Strong Generalization and Efficiency in Neural Programs

Li, Yujia; Gimeno, Felix; Kohli, Pushmeet; Vinyals, Oriol

doi:10.48550/arxiv.2007.03629

Cited by 4 publications

(4 citation statements)

References 22 publications

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“…Neural SFEs are heavily inspired by the Goemans-Williamson (Goemans & Williamson, 1995) algorithm and other SDP techniques (Iguchi et al, 2015), which lift problems onto higher dimensional spaces, solve them, and then project back down. Our approach to lifting set functions to high dimensions is motivated by the algorithmic alignment principle (Xu et al, 2019): neural networks whose computations emulate classical algorithms often generalize better with improved sample complexity Li et al, 2020;Xu et al, 2019). Emulating algorithmic and logical operations is the focus of Neural Algorithmic Reasoning (Veličković et al, 2019;Dudzik & Veličković, 2022;Deac et al, 2021) and work on knowledge graphs (Hamilton et al, 2018;Ren et al, 2019;Arakelyan et al, 2020), which also emphasize operating in higher dimensions.…”

Section: Related Workmentioning

confidence: 99%

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Karalias¹,

Robinson²,

Loukas³

et al. 2022

Preprint

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Integrating functions on discrete domains into neural networks is key to developing their capability to reason about discrete objects. But, discrete domains are (1) not naturally amenable to gradient-based optimization, and (2) incompatible with deep learning architectures that rely on representations in high-dimensional vector spaces. In this work, we address both difficulties for set functions, which capture many important discrete problems. First, we develop a framework for extending set functions onto low-dimensional continuous domains, where many extensions are naturally defined. Our framework subsumes many well-known extensions as special cases. Second, to avoid undesirable low-dimensional neural network bottlenecks, we convert low-dimensional extensions into representations in high-dimensional spaces, taking inspiration from the success of semidefinite programs for combinatorial optimization. Empirically, we observe benefits of our extensions for unsupervised neural combinatorial optimization, in particular with high-dimensional representations. * Equal contribution.Preprint. Under review.

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Section: Related Workmentioning

confidence: 99%

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Karalias¹,

Robinson²,

Loukas³

et al. 2022

Preprint

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“…General reasoning systems, however, need to be able to expand beyond this type of generalization. OOD generalization (Li et al, 2020) is paramount, as generally one can not control the distribution a model will face over time when deployed.…”

Section: Motivationmentioning

confidence: 99%

Neural algorithmic reasoning

Veličković

Blundell

2021

Patterns

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“…Neural program induction and synthesis. Program induction methods [20,[24][25][26][27][28][29][30][31][32][33][34][35][36] aim to implicitly induce the underlying programs to mimic the behaviors demonstrated in given task specifications such as input/output pairs or expert demonstrations. On the other hand, program synthesis methods [16-19, 21, 37-58] explicitly synthesize the underlying programs and execute the programs to perform the tasks from task specifications such input/output pairs, demonstrations, language instructions.…”

Section: Related Workmentioning

confidence: 99%

Learning to Synthesize Programs as Interpretable and Generalizable Policies

Trivedi¹,

Zhang²,

Sun³

et al. 2021

Preprint

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Recently, deep reinforcement learning (DRL) methods have achieved impressive performance on tasks in a variety of domains. However, neural network policies produced with DRL methods are not human-interpretable and often have difficulty generalizing to novel scenarios. To address these issues, prior works explore learning programmatic policies that are more interpretable and structured for generalization. Yet, these works either employ limited policy representations (e.g. decision trees, state machines, or predefined program templates) or require stronger supervision (e.g. input/output state pairs or expert demonstrations). We present a framework that instead learns to synthesize a program, which details the procedure to solve a task in a flexible and expressive manner, solely from reward signals. To alleviate the difficulty of learning to compose programs to induce the desired agent behavior from scratch, we propose to first learn a program embedding space that continuously parameterizes diverse behaviors in an unsupervised manner and then search over the learned program embedding space to yield a program that maximizes the return for a given task. Experimental results demonstrate that the proposed framework not only learns to reliably synthesize task-solving programs but also outperforms DRL and program synthesis baselines while producing interpretable and more generalizable policies. We also justify the necessity of the proposed two-stage learning scheme as well as analyze various methods for learning the program embedding.

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Strong Generalization and Efficiency in Neural Programs

Cited by 4 publications

References 22 publications

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Neural Set Function Extensions: Learning with Discrete Functions in High Dimensions

Neural algorithmic reasoning

Learning to Synthesize Programs as Interpretable and Generalizable Policies

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