CosmosAlpha: Multi-Relational Graph Search with Pareto-Guided Exploration for LLM-Driven Alpha Mining

Zhan-He Wang; Zi-Yang Lang; Yi-Yang Li; Qing-Yu Lan; Yun-Song Piao

q-fin.CPNov 3, 2026

CosmosAlpha: Multi-Relational Graph Search with Pareto-Guided Exploration for LLM-Driven Alpha Mining

Authors: Zhan-He Wang, Zi-Yang Lang, Yi-Yang Li, Qing-Yu Lan, Yun-Song Piao

Organizations: Artificial Intelligence and Quantitative Finance Laboratory, School of Physical Sciences, University of Chinese Academy of Sciences · School of Physics and Astronomy, Shanghai Jiao Tong University · School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS

Abstract

Discovering predictive alpha factors from noisy financial data is a fundamental yet challenging problem in quantitative finance. LLM-driven formulaic alpha mining offers an attractive paradigm by combining interpretable symbolic expressions with iterative generation and refinement guided by quantitative feedback. However, existing generation-centric and tree-based search strategies primarily organize factors through generation lineage, leaving structural and statistical relationships across search branches underutilized. Consequently, information remains localized along parent--child trajectories, which can confine exploration to redundant regions. Moreover, effective factor discovery must account for multiple distinct objectives that cannot be adequately captured by a single search criterion. We introduce CosmosAlpha, a graph-based LLM factor-mining framework that represents discovered factors as a multi-relational graph encoding generation lineage, expression-structure similarity, and cross-sectional exposure correlation. A Graph Flow mechanism propagates search utilities across the graph, allowing each factor to be assessed using relational evidence from nearby factors rather than in isolation. Pareto-guided selection jointly considers quality, fertility and diversity, explicitly modeling their trade-offs within a multi-objective search framework. Across CSI 300 and CSI 500, CosmosAlpha-Graph achieves the best mean rank over seven predictive and portfolio metrics and outperforms its controlled CosmosAlpha-MCTS counterpart on every reported metric, showing a consistent advantage for relational graph search in LLM-driven factor mining. The source code is available at https://github.com/wzhmtldswz/CosmosAlpha

Figures & tables

Figure 1: Overview of CosmosAlpha. (1) Evaluated factors form a pool-level multi-relational graph with generation, structure, and exposure-correlation edges. (2) Graph Flow propagates Quality, Fertility, and Diversity, after which Pareto-guided selection chooses parents for LLM-driven mutation and evaluated children return to the graph. (3) The fixed factor pool is preprocessed and integrated with LightGBM for common predictive and portfolio evaluation.

	Predictive Performance				Portfolio Performance			Overall
Method	IC $\uparrow$	ICIR $\uparrow$	RankIC $\uparrow$	RankICIR $\uparrow$	ARR (%) $\uparrow$	IR $\uparrow$	MDD (%) $\uparrow$	Mean rank $\downarrow$
Alpha158	0.0320	0.3474	0.0479	0.5668	6.32	0.3945	-29.73	3.86
GP	0.0231	0.3098	0.0300	0.4483	4.32	0.2215	-42.45	9.71
AlphaGen	0.0301	0.3128	0.0452	0.5461	4.25	0.2490	-32.47	7.29
AlphaForge	0.0304	0.3404	0.0469	0.5615	6.88	0.4164	-25.41	3.86
AlphaSAGE	0.0243	0.2574	0.0432	0.4750	6.57	0.4007	-27.50	6.57

Table 1: Performance on CSI 300. All metrics are computed on the held-out test set after LightGBM integration of each method’s factor pool. ARR and signed MDD are percentages; the remaining metrics are on their native scales. The final column averages ranks over the seven metrics (rank 1 is best; ties receive average ranks). Best and second-best results in each column are bolded and underlined, respectively.

