Neuro-Symbolic Learning for Reasoning

Neuro-Symbolic Learning for Reasoning

Table of Contents:

I. Introduction II. Mathematical Reasoning A. Extrapolation B. Learning Distributed Representations C. Mathematical Question Answering D. Mathematical Equation Verification E. Solving Differential Equations III. Common-Sense Reasoning A. Multi-Hop Reasoning B. Logical Inference C. Conversational Learning IV. Conclusion V. FAQ

Article:

Introduction

Artificial intelligence has long been a dream of computer scientists, who have sought to Create machines that can learn and reason like humans. However, despite decades of research, common Sense and automated reasoning remain unsolved challenges at the heart of AI. In this article, we will explore the field of neural symbolic learning algorithms, which combine neural networks and symbolic reasoning to address these challenges. We will discuss different applications of these learning algorithms for problems in reasoning, including mathematical reasoning and logical reasoning for the problem of common sense.

Mathematical Reasoning

Extrapolation

One of the major challenges in reasoning is extrapolation, where the computer encounters problems that are much harder than what it has seen before during training. To address this challenge, we can extract hierarchical structures from data that help break down problems into smaller subproblems that are easier to solve. For example, we can use latent variable models to model high-dimensional time series data, such as predicting the behavior of students in a massive open online course or the behavior of social network attendees like Twitter or Facebook. We can also use deep learning models, such as structured neural networks, for the problem of mathematical reasoning, mathematical question answering, and verification. By augmenting these recursive neural networks with external memory, we can improve their extrapolation capability to Extrapolate to harder mathematical reasoning problems.

Learning Distributed Representations

To learn distributed representations for different functions and symbols in the mathematics domain, we can use a tree-structured model that assigns different neural network blocks for modeling different functions in the domain, such as sine and Cosine, and different symbols like theta and numbers like 2.45. We can also use function evaluation expressions to model evaluations of different functions in the domain, such as sine of -2.5, and number encoding expressions to represent floating-point numbers by their decimal expansion tree. By learning these distributed representations, we can achieve extrapolation by distributing the representation for each symbol across all the entries of the vector, which allows us to generalize to an unseen floating-point number.

Mathematical Question Answering

In mathematical question answering, We Are given a mathematical expression, and the goal is to find a value for the blank that satisfies this equation. We can use the blocks that were trained previously to generate random candidate predictions from the vocabulary for this blank and then plug in these candidates into this expression and use the previous model to rank these candidates at equality to see which one is correct. We get the output probability of the model as a ranking metric and rank these predictions. If the correct prediction is at the top prediction, we are going to count that as a success.

Mathematical Equation Verification

In mathematical equation verification, we are given an input equation, and we want to verify if it's correct or incorrect. We split our train and test data such that we have equations of depth 1 through 4 in the train and that's 1 through 4 in the test data. We compare the model against a symbolic solver called Senpai and the chain-structured model. We can gain about a 15% performance improvement just by accounting for hierarchical structures in the data.

Solving Differential Equations

We can use our model to model ordinary differential equations, which are used to model numerous phenomena in the real world. We have shown that our model can drastically improve the accuracy of Current statistical machine learning models.

Common-Sense Reasoning

Multi-Hop Reasoning

In common-sense reasoning, we are given statements in the form of if state s then perform action a because I want to achieve goal G. We can use a logic programming language to program a background knowledge called KT containing these if-then logical statements. We take the user's goal as a query and submit it against our background knowledge. If the goal is not in the background knowledge, we engage in a conversation with the user to extract the goal from the user just in time. If the goal was in the knowledge base, we use our learned distributed representations to extract proof traces in which we can have the user's understanding.

Logical Inference

We can learn distributed representations for different statements in logic and extract users' underspecified intents by extracting proof traces. This allows us to achieve explainability because these distributed representations have a corresponding logic rule that can be easily interpreted. We can also engage in a conversation with the user to extract the goal from the user just in time.

Conversational Learning

Conversational learning is a new learning paradigm in which humans can directly instruct computers in natural language to achieve new tasks. By using natural language explanations, we can achieve more simple and efficient algorithms and improve the accuracy of current statistical machine learning models.

Conclusion

Neural symbolic learning algorithms combine neural networks and symbolic reasoning to address the challenges of common sense and automated reasoning. By extracting hierarchical structures from data, we can achieve extrapolation and improve the performance of symbolic solvers. By learning distributed representations for different functions and symbols in the mathematics domain, we can achieve extrapolation by distributing the representation for each symbol across all the entries of the vector. By using logic programming languages, we can extract users' underspecified intents and achieve explainability. By engaging in a conversation with the user, we can extract the goal from the user just in time. Conversational learning is a new learning paradigm that allows humans to directly instruct computers in natural language to achieve new tasks.

FAQ

Q: What is the difference between neural networks and symbolic reasoning? A: Neural networks are used to model complex functions that are difficult to express in a symbolic form, while symbolic reasoning is used to represent knowledge in terms of facts and rules that are typically encoded in logic and perform logical inference to make inferences about that knowledge.

Q: What is the challenge of extrapolation in reasoning? A: Extrapolation refers to the challenge of encountering problems that are much harder than what the computer has seen before during training. To address this challenge, we can extract hierarchical structures from data that help break down problems into smaller subproblems that are easier to solve.

Q: What is conversational learning? A: Conversational learning is a new learning paradigm in which humans can directly instruct computers in natural language to achieve new tasks. By using natural language explanations, we can achieve more simple and efficient algorithms and improve the accuracy of current statistical machine learning models.

Q: What is the benefit of using logic in common-sense reasoning? A: By using logic, we can achieve multi-hop inference, which allows us to extract users' underspecified intents. This also provides us with explainability because these distributed representations have a corresponding logic rule that can be easily interpreted.