Self-Evolving Multi-Agent Symbolic Discovery for Financial Fundamental Analysis

Kelvin J. L. Koa; Filip Orestav; Shengqiong Wu; Michael J. Wooldridge; Ke-Wei Huang

cs.MASep 26, 2026

Self-Evolving Multi-Agent Symbolic Discovery for Financial Fundamental Analysis

Authors: Kelvin J. L. Koa, Filip Orestav, Shengqiong Wu, Michael J. Wooldridge, Ke-Wei Huang

Organizations: National University of Singapore · Asian Institute of Digital Finance · KTH Royal Institute of Technology · University of Oxford

Abstract

While symbolic regression (SR) has been successfully used in science to discover new equations, its use in financial valuation is hindered by several limitations. Whereas the natural sciences provide objectively correct relationships, financial valuation constitutes a distinct class of symbolic discovery problems, as it admits multiple valid perspectives, operates under non-stationary market conditions, and involves noisy, continuous performance signals. In this work, we propose Multi-Agent Fundamental Analysis with Symbolic Adaptive learning (MUFASA), a hierarchical multi-agent framework for symbolic discovery in finance. MUFASA introduces (1) disentangled equation discovery via specialized agents representing distinct valuation perspectives, (2) a meta-coordinator that performs hierarchical-level reasoning over market context information, and (3) a memory mechanism that reasons over statistical performance summaries (e.g., accuracy, stability, and tail risk) to guide learning under noisy feedback. Experiments across datasets from multiple countries show that MUFASA achieves state-of-the-art performance on the valuation task compared to classical finance methods, financial large language models, and SR approaches, while simultaneously producing interpretable equations, which we share with the community. We also make publicly available the distilled learnings across evolution iterations and context-dependent strategy weights, which might offer useful insights for future research on financial fundamental analysis.

Figures & tables

Figure 1: Overview of the challenges in financial SR across different levels of the self-evolving loop.

Figure 2: Overview of the mufasa framework. mufasa uses disentangled multi-agent systems to encourage symbolic expression diversity. A meta-coordinator agent reasons over the non-stationary environment to integrate these expressions. Each agent maintains a memory to identify past statistical patterns.

Category	What is stored	Why
Accuracy	Mean MAPE, Median MAPE	Captures overall predictive accuracy while reducing sensitivity to outliers and skewed observations.
Stability	Standard Deviation, IQR, Coefficient of Variation	Measures whether performance is consistent or highly variable across samples or time periods.
Tail Risk	$p90/p95$ Error, Worst-Decile Mean	Exposes extreme failure modes that are often hidden by average performance metrics.
Complexity	Variable + Operator Count, Prediction Coverage	Reflects interpretability and numerical reliability of the expression in practical use.
Bias	Mean Signed Percentage Error (MSPE)	Detects systematic over- or under-prediction across observations rather than isolated errors.
Ranking	Spearman Rank Correlation	Captures whether the expression preserves cross-sectional ordering beyond absolute scale accuracy.

Table 1: Statistical information collected by mufasa to enable learning under continuous feedback.

Model	S&P 500	Russell 2000	STOXX 600	FTSE APAC	CSI 300	All Data	Avg $\Delta$
Machine Learning Based Methods
Random Forest	0.4812	0.6551	0.7490	0.8436	0.5605	0.6579	0.1498
HistGBM	0.5916	0.8121	0.9774	1.3771	0.6041	0.8725	0.3644
NeuralNet	0.6130	1.0302	0.8963	1.5292	0.5242	0.9186	0.4105
Financial LLMs
Fino1 ( Qian and others 2025 )	1.0230	2.1244	1.0958	1.2587	1.3388	1.3681	0.8600

Table 2: Performance comparison. The best baselines are underlined, and the best results are bolded.

Model Variant	S&P 500	Russell 2000	STOXX 600	FTSE APAC	CSI 300
S.P Agent	0.4971	0.8994	0.7608	0.6095	0.5928
M.P (Equal Weights)	0.4652	0.8768	0.5448	0.6442	0.5309
M.P (No Stats Memory)	0.4702	0.7525	0.5398	0.5852	0.4852
M.P (Best Single Agent)	0.4676	1.9173	0.5256	0.5833	0.4739
mufasa (Ours)	0.4465	0.5718	0.5064	0.5814	0.4343

Table 3: Ablation study on perspective variant. S.P and M.P denote the single-/multiple perspective, respectively. Best results are bolded, second best are underlined.