	Predictive Performance				Portfolio Performance			Overall
Method	IC $\uparrow$	ICIR $\uparrow$	RankIC $\uparrow$	RankICIR $\uparrow$	ARR (%) $\uparrow$	IR $\uparrow$	MDD (%) $\uparrow$	Mean rank $\downarrow$
Alpha158	0.0339	0.3927	0.0618	0.7898	11.07	0.5856	-28.41	4.43
GP	0.0213	0.2752	0.0438	0.6092	12.52	0.6101	-38.06	8.57
AlphaGen	0.0296	0.3613	0.0573	0.7147	11.82	0.6077	-34.26	6.43
AlphaForge	0.0284	0.3129	0.0590	0.7076	11.08	0.5758	-28.70	6.64
AlphaSAGE	0.0245	0.2652	0.0531	0.6394	10.51	0.5533	-27.69	8.71

Table 2: Performance on CSI 500 under the protocol of Table 1 . All rows report final results. The final column averages ranks over the seven metric columns (rank 1 is best; ties receive average ranks). Best and second-best results in each column are bolded and underlined, respectively; for signed MDD, a value closer to zero is better.

	Predictive Performance				Portfolio Performance
Variant	IC $\uparrow$	ICIR $\uparrow$	RankIC $\uparrow$	RankICIR $\uparrow$	ARR (%) $\uparrow$	IR $\uparrow$	MDD (%) $\uparrow$
Full Graph: $(Q,F,D)$ ; relations $(G,S,C)$	0.0324	0.3441	0.0494	0.5670	8.44	0.5332	-25.07
w/o Flow: $\gamma=0$	0.0278	0.2929	0.0436	0.4937	5.90	0.3541	-28.73
Quality scalarization: intrinsic quality	0.0284	0.3107	0.0452	0.5117	5.80	0.3539	-27.13
Flow scalarization: normalized $(Q,F,D)$	0.0289	0.2987	0.0474	0.5201	5.80	0.3486	-26.86
w/o Fertility: Pareto $(Q,D)$	0.0297	0.3181	0.0456	0.5286	6.71	0.4132	-26.35

Table 3: Ablation study on CSI 300 after LightGBM integration. Quality scalarization changes the intrinsic-quality archive, reference-set construction, and Fertility computation; Flow scalarization changes parent ranking after Graph Flow. Remaining variants remove the named utility or relation. Higher is better for all seven metrics, including signed MDD; bold indicates the best result in each column.

Figure 2: Search-state trajectories of CosmosAlpha-Graph and CosmosAlpha-MCTS over cumulative factor-generation steps. From left to right, the panels show node-level Quality, Fertility, and AverageDistance. Each point reports these quantities for the newly generated factor at the aligned diagnostic factor-generation index. Panels use native vertical scales.

Appendix figures & tables18 assets

Supplementary material from the paper’s appendix.

Appendix

Setting	Value	Scope or provenance
Universes	CSI 300 and CSI 500 with historical membership	Shared across methods
Frequency and prices	Daily; post-adjusted prices	Shared data protocol
Rolling lookback start	January 4, 2010	Supports lagged operators
Mining and training	April 1, 2010–May 31, 2019	Search feedback and LightGBM fitting
Validation	June 1, 2019–December 31, 2020	LightGBM early stopping only
Test	January 1, 2021–December 31, 2025	Final prediction and portfolio evaluation only

Appendix

Table 4: Shared data, preprocessing, and factor-evaluation configuration.

Setting	Value	Role
Initial Graph factors	$2$	LLM-generated factors evaluated before the first expansion round
Parents per round	Up to $4$	Parallel expansion width
Expansion cap per node	$5$ attempts	Prevents repeated use of one parent
Child proposals per attempt	Up to $2$	Parent-grounded mutations
Factor-pool target	Approximately $150$ evaluable factors	Common downstream budget across automated methods
Maximum expression depth	$15$	Expression-complexity constraint

Appendix

Table 5: Search and expression-generation settings for CosmosAlpha-Graph.

