The remarkable capabilities of neural networks are widely recognized, yet they typically demand large amounts of training data that closely match the distribution of the target test domain. In contrast, inductive logic programming (ILP) in the symbolic domain requires only a small amount of data but struggles with noise and has limited applicability.
In a recent paper published by DeepMind, a novel approach called differential inductive logic programming (∂ILP) was introduced. This method not only tackles the symbolic tasks traditionally handled by ILP but also demonstrates some resilience to noisy data and training errors, all while being trained through gradient descent.
So, what exactly is ∂ILP? Let’s take a closer look at how DeepMind explains this groundbreaking technique on their official blog:
[Image: DeepMind proposes a differential induction programming method ∂ILP and interprets it]
Imagine playing football, where you have the ball at your feet and decide to pass it to a striker who isn’t looking. This seemingly simple action involves two distinct cognitive processes.
First, you instinctively know that you have the ball beneath your feet—this is intuitive and emotional thinking, something that can't be easily articulated. Second, you make a decision based on reasoning: you pass the ball because the striker is unguarded.
This distinction is fascinating because it mirrors two different approaches in machine learning: deep learning and symbolic reasoning. Deep learning excels at perceptual tasks and can handle noisy data, but it lacks interpretability and requires large datasets. On the other hand, symbolic systems are more transparent and require less data, but they are fragile when faced with noise.
Human cognition seamlessly blends these two modes of thinking, but replicating this in AI remains a challenge. Our recent paper in the Journal of Artificial Intelligence Research shows that combining intuitive perception with conceptual reasoning is indeed possible. The ∂ILP system we developed achieves this by being robust to noise, efficient in data usage, and capable of generating interpretable rules.
[Image: DeepMind proposes a differential induction programming method ∂ILP and interprets it]
To demonstrate how ∂ILP works, we used an inductive task: given two images representing numbers, the system must determine whether the number on the left is smaller than the one on the right.
[Image: DeepMind proposes a differential induction programming method ∂ILP and interprets it]
Solving this task requires both intuitive perception (recognizing the numbers) and conceptual understanding (understanding the "less than" relationship). While a standard deep learning model like a CNN with an MLP can solve this problem effectively with enough data, it struggles when it comes to generalization beyond the training examples.
For instance, it may perform well on seen number pairs but fail when presented with new numbers. In contrast, ∂ILP can generalize symbolically, even with limited examples.
[Image: DeepMind proposes a differential induction programming method ∂ILP and interprets it]
Unlike traditional neural networks, ∂ILP is capable of symbolic generalization. It doesn’t just rely on visual patterns—it learns readable, interpretable, and verifiable procedures from the data. Given a few examples of desired outcomes, ∂ILP can generate a program that meets those requirements. It uses gradient descent to search through the program space, adjusting its output to better align with the reference data.
[Image: DeepMind proposes a differential induction programming method ∂ILP and interprets it]
As shown in the figure above, ∂ILP can generalize symbolically when provided with sufficient input-output pairs.
[Image: DeepMind proposes a differential induction programming method ∂ILP and interprets it]
The graph above summarizes our “less than†experiment: the blue curve represents a standard deep neural network that fails to generalize to unseen number pairs, especially when only 40% of the data is used for training. The green curve, however, shows that ∂ILP maintains a low error rate, proving its ability to generalize symbolically.
We believe that ∂ILP offers promising insights into whether symbolic generalization can be achieved within deep learning frameworks. Looking ahead, we plan to integrate ∂ILP-like systems into reinforcement learning agents and larger deep learning modules, enabling AI systems to reason and react more effectively.
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