TPSR
Transformer-based Planning for Symbolic Regression
Wraps Monte Carlo Tree Search and BFGS numerical constant optimization around a pre-trained symbolic regression transformer.
The loop
- Proposes
A pre-trained symbolic regression transformer (E2E / NeSymReS) provides prior probabilities over next mathematical operators in a prefix expression tree.
- Judged by
Once a complete equation skeleton is reached, BFGS optimizes its continuous constants and computes complexity-regularized NMSE fit on the dataset.
- Steers
UCB tree search backpropagates the exact numerical fit reward to steer subsequent expression-tree expansions.
Headline result
Significantly improved symbolic equation recovery and extrapolation R^2 on SRBench and Feynman physics datasets over beam search or sampling.
What this does not prove
Running BFGS constant optimization at leaf rollouts adds numerical overhead compared to single-pass forward decoding.
How it generalizes the harness
- The algorithm is the solver
- Inverted control
- A domain authority judges
- Search over a population
- The generator is not an LLM
- Continuous-discrete duality
- Intra-algorithmic surgery (inside the while-loop)
Monte Carlo Tree Search and BFGS numerical optimization control decoding over a pre-trained symbolic transformer.
Classification
| What it proposes | Equation |
|---|---|
| Generative model | Pre-trained symbolic regression transformer (E2E) |
| Algorithmic authority | Monte Carlo Tree Search and BFGS numerical optimizer |
| Feedback | Reward signal |
| What gets updated | Search tree |
| When it runs | At inference time |
| Validity | Empirical (measured) |
| Evidence | Code released |
| Lineage | Original system |