Model	Equation	Theory Equation	Theory
Fino1	$\dfrac{EV/EBITDA\cdot(1+g_{EPS}/100)}{EV/EBITDA_{mkt}\cdot EBITDA}$	-	-
Fin-R1	$EPS_{TTM}\cdot PE$	$EPS\cdot PE$	Earnings Multiple
PySR	$\sqrt{1.79\cdot\|BVPS\|\cdot\sqrt{\sqrt{\|Tax\|+Tax}\cdot\left\|EPS\cdot e^{2.43}-e^{\sqrt{Y_{30}}}+\left(e^{PB_{mkt,med}}+EPS\right)\cdot 4.23\right\|}}$	-	-
FunSearch	$0.40\cdot EBITDA_{ps}+0.30\cdot Revenue_{ps}+0.20\cdot ROE+0.10\cdot PE$	-	-
LLM-SR	$0.01\cdot PE-0.03\cdot\dfrac{EV}{EBIT}-0.04\cdot\dfrac{EV}{EBITDA}+0.58\cdot PB+13.99\cdot NI_{ps}-0.01\cdot Revenue_{ps}$	$R_{i}=\alpha+\beta_{1}X_{1,i}+\beta_{2}X_{2,i}+\cdots$	Linear Factor
mufasa agents

Table 4: Learnt equations vs. related valuation forms in finance literature, for the S&P500 dataset.

Panel of Figure 3 — Figure 3: Best error trajectories over the self-evolving iterations for each perspective agent.

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Baseline	S&P 500	Russell 2000	STOXX 600	FTSE Asia	CSI 300
Financial LLMs
Fino1	-0.7283***	-0.4515***	-0.3067***	-0.7925***	-0.3408***
Fin-R1	-0.1207***	-0.0375***	-0.1801***	-0.5919***	-0.4835***
Financial Valuation
P/E	-0.1628***	-0.0371***	-0.0691***	-0.3519***	-0.1158***
EV/EBITDA	-0.1174***	-0.1622***	-0.0802***	-0.2941***	-0.0933***

Appendix

Table 5: Diebold–Mariano (DM) tests comparing mufasa against valuation and learning-based baselines. Entries report mufasa minus baseline in decimal form. Negative values indicate lower error (better performance). Significance: ***

p<0.001

, **

p<0.01

, *

p<0.05

Model	Equation	Theory Equation	Theory
Fino1	$\dfrac{EV/EBITDA\cdot(1+g_{EPS}/100)}{EV/EBITDA_{mkt}\cdot EBITDA}$	-	-
Fin-R1	$EPS_{TTM}\cdot PE$	$EPS\cdot PE$	Earnings Multiple
PySR	$(PB_{mkt,mean}+0.16)\cdot\left(\sqrt{\|BVPS\|+\|e^{0.98}-BVPS\|}+2.09-\dfrac{BVPS}{-0.55}-2.09\right)-0.29$	-	-
FunSearch	$2\cdot BVPS+10\cdot NI_{ps}$	-	-
LLM-SR	$0.11\cdot(PE-Y_{1})-0.01\cdot Y_{2}+0.20\cdot NI$	$R_{i}=\alpha+\beta_{1}X_{1,i}+\beta_{2}X_{2,i}+\cdots$	Linear Factor
mufasa agents

Appendix

Table 6: Learnt equations for the Russell 2000 dataset.

Model	Equation	Theory Equation	Theory
Fino1	$\dfrac{EV/EBITDA\cdot(1+g_{EPS}/100)}{EV/EBITDA_{mkt}\cdot EBITDA}$	-	-
Fin-R1	$EPS_{TTM}\cdot PE$	$EPS\cdot PE$	Earnings Multiple
PySR	$\left\|\dfrac{\left((-0.99+Div-(EBITDA+R\&D+\|NI\|)-NI)\cdot PB_{mkt,std}\right)+\left(EBITDA-(0.30\cdot Rev+IntInc)\right)}{Shares}\right\|+0.68$	-	-
FunSearch	$0.25\cdot EBITDA_{ps}+0.35\cdot OCF_{ps}+0.20\cdot ROE+0.20\cdot BVPS_{lag4}$	-	-
LLM-SR	$-0.01\cdot PE+0.37\cdot PB+0.22\cdot(EV/EBIT)+0.36\cdot PB$	$R_{i}=\alpha+\beta_{1}X_{1,i}+\beta_{2}X_{2,i}+\cdots$	Linear Factor
mufasa agents

Appendix

Table 7: Learnt equations for the STOXX 600 dataset.

