Let’s assume you’re enjoying a game of football. The ball gets to your feet, and you make the decision to pass it to the unmarked forward. What appears to be one simplistic action needs two differing types of thought. 

To start with, you identify that there is a football at your feet. The identification needs intuitive perceptual thought – you cannot simply articulate how you came across the knowledge that there is a football at your feet, you just observe that it is present. Secondly, you make the decision to pass on the ball to a specific forward. This decision needs conceptual thought. Your decision is connected to a justification – the reason you made the pass is because the forward was not marked by a defender – increasing the probability of a goal being scored. 

The distinction is fascinating to us as there are dual types of thinking corresponding to two differing strategies to machine learning: symbolic program synthesis and deep learning. Deep learning focuses on intuitive perceptual thought  while symbolic program synthesis concentrates on conceptual, rule-based thought. Every system possesses differing advantages – deep learning frameworks are robust to noisy data but are tough to interpret and need massive amounts of data to go about training, while on the other hand, symbolic systems are much simpler to go about interpreting and need less training information but have issues with noisy data. While human cognition seamlessly brings together these two unique ways of thought, it is much less obvious if or how it is doable to emulate this in a singular artificial intelligence system. 

A research paper, put out in the journal JAIR, illustrates it is doable for systems to bring together intuitive perceptual with conceptual interpretable reasoning. The system that is described, ∂ILP, is robust to noise, data-efficient, and generates interpretable rules. 

It is illustrated how ∂ILP operates with an induction activity. It is provided a pairing of images indicating numbers, and has to output a label (0 or 1) suggesting if the number of the left image is less than the number of the right image. Finding a solution to this issue needs both variants of thought: you require intuitive perceptual thinking to identify the image as a representation of a specific digit, and you require conceptual thought to comprehend the less-than relation in its complete generality. 

If you provide a standard deep learning model – like a convolutional neural network with an MLP adequate training information, it is capable to find a solution to this task efficiently. After it has received its training, you can provide to it a new pairing of images it has never observed prior, and it will categorize accurately. Although, it will just generalize correctly if you provide it several instances of each pairing of digits. The model is good at visual generalization: generalizing to fresh images, under the assumption it has observed every pairing of digits in the evaluation set. But it does not have the capability of symbolic generalization: generalizing to a fresh pairing of digits it has not observed prior. Researchers such as Gary Marcus and Joel Grus have highlighted this in thought-provoking pieces. 

∂ILP is different from typical neural nets as it is capable of generalizing symbolically, and it is different from conventional symbolic programs as it is able to generalize visually. It goes about learning explicit programs from instances that are readable, interpretable, and verifiable. ∂ILP is provided an incomplete grouping of instances (the desired outcome) and generates a program that fulfils them. It looks through the space of programs leveraging gradient descent. If the outputs of the program conflict with the desired results from the reference information, the system revises the program to be an improved matching with the data. 

∂ILP is capable of generalizing symbolically. After it has observed enough instances of x < y, y < z, x < z, it will look at the possibility that the < relation is transitive. After it has realized this general rule, it can go about applying it to a new pairing of numbers it has never observed prior. 

The system goes some way to providing a solution to question of if accomplishing symbolic generalization within deep neural networks is doable. Future research intends to integrate similar systems with the capability to reason in addition to reacting.