analyzing video from cable TV news broadcasts, films, static-camera vehicular video streams, and commercial autonomous vehicle logs. In these efforts, domain experts were able to quickly (in a few hours to a day) author queries that enabled the accurate detection of new events (on par with, and in some cases much more accurate than, learned approaches) and to rapidly retrieve video clips for human-in-the-loop tasks such as video content curation and training data curation. Finally, in a user study, novice users of Rekall were able to author queries to retrieve new events in video given just one hour of query development time.

Scanner: Efficient Video Analysis at Scale

A growing number of visual computing applications depend on the analysis of large video collections. The challenge is that scaling applications to operate on these datasets requires efficient systems for pixel data access and parallel processing across large numbers of machines. Few programmers have the capability to operate efficiently at these scales, limiting the field's ability to explore new applications that leverage big video data. In response, we have created Scanner, a system for productive and efficient video analysis at scale. Scanner organizes video collections as tables in a data store optimized for sampling frames from compressed video, and executes pixel processing computations, expressed as dataflow graphs, on these frames. Scanner schedules video analysis applications expressed using these abstractions onto heterogeneous throughput computing hardware, such as multi-core CPUs, GPUs, and media processing ASICs, for high-throughput pixel processing. We demonstrate the productivity of Scanner by authoring a variety of video processing applications including the synthesis of stereo VR video streams from multi-camera rigs, markerless 3D human pose reconstruction from video, and data-mining big video datasets such as hundreds of feature-length films or over 70,000 hours of TV news. These applications achieve near-expert performance on a single machine and scale efficiently to hundreds of machines, enabling formerly long-running big video data analysis tasks to be carried out in minutes to hours.