# SymbolicArena: A Unified Infrastructure for Benchmark Distillation and Dynamic Evaluation in Symbolic Regression

arXiv: https://arxiv.org/abs/2609.35113 · HTML: https://mlsanity.com/paper/2609.35113/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 22 of 22)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Dynabench: Rethinking Benchmarking in NLP](https://mlsanity.com/paper/2104.14337/) (2021)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [DataPerf: Benchmarks for Data-Centric AI Development](https://mlsanity.com/paper/2207.10062/) (2022)
- [Anchor Points: Benchmarking Models with Much Fewer Examples](https://mlsanity.com/paper/2309.08638/) (2023)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Efficient Benchmarking of Language Models](https://mlsanity.com/paper/2308.11696/) (2023)
- [Dynaboard: An Evaluation-As-A-Service Platform for Holistic Next-Generation Benchmarking](https://mlsanity.com/paper/2106.06052/) (2021)
- [Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discovery](https://mlsanity.com/paper/2206.10540/) (2022)
- [Deep Generative Symbolic Regression with Monte-Carlo-Tree-Search](https://mlsanity.com/paper/2302.11223/) (2023)
- [An Approach to Symbolic Regression Using Feyn](https://mlsanity.com/paper/2104.05417/) (2021)
- [Call for Action: towards the next generation of symbolic regression benchmark](https://mlsanity.com/paper/2505.03977/) (2025)
- [Improving Monte Carlo Tree Search for Symbolic Regression](https://mlsanity.com/paper/2509.15929/) (2025)
- [SymbolFit: Automatic Parametric Modeling with Symbolic Regression](https://mlsanity.com/paper/2411.09851/) (2024)
- [FePySR: A Neural Feature Extraction Framework for Efficient and Scalable Symbolic Regression](https://mlsanity.com/paper/2605.12704/) (2026)

## Abstract (arXiv)

Symbolic regression (SR) seeks concise and interpretable mathematical expressions from data for scientific equation discovery. Existing SR benchmarks face a tradeoff between evaluation cost and benchmark validity. Repeated evaluation of large task pools is expensive, and compact benchmarks lack systematic evidence of preserved task diversity and algorithm discriminability. SymbolicArena provides a unified infrastructure for benchmark distillation and dynamic evaluation. The framework standardizes 664 heterogeneous tasks with executable ground truth expressions and distills the Full Task Set into Core50, a validated benchmark of 50 tasks. The distillation process preserves task coverage and algorithm discrimination under explicit balance constraints. SymbolicArena applies a unified execution protocol to heterogeneous SR algorithms and produces comparable outputs and search trajectories. Multi Axis Evaluation characterizes numerical quality, symbolic quality, and search behavior. Core50 reduces evaluation workload by 92.5% and maintains agreement with Full Task Set evaluations. Experiments show that SymbolicArena achieves 72.6% to 86.7% lower approximation error than alternative selectors, further supporting its fidelity to the Full Task Set. Evaluation reveals a substantial gap between numerical fitting and symbolic recovery across current SR methods, suggesting that reliable equation recovery remains an open challenge.