Setting	Value	Role
Structure edge threshold	$0.20$	Minimum Jaccard similarity
Structure neighbors	Top- $30$ per node	Local structure neighborhood before union symmetrization
Correlation edge threshold	$\|C_{ij}\|\geq 0.10$	Minimum exposure-correlation strength
Correlation neighbors	Top- $30$ per node	Local correlation neighborhood before union symmetrization
Correlation daily validity	$100$ stocks and $80\%$ coverage	Reliable daily cross-sectional correlation
Correlation date validity	$80\%$ of the evaluation calendar and $80\%$ of overlapping dates	Reliable pairwise relation

Appendix

Table 6: Graph relation and neighborhood settings.

Setting	Value	Role
$\|\overline{\mathrm{RankIC}}\|$ anchors	$[0,0.05]$	Quality and hypervolume normalization
RankIC standard-deviation anchors	$[0.05,0.09]$ , reversed	Quality and hypervolume normalization
Top-20% return anchors	$[0,8\times 10^{-4}]$	Quality and hypervolume normalization
Hypervolume reference point	$(0,0,0)$	Quality Pareto Archive
Fertility history	Top- $3$ attempt outcomes	Productive-potential aggregation
Relation weights	$1/3$ each	Equal generation, structure, and correlation contribution

Appendix

Table 7: Quality, Fertility, Graph Flow, and parent-selection settings.

Use	Model identifier	Temperature	Reasoning control
Main	DeepSeek-V4-Flash	$0.0$	Maximum
Sensitivity	GPT-5.6-Sol	$0.0$	xhigh
Sensitivity	Kimi K3	$1.0$	Maximum

Appendix

Table 8: LLM settings used in the main and backbone-sensitivity experiments.

Component	Setting	Value
LightGBM	Objective	Mean squared error
LightGBM	Learning rate; boosting cap; early stopping	$0.2$ ; $1000$ rounds; $50$ rounds
LightGBM	Column and row subsampling	$0.8879$ and $0.8789$
LightGBM	$L_{1}$ and $L_{2}$ penalties	$205.6999$ and $580.9768$
LightGBM	Maximum depth; leaves	$8$ ; $210$
Portfolio	Initial account; invested fraction	$10^{8}$ ; $0.95$

Appendix

Table 9: Shared downstream LightGBM and portfolio configuration.

Setting	Value	Provenance
Quality-scalar archive capacity	$20$ factors	Fixed ablation design
Flow Quality interval	$[0.44,0.71]$	Repeated Graph-run statistics
Flow Fertility interval	$[0,0.004]$	Repeated Graph-run statistics
Flow AverageDistance interval	$[0.60,0.86]$	Repeated Graph-run statistics
Flow scalar weights	$1/3$ each	Equal-weight control

Appendix

Table 10: Parameters used only by the scalarization ablations.

Template	Version	Search stage	Structured output
Hypothesis	2.3.0	Graph initialization and expansion; MCTS root and expansion; Chain	One testable hypothesis
Factor design	2.2.0	Graph initialization; Chain	One or two semantic designs
Graph factor design	2.2.0	Graph expansion	Parent-grounded mutations
MCTS factor design	2.3.0	MCTS root and expansion	Initial designs or parent-grounded refinements
Factor expression	2.1.0	Shared	One DSL expression per design
Expression repair	2.1.0	Shared, when validation fails	One corrected DSL expression

Appendix

Table 11: Versioned prompt routes used for candidate generation.

Placeholder	Runtime content
context_json	Research goal, market, stock universe, frequency, available fields, search constraints, and bounded prior search summaries. For Graph expansion, the search constraint carries the selected parent’s current guidance.
request_json	The current hypothesis and stage-specific request. A design request includes the universe, frequency, generation limit, and relevant parent reference. MCTS expansion additionally supplies the parent expression, scores, and target dimension. An expression request contains one semantic design and expression limits; a repair request contains the previous expression and its deterministic validation issues.
prompt_view_json	The runtime capability view: admissible raw fields, canonical operators and signatures, supported windows, and the bounded context permitted at that stage.

Appendix

Table 12: Runtime placeholders appearing in the prompt templates.

DSL field	Symbol	Definition	Scale or natural domain
open	$O_{i,t}$	Opening price on trading day $t$	Post-adjusted price; positive on eligible rows
high	$H_{i,t}$	Intraday