Model	Equation	Theory Equation	Theory
Fino1	$\dfrac{EV/EBITDA\cdot(1+g_{EPS}/100)}{EV/EBITDA_{mkt}\cdot EBITDA}$	-	-
Fin-R1	$EPS_{TTM}\cdot PE$	$EPS\cdot PE$	Earnings Multiple
PySR	$\dfrac{1}{\sqrt{e^{-1.27}}}\cdot\log\left(\left\|\dfrac{BVPS\cdot Debt_{ps}}{-2.91\times 10^{-3}-\dfrac{Debt_{ps}-InterestExpense}{R\&D+PB_{mkt,mean}}}\cdot\dfrac{1}{\log(PB_{mkt,mean})}\right\|+1.00\right)$	-	-
FunSearch	$0.20\cdot EBITDA_{ps}+0.15\cdot BVPS_{lag4}+0.10\cdot ROE_{lag8}+0.10\cdot EBIT_{ps}+0.10\cdot EPS_{lag1}+0.05\cdot\dfrac{EV}{EBIT}$	-	-
LLM-SR	$5.86\times 10^{-4}\cdot(EBIT-InterestExpense)-0.21\cdot R\&D-4.00\times 10^{-3}\cdot GrossProfit+0.76\cdot BVPS$	$R_{i}=\alpha+\beta_{1}X_{1,i}+\beta_{2}X_{2,i}+\cdots$	Linear Factor
mufasa agents

Appendix

Table 8: Learnt equations for the FTSE Asia ex Japan dataset.

Model	Equation	Theory Equation	Theory
Fino1	$\dfrac{EV/EBITDA\cdot(1+g_{EPS}/100)}{EV/EBITDA_{mkt}\cdot EBITDA}$	-	-
Fin-R1	$EPS_{TTM}\cdot PE$	$EPS\cdot PE$	Earnings Multiple
PySR	$\sqrt{\left\|\dfrac{PB_{mkt,mean}\cdot 0.10\cdot BVPS}{EBITDA-0.03+0.17\cdot EPS}+0.48+2.16\cdot Debt_{ps}\right\|+\left\|\dfrac{BVPS}{0.06-GrossProfit}\right\|}+EPS$	-	-
FunSearch	$2\cdot BVPS+10\cdot NI_{ps}$	-	-
LLM-SR	$-0.02\cdot Debt_{ps}+1.53\times 10^{-4}\cdot g_{Revenue}+0.54\cdot EV/Sales+0.52\cdot Revenue_{ps}$	$R_{i}=\alpha+\beta_{1}X_{1,i}+\beta_{2}X_{2,i}+\cdots$	Linear Factor
mufasa agents

Appendix

Table 9: Learnt equations for the CSI 300 dataset.

Panel of Figure 4 — Figure 4: Learnt agent weighting across company sectors and market regimes for all datasets.

Model Variant	S&P 500	Russell 2000	STOXX 600	FTSE APAC	CSI 300
Binary Memory (Pass/Fail Signals Only)
Single-Perspective Agent	0.5699	0.7527	0.7220	0.6095	0.5735
Multi-Agent (Equal Weights)	0.5466	1.0459	0.6454	0.7088	0.5599
Multi-Agent (Best Single Agent)	0.5127	1.5160	0.6212	0.6083	0.5761
Multi-Agent (Meta-Coordinator)	0.4646	0.6445	0.5759	0.6086	0.5070
MAPE-Only Memory (No Additional Statistics)

Appendix

Table 10: Extended ablation study. We compare strategies under different memory settings.

Panel of Figure 5 — Figure 5: Predicted vs. True log prices across Symbolic Regression models on the S&P 500 dataset.

Figure 6: Error distribution across sectors. The center lines show median errors, while the top and bottom edges of the box plots show the 25 th and 75 th percentile errors, respectively. Lower is better.

Model	25 th pct. ( $\downarrow$ )	Median ( $\downarrow$ )	75 th pct. ( $\downarrow$ )
PySR	0.4103	0.6249	0.8322
FunSearch	0.6136	0.7500	0.8283
LLM-SR	0.2663	0.4475	0.6086
mufasa	0.1725	0.3382	0.5556

Appendix

Figure 7: Aggregate APE distributions.

Figure 8: Mean Signed Percentage Error across valuation quartiles (Q1: Cheap to Q4: Expensive).

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