deep-symbolic-mathematics TPSR: NeurIPS 2023 This is the official code for the paper “TPSR: Transformer-based Planning for Symbolic Regression”

For comparison with the gold grammar or with human behaviour via log-likelihood, averaged over 100 random word/colour assignments. Samples from the model (for example, as shown in Fig. 2 and reported in Extended Data Fig. 1) were based on an arbitrary random assignment that varied for each query instruction, with the number of samples scaled to 10× the number of human participants. Finally, each epoch also included an additional 100,000 episodes as a unifying bridge between the two types of optimization. These bridge episodes revisit the same 100,000 few-shot instruction learning episodes, although with a smaller number of the study examples provided (sampled uniformly from 0 to 14).

McCarthy’s approach to fix the frame problem was circumscription, a kind of non-monotonic logic where deductions could be made from actions that need only specify what would change while not having to explicitly specify everything that would not change. Other non-monotonic logics provided truth maintenance systems that revised beliefs leading to contradictions. Cognitive architectures such as ACT-R may have additional capabilities, such as the ability to compile frequently used knowledge into higher-level chunks. Our chemist was Carl Djerassi, inventor of the chemical behind the birth control pill, and also one of the world’s most respected mass spectrometrists. We began to add in their knowledge, inventing knowledge engineering as we were going along.

Symbolic AI

For Vygotsky, who published his theories in the early 20th century, playing make-believe is essential to a child’s healthy development. Symbolic play is the way children overcome their impulsiveness and develop the thought-out behaviors that will help them with more complicated cognitive functions. While you’re probably running to find your phone so that you can snap a picture, don’t forget to celebrate when you repack that cabinet — because your child has just reached another milestone on their journey through life. In the symbolic stage, knowledge is stored primarily as words, mathematical symbols, or other symbol systems, such as music.

A standard transformer encoder (bottom) processes the query input along with a set of study examples (input/output pairs; examples are delimited by a vertical line (∣) token). The standard decoder (top) receives the encoder’s messages and produces an output sequence in response. After optimization on episodes generated from various grammars, the transformer performs novel tasks using frozen weights. Each box is an embedding (vector); input embeddings are light blue (latent are dark). To date, neural networks have demonstrated remarkable accomplishments in perception-related tasks, such as image recognition (Rissati, Molina, & Anjos, 2020).

Methods of neural-symbolic learning systems

Expert systems are monotonic; that is, the more rules you add, the more knowledge is encoded in the system, but additional rules can’t undo old knowledge. Monotonic basically means one direction; i.e. when one thing goes up, another thing goes up. Each approach—symbolic, connectionist, and behavior-based—has advantages, but has been criticized by the other approaches. Symbolic AI has been criticized as disembodied, liable to the qualification problem, and poor in handling the perceptual problems where deep learning excels.

We showed how MLC enables a standard neural network optimized for its compositional skills to mimic or exceed human systematic generalization in a side-by-side comparison. MLC shows much stronger systematicity than neural networks trained in standard ways, and shows more nuanced behaviour than pristine symbolic models. MLC also allows neural networks to tackle other existing challenges, including making systematic use of isolated primitives11,16 and using mutual exclusivity to infer meanings44. Deep reinforcement learning (DRL) brings the power of deep neural networks to bear on the generic task of trial-and-error learning, and its effectiveness has been convincingly demonstrated on tasks such as Atari video games and the game of Go. However, contemporary DRL systems inherit a number of shortcomings from the current generation of deep learning techniques.

You’re getting rejected for a reason, but it’s almost always something you can fix.

A separate inference engine processes rules and adds, deletes, or modifies a knowledge store. Each step is annotated with the next re-write rules to be applied, and how many times (e.g., 3 × , since some steps have multiple parallel applications). In addition to the range of MLC variants specified above, the following additional neural and symbolic models were evaluated.

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