When AI starts discovering physical laws on its own: the birth of a self-reflecting scientist.
Physicists have an old dream: hand a computer a pile of experimental data and let it find the mathematical规律... let it find the mathematical laws behind the data itself.
This is not fantasy. Kepler spent twenty years analyzing Tycho Brahe's observations to derive the laws of planetary motion. If a human can do it, why can't an AI?
This field is called Symbolic Regression — automatically discovering mathematical formulas from data. With the rise of LLMs in recent years, using AI for this has become a hot research direction. But reality is harsh: most systems are still stuck in a generate-fit-score-repeat loop, with painfully low efficiency.
A recent paper proposes an idea that caught my attention — letting the AI "stop and reflect" during the formula discovery process. This capacity for self-examination may be the key to AI genuinely learning to do scientific discovery.
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📐 A Stubborn Problem: How Do You Teach AI to Discover Formulas?
First, why is this problem hard?
Physical laws usually look like this: \(F = ma\) (Newton's second law), \(E = mc^2\) (mass-energy equivalence). They are symbolic — containing variables, constants, and operators; simple in form but profound in meaning.
Reverse-engineering these formulas from data is challenging for three reasons:
First, the search space is enormous. You can combine numbers and variables in infinitely many ways, and nearly all combinations are wrong. Finding the correct formula is like finding one specific grain of sand in a cosmic beach.
Second, evaluation criteria are unstable. With noisy data, a "roughly right" formula may score higher than a "completely correct one with small parameter errors." This causes AI systems to discard genuinely good formulas and keep wrong ones.
Third, memory redundancy. Many systems accumulate large numbers of "failed candidate formulas" as experience, but this experience is mixed in quality, bloating the context and making it harder for the AI to think.
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🔄 STRIDE's Approach: Not Generation, but Orchestration
Most existing LLM-based equation discovery systems follow a generation-centric loop — propose a candidate formula, fit parameters, score it, keep the good ones, discard the bad, repeat.
This paradigm has three fatal problems:
1. Misjudging useful formula skeletons when fitting is unreliable. A formula whose structure is correct but whose parameters are poorly fit gets thrown away. 2. Discarding equations that are "almost right but need a fix". Some formulas are one step away from working, but the system lacks the ability to repair them. 3. Accumulating redundant memory that interferes with judgment. Failed candidates pile up, but they repeat each other and add no informational value.
STRIDE's solution: stop letting "generation" dominate everything and introduce an orchestration framework where multiple roles each do their own job.
It has four core components:
Data-aware Generation: Instead of generating candidates blindly, generation is guided by structural features of the data. For example, if the data shows exponential decay, the AI prioritizes formulas containing exponential functions rather than random combinations.
Mixed-fitting Evaluation: Traditional methods first fix the formula structure, then fit parameters. STRIDE introduces "mixed fitting" — simultaneously considering structural correctness and parameter-fit quality, to more accurately assess a candidate's true potential.
Critic-Executor Repair: This is STRIDE's most critical innovation. A "critic" role specializes in analyzing failure cases — what's wrong with this formula? Is the structure wrong or the parameters? It then guides an "executor" to perform targeted repairs instead of simply discarding the formula.
Diversity-Preserving Semantic Memory: Traditional memory systems accumulate all failed candidates, but STRIDE keeps only "meaningful failures" — experiences that provide new information or represent a class of errors. It automatically deduplicates, ensuring high "information density" in memory.
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🎯 Results: More Accurate, More Stable, More Robust
The experimental results are persuasive.
On representative symbolic regression benchmarks and the LSR-Synth suite, STRIDE achieves significant improvements in accuracy, out-of-distribution robustness, and structure recovery.
Particularly noteworthy are the ablation studies — disabling each component individually to see how much it contributes.
Results show all four components are indispensable. The critic-executor repair module in particular shows the largest performance drop when removed. This confirms that the design choice of "repair rather than discard" delivers real gains.
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🤔 A Deeper Question: What Is "Automated Scientific Discovery"?
STRIDE makes me think about something more fundamental: how does scientific discovery actually happen?
We usually describe scientific discovery as a loop of "propose hypothesis — design experiment — validate conclusion." But real discovery is far messier, more iterative, and far more dependent on "reflection."
Often, a seemingly failed experiment contains exactly the right clue — it's just deeply hidden and requires stopping to re-examine. Real scientists don't mechanically collect data; they constantly reflect: Did I look at this wrong? What am I missing?
STRIDE is essentially adding this "reflection" capability to AI. It doesn't make the AI generate more formulas; it teaches the AI to stop and ask: was my path right? Why does this formula that looks right actually fail?
This metacognitive ability may be the key watershed for whether AI can genuinely do scientific discovery.
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🔮 What Kind of Scientist Will AI Become?
STRIDE demonstrates how an AI with "self-examination" can do symbolic regression more effectively. But this is not yet a true "AI scientist."
What does a real AI scientist need? Probably more than finding patterns in data — it needs to pose good questions, design suitable experiments, and express discovered laws in ways humans can understand.
Symbolic regression is only a small step. But STRIDE proves one point: teaching AI to "stop and reflect" may be a crucial step toward higher-level intelligence.
Kepler spent twenty years analyzing Tycho's data. How long would a STRIDE-like system take? A week? A day?
I don't know. But STRIDE shows me a possibility — maybe one day AI really will become a tireless scientist that is always reflecting, always learning how to be smarter.
And what we humans must do is ensure its goals stay aligned with ours.
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References
1. Su, J., Tu, S., Sun, B., & Liang, X. (2026). *STRIDE: A Self-Reflective Agent Framework for Reliable Automatic Equation Discovery*. arXiv:2605.17790. 2. Cranmer, M., et al. (2023). *Discovering symbolic laws of physics with deep learning*. Nature Communications, 14(1), 4321. 3. Udrescu, S., & Tegmark, M. (2020). *AI Feynman: A physics-inspired neural network method for symbolic regression*. Science Advances, 6(16), eaay2631. 4. Lample, G., & Charton, F. (2020). *Deep learning for symbolic mathematics*. ICLR. 5. Landajuela, D., et al. (2022). *Symbolic regression via end-to-end neural network*. arXiv:2204.10532.