The capabilities of neural networks are widely recognized, yet they typically demand a substantial amount of training data that closely matches the distribution of the target test domain. In contrast, inductive logic programming (ILP) in the symbolic domain requires only a small dataset, but it struggles with noisy data and has limited applicability.
In a recent paper published by DeepMind, a novel approach called differential inductive logic programming, or ∂ILP, was introduced. This method not only excels at solving traditional symbolic tasks but also demonstrates robustness to noise and training errors, while being trained through gradient descent.
Let’s take a closer look at how DeepMind explains this innovative method on their official blog:
[Image: DeepMind proposes a differential induction programming method ∂ILP and interprets it]
Imagine playing football, where the ball is at your feet, and you decide to pass it to a striker who isn’t looking. This seemingly simple action involves two distinct cognitive processes.
First, you instinctively recognize that you have the ball beneath you — an intuitive, almost emotional understanding. You can't easily articulate how you know you're holding the ball.
Second, you make a decision based on reasoning: you choose to pass to the striker because she's unguarded. This conceptual thinking is essential for making logical decisions.
This distinction intrigued us because it mirrors two different machine learning approaches: deep learning and symbolic reasoning. Deep learning excels at perceptual tasks, adapting well to noisy data but often lacking interpretability. On the other hand, symbolic systems are more transparent and require less data, but they struggle with noise and generalization.
Humans seamlessly combine these two modes of thinking, but replicating this in AI remains a challenge. Our latest paper in the Journal of AI Research shows that it is possible to integrate both intuitive and conceptual reasoning into a single system.
The ∂ILP system we developed offers several key advantages: it is noise-tolerant, data-efficient, and produces interpretable rules. Here’s a visual representation of how it works:
[Image: DeepMind proposes a differential induction programming method ∂ILP and interprets it]
To demonstrate ∂ILP, we used an inductive task where the system had to determine whether the number on the left image is smaller than the one on the right. The process involved both perceptual recognition and conceptual understanding of the “less than†relationship.
While a standard deep learning model like a CNN with an MLP can solve this task effectively given enough data, it struggles with symbolic generalization. For instance, it may fail when presented with numbers it hasn’t seen before.
In contrast, ∂ILP can generalize symbolically. It learns readable, interpretable programs from examples and uses gradient descent to refine its output. If the program doesn’t match the desired result, it adjusts accordingly.
Here’s a visual of the training process:
[Image: DeepMind proposes a differential induction programming method ∂ILP and interprets it]
∂ILP can generalize symbols effectively when provided with sufficient input pairs. The following graph illustrates this in the “less than†experiment: the blue curve represents a standard neural network that performs poorly on unseen number pairs, while the green curve shows ∂ILP maintaining low error rates even with minimal training.
We believe this work takes a significant step toward bridging the gap between symbolic and neural approaches. In the future, we plan to integrate ∂ILP into reinforcement learning agents and larger deep learning systems, enabling AI to reason and react more effectively.
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