Nova$^+$: Generative Language Models for Binaries

Generative large language models (LLMs) pre-trained on code have shown impressive effectiveness in code generation, program repair, and document analysis. However, existing generative LLMs focus on source code and are not specialized for binaries. There are three main challenges for LLMs to model and learn binary code: hex-decimal values, complex global dependencies, and compiler optimization levels. To bring the benefit of LLMs to the binary domain, we develop Nova and Nova$^+$, which are LLMs pre-trained on binary corpora. Nova is pre-trained with the standard language modeling task, showing significantly better capability on five benchmarks for three downstream tasks: binary code similarity detection (BCSD), binary code translation (BCT), and binary code recovery (BCR), over GPT-3.5 and other existing techniques. We build Nova$^+$ to further boost Nova using two new pre-training tasks, i.e., optimization generation and optimization level prediction, which are designed to learn binary optimization and align equivalent binaries. Nova$^+$ shows overall the best performance for all three downstream tasks on five benchmarks, demonstrating the contributions of the new pre-training tasks.

Model-agnostic Measure of Generalization Difficulty

The measure of a machine learning algorithm is the difficulty of the tasks it can perform, and sufficiently difficult tasks are critical drivers of strong machine learning models. However, quantifying the generalization difficulty of machine learning benchmarks has remained challenging. We propose what is to our knowledge the first model-agnostic measure of the inherent generalization difficulty of tasks. Our inductive bias complexity measure quantifies the total information required to generalize well on a task minus the information provided by the data. It does so by measuring the fractional volume occupied by hypotheses that generalize on a task given that they fit the training data. It scales exponentially with the intrinsic dimensionality of the space over which the model must generalize but only polynomially in resolution per dimension, showing that tasks which require generalizing over many dimensions are drastically more difficult than tasks involving more detail in fewer dimensions. Our measure can be applied to compute and compare supervised learning, reinforcement learning and meta-learning generalization difficulties against each other. We show that applied empirically, it formally quantifies intuitively expected trends, e.g. that in terms of required inductive bias, MNIST < CIFAR10 < Imagenet and fully observable Markov decision processes (MDPs) < partially observable MDPs. Further, we show that classification of complex images $<$ few-shot meta-learning with simple images. Our measure provides a quantitative metric to guide the construction of more complex tasks requiring greater inductive bias, and thereby encourages the development of more sophisticated architectures and learning algorithms with more powerful generalization capabilities.

Deep Learning Predicts Prevalent and Incident Parkinson's Disease From UK Biobank Fundus Imaging

Parkinson's disease is the world's fastest growing neurological disorder. Research to elucidate the mechanisms of Parkinson's disease and automate diagnostics would greatly improve the treatment of patients with Parkinson's disease. Current diagnostic methods are expensive with limited availability. Considering the long progression time of Parkinson's disease, a desirable screening should be diagnostically accurate even before the onset of symptoms to allow medical intervention. We promote attention for retinal fundus imaging, often termed a window to the brain, as a diagnostic screening modality for Parkinson's disease. We conduct a systematic evaluation of conventional machine learning and deep learning techniques to classify Parkinson's disease from UK Biobank fundus imaging. Our results suggest Parkinson's disease individuals can be differentiated from age and gender matched healthy subjects with 71% accuracy. This accuracy is maintained when predicting either prevalent or incident Parkinson's disease. Explainability and trustworthiness is enhanced by visual attribution maps of localized biomarkers and quantified metrics of model robustness to data perturbations.

Open Set Recognition For Music Genre Classification

We explore segmentation of known and unknown genre classes using the open source GTZAN and FMA datasets. For each, we begin with best-case closed set genre classification, then we apply open set recognition methods. We offer an algorithm for the music genre classification task using OSR. We demonstrate the ability to retrieve known genres and as well identification of aural patterns for novel genres (not appearing in a training set). We conduct four experiments, each containing a different set of known and unknown classes, using the GTZAN and the FMA datasets to establish a baseline capacity for novel genre detection. We employ grid search on both OpenMax and softmax to determine the optimal total classification accuracy for each experimental setup, and illustrate interaction between genre labelling and open set recognition accuracy.

ZeroC: A Neuro-Symbolic Model for Zero-shot Concept Recognition and Acquisition at Inference Time

Humans have the remarkable ability to recognize and acquire novel visual concepts in a zero-shot manner. Given a high-level, symbolic description of a novel concept in terms of previously learned visual concepts and their relations, humans can recognize novel concepts without seeing any examples. Moreover, they can acquire new concepts by parsing and communicating symbolic structures using learned visual concepts and relations. Endowing these capabilities in machines is pivotal in improving their generalization capability at inference time. In this work, we introduce Zero-shot Concept Recognition and Acquisition (ZeroC), a neuro-symbolic architecture that can recognize and acquire novel concepts in a zero-shot way. ZeroC represents concepts as graphs of constituent concept models (as nodes) and their relations (as edges). To allow inference time composition, we employ energy-based models (EBMs) to model concepts and relations. We design ZeroC architecture so that it allows a one-to-one mapping between a symbolic graph structure of a concept and its corresponding EBM, which for the first time, allows acquiring new concepts, communicating its graph structure, and applying it to classification and detection tasks (even across domains) at inference time. We introduce algorithms for learning and inference with ZeroC. We evaluate ZeroC on a challenging grid-world dataset which is designed to probe zero-shot concept recognition and acquisition, and demonstrate its capability.

A Neural Network Solves and Generates Mathematics Problems by Program Synthesis: Calculus, Differential Equations, Linear Algebra, and More

We demonstrate that a neural network pre-trained on text and fine-tuned on code solves Mathematics problems by program synthesis. We turn questions into programming tasks, automatically generate programs, and then execute them, perfectly solving university-level problems from MIT's large Mathematics courses (Single Variable Calculus 18.01, Multivariable Calculus 18.02, Differential Equations 18.03, Introduction to Probability and Statistics 18.05, Linear Algebra 18.06, and Mathematics for Computer Science 6.042), Columbia University's COMS3251 Computational Linear Algebra course, as well as questions from a MATH dataset (on Prealgebra, Algebra, Counting and Probability, Number Theory, and Precalculus), the latest benchmark of advanced mathematics problems specifically designed to assess mathematical reasoning. We explore prompt generation methods that enable Transformers to generate question solving programs for these subjects, including solutions with plots. We generate correct answers for a random sample of questions in each topic. We quantify the gap between the original and transformed questions and perform a survey to evaluate the quality and difficulty of generated questions. This is the first work to automatically solve, grade, and generate university-level Mathematics course questions at scale. This represents a milestone for higher education.

Competing Bandits: The Perils of Exploration under Competition

We empirically study the interplay between exploration and competition. Systems that learn from interactions with users often engage in exploration: making potentially suboptimal decisions in order to acquire new information for future decisions. However, when multiple systems are competing for the same market of users, exploration may hurt a system's reputation in the near term, with adverse competitive effects. In particular, a system may enter a "death spiral", when the short-term reputation cost decreases the number of users for the system to learn from, which degrades its performance relative to competition and further decreases its market share. We ask whether better exploration algorithms are incentivized under competition. We run extensive numerical experiments in a stylized duopoly model in which two firms deploy multi-armed bandit algorithms and compete for myopic users. We find that duopoly and monopoly tend to favor a primitive "greedy algorithm" that does not explore and leads to low consumer welfare, whereas a temporary monopoly (a duopoly with an early entrant) may incentivize better bandit algorithms and lead to higher consumer welfare. Our findings shed light on the first-mover advantage in the digital economy by exploring the role that data can play as a barrier to entry in online markets.