Dual Algorithmic Reasoning

• URL: http://arxiv.org/abs/2302.04496v1
• Date: Thu, 9 Feb 2023 08:46:23 GMT
• Title: Dual Algorithmic Reasoning
• Authors: Danilo Numeroso, Davide Bacciu, Petar Veli\v{c}kovi\'c
• Abstract summary: We propose to learn algorithms by exploiting duality of the underlying algorithmic problem. We demonstrate that simultaneously learning the dual definition of these optimisation problems in algorithmic learning allows for better learning. We then validate the real-world utility of our dual algorithmic reasoner by deploying it on a challenging brain vessel classification task.
• Score: 9.701208207491879
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neural Algorithmic Reasoning is an emerging area of machine learning which seeks to infuse algorithmic computation in neural networks, typically by training neural models to approximate steps of classical algorithms. In this context, much of the current work has focused on learning reachability and shortest path graph algorithms, showing that joint learning on similar algorithms is beneficial for generalisation. However, when targeting more complex problems, such similar algorithms become more difficult to find. Here, we propose to learn algorithms by exploiting duality of the underlying algorithmic problem. Many algorithms solve optimisation problems. We demonstrate that simultaneously learning the dual definition of these optimisation problems in algorithmic learning allows for better learning and qualitatively better solutions. Specifically, we exploit the max-flow min-cut theorem to simultaneously learn these two algorithms over synthetically generated graphs, demonstrating the effectiveness of the proposed approach. We then validate the real-world utility of our dual algorithmic reasoner by deploying it on a challenging brain vessel classification task, which likely depends on the vessels' flow properties. We demonstrate a clear performance gain when using our model within such a context, and empirically show that learning the max-flow and min-cut algorithms together is critical for achieving such a result.

Related papers

• Neural Algorithmic Reasoning Without Intermediate Supervision [21.852775399735005]
  We focus on learning neural algorithmic reasoning only from the input-output pairs without appealing to the intermediate supervision. We build a self-supervised objective that can regularise intermediate computations of the model without access to the algorithm trajectory. We demonstrate that our approach is competitive to its trajectory-supervised counterpart on tasks from the CLRSic Algorithmic Reasoning Benchmark.
  arXiv  Detail & Related papers  (2023-06-23T09:57:44Z)
• Representation Learning with Multi-Step Inverse Kinematics: An Efficient and Optimal Approach to Rich-Observation RL [106.82295532402335]
  Existing reinforcement learning algorithms suffer from computational intractability, strong statistical assumptions, and suboptimal sample complexity. We provide the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics.
  arXiv  Detail & Related papers  (2023-04-12T14:51:47Z)
• Improved Algorithms for Neural Active Learning [74.89097665112621]
  We improve the theoretical and empirical performance of neural-network(NN)-based active learning algorithms for the non-parametric streaming setting. We introduce two regret metrics by minimizing the population loss that are more suitable in active learning than the one used in state-of-the-art (SOTA) related work.
  arXiv  Detail & Related papers  (2022-10-02T05:03:38Z)
• Learning with Differentiable Algorithms [6.47243430672461]
  This thesis explores combining classic algorithms and machine learning systems like neural networks. The thesis formalizes the idea of algorithmic supervision, which allows a neural network to learn from or in conjunction with an algorithm. In addition, this thesis proposes differentiable algorithms, such as differentiable sorting networks, differentiable sorting gates, and differentiable logic gate networks.
  arXiv  Detail & Related papers  (2022-09-01T17:30:00Z)
• On the Convergence of Distributed Stochastic Bilevel Optimization Algorithms over a Network [55.56019538079826]
  Bilevel optimization has been applied to a wide variety of machine learning models. Most existing algorithms restrict their single-machine setting so that they are incapable of handling distributed data. We develop novel decentralized bilevel optimization algorithms based on a gradient tracking communication mechanism and two different gradients.
  arXiv  Detail & Related papers  (2022-06-30T05:29:52Z)
• Practical, Provably-Correct Interactive Learning in the Realizable Setting: The Power of True Believers [12.09273192079783]
  We consider interactive learning in the realizable setting and develop a general framework to handle problems ranging from best arm identification to active classification. We design novel computationally efficient algorithms for the realizable setting that match the minimax lower bound up to logarithmic factors.
  arXiv  Detail & Related papers  (2021-11-09T02:33:36Z)
• Provably Faster Algorithms for Bilevel Optimization [54.83583213812667]
  Bilevel optimization has been widely applied in many important machine learning applications. We propose two new algorithms for bilevel optimization. We show that both algorithms achieve the complexity of $mathcalO(epsilon-1.5)$, which outperforms all existing algorithms by the order of magnitude.
  arXiv  Detail & Related papers  (2021-06-08T21:05:30Z)
• Neural Algorithmic Reasoning [11.566653801306844]
  We argue that algorithms possess fundamentally different qualities to deep learning methods. By representing elements in a continuous space of learnt algorithms, neural networks are able to adapt known algorithms more closely to real-world problems.
  arXiv  Detail & Related papers  (2021-05-06T15:33:57Z)
• Evolving Reinforcement Learning Algorithms [186.62294652057062]
  We propose a method for meta-learning reinforcement learning algorithms. The learned algorithms are domain-agnostic and can generalize to new environments not seen during training. We highlight two learned algorithms which obtain good generalization performance over other classical control tasks, gridworld type tasks, and Atari games.
  arXiv  Detail & Related papers  (2021-01-08T18:55:07Z)
• Towards Optimally Efficient Tree Search with Deep Learning [76.64632985696237]
  This paper investigates the classical integer least-squares problem which estimates signals integer from linear models. The problem is NP-hard and often arises in diverse applications such as signal processing, bioinformatics, communications and machine learning. We propose a general hyper-accelerated tree search (HATS) algorithm by employing a deep neural network to estimate the optimal estimation for the underlying simplified memory-bounded A* algorithm.
  arXiv  Detail & Related papers  (2021-01-07T08:00:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.