EXPLAIN, AGREE, LEARN: Scaling Learning for Neural Probabilistic Logic

• URL: http://arxiv.org/abs/2408.08133v1
• Date: Thu, 15 Aug 2024 13:07:51 GMT
• Title: EXPLAIN, AGREE, LEARN: Scaling Learning for Neural Probabilistic Logic
• Authors: Victor Verreet, Lennert De Smet, Luc De Raedt, Emanuele Sansone,
• Abstract summary: We propose a sampling based objective to scale learning to more complex systems. We prove that the objective has a bounded error with respect to the likelihood, which vanishes when increasing the sample count. We then develop the EXPLAIN, AGREE, LEARN (EXAL) method that uses this objective. In contrast to previous NeSy methods, EXAL can scale to larger problem sizes while retaining theoretical guarantees on the error.
• Score: 14.618208661185365
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural probabilistic logic systems follow the neuro-symbolic (NeSy) paradigm by combining the perceptive and learning capabilities of neural networks with the robustness of probabilistic logic. Learning corresponds to likelihood optimization of the neural networks. However, to obtain the likelihood exactly, expensive probabilistic logic inference is required. To scale learning to more complex systems, we therefore propose to instead optimize a sampling based objective. We prove that the objective has a bounded error with respect to the likelihood, which vanishes when increasing the sample count. Furthermore, the error vanishes faster by exploiting a new concept of sample diversity. We then develop the EXPLAIN, AGREE, LEARN (EXAL) method that uses this objective. EXPLAIN samples explanations for the data. AGREE reweighs each explanation in concordance with the neural component. LEARN uses the reweighed explanations as a signal for learning. In contrast to previous NeSy methods, EXAL can scale to larger problem sizes while retaining theoretical guarantees on the error. Experimentally, our theoretical claims are verified and EXAL outperforms recent NeSy methods when scaling up the MNIST addition and Warcraft pathfinding problems.

Related papers

• On the Hardness of Probabilistic Neurosymbolic Learning [10.180468225166441]
  We study the complexity of differentiating probabilistic reasoning in neurosymbolic models. We introduce WeightME, an unbiased gradient estimator based on model sampling. Our experiments indicate that the existing biased approximations indeed struggle to optimize even when exact solving is still feasible.
  arXiv  Detail & Related papers  (2024-06-06T19:56:33Z)
• Injecting Logical Constraints into Neural Networks via Straight-Through Estimators [5.6613898352023515]
  Injecting discrete logical constraints into neural network learning is one of the main challenges in neuro-symbolic AI. We find that a straight-through-estimator, a method introduced to train binary neural networks, could effectively be applied to incorporate logical constraints into neural network learning.
  arXiv  Detail & Related papers  (2023-07-10T05:12:05Z)
• Utility-Probability Duality of Neural Networks [4.871730595406078]
  We propose an alternative utility-based explanation to the standard supervised learning procedure in deep learning. The basic idea is to interpret the learned neural network not as a probability model but as an ordinal utility function. We show that for all neural networks with softmax outputs, the SGD learning dynamic of maximum likelihood estimation can be seen as an iteration process.
  arXiv  Detail & Related papers  (2023-05-24T08:09:07Z)
• Less is More: Rethinking Few-Shot Learning and Recurrent Neural Nets [2.824895388993495]
  We provide theoretical guarantees for reliable learning under the information-theoretic AEP. We then focus on a highly efficient recurrent neural net (RNN) framework and propose a reduced-entropy algorithm for few-shot learning. Our experimental results demonstrate significant potential for improving learning models' sample efficiency, generalization, and time complexity.
  arXiv  Detail & Related papers  (2022-09-28T17:33:11Z)
• Look beyond labels: Incorporating functional summary information in Bayesian neural networks [11.874130244353253]
  We present a simple approach to incorporate summary information about the predicted probability. The available summary information is incorporated as augmented data and modeled with a Dirichlet process. We show how the method can inform the model about task difficulty or class imbalance.
  arXiv  Detail & Related papers  (2022-07-04T07:06:45Z)
• Why Lottery Ticket Wins? A Theoretical Perspective of Sample Complexity on Pruned Neural Networks [79.74580058178594]
  We analyze the performance of training a pruned neural network by analyzing the geometric structure of the objective function. We show that the convex region near a desirable model with guaranteed generalization enlarges as the neural network model is pruned.
  arXiv  Detail & Related papers  (2021-10-12T01:11:07Z)
• Training Feedback Spiking Neural Networks by Implicit Differentiation on the Equilibrium State [66.2457134675891]
  Spiking neural networks (SNNs) are brain-inspired models that enable energy-efficient implementation on neuromorphic hardware. Most existing methods imitate the backpropagation framework and feedforward architectures for artificial neural networks. We propose a novel training method that does not rely on the exact reverse of the forward computation.
  arXiv  Detail & Related papers  (2021-09-29T07:46:54Z)
• The Causal Neural Connection: Expressiveness, Learnability, and Inference [125.57815987218756]
  An object called structural causal model (SCM) represents a collection of mechanisms and sources of random variation of the system under investigation. In this paper, we show that the causal hierarchy theorem (Thm. 1, Bareinboim et al., 2020) still holds for neural models. We introduce a special type of SCM called a neural causal model (NCM), and formalize a new type of inductive bias to encode structural constraints necessary for performing causal inferences.
  arXiv  Detail & Related papers  (2021-07-02T01:55:18Z)
• FF-NSL: Feed-Forward Neural-Symbolic Learner [70.978007919101]
  This paper introduces a neural-symbolic learning framework, called Feed-Forward Neural-Symbolic Learner (FF-NSL) FF-NSL integrates state-of-the-art ILP systems based on the Answer Set semantics, with neural networks, in order to learn interpretable hypotheses from labelled unstructured data.
  arXiv  Detail & Related papers  (2021-06-24T15:38:34Z)
• Reinforcement Learning with External Knowledge by using Logical Neural Networks [67.46162586940905]
  A recent neuro-symbolic framework called the Logical Neural Networks (LNNs) can simultaneously provide key-properties of both neural networks and symbolic logic. We propose an integrated method that enables model-free reinforcement learning from external knowledge sources.
  arXiv  Detail & Related papers  (2021-03-03T12:34:59Z)
• Towards Understanding Hierarchical Learning: Benefits of Neural Representations [160.33479656108926]
  In this work, we demonstrate that intermediate neural representations add more flexibility to neural networks. We show that neural representation can achieve improved sample complexities compared with the raw input. Our results characterize when neural representations are beneficial, and may provide a new perspective on why depth is important in deep learning.
  arXiv  Detail & Related papers  (2020-06-24T02:44:54Z)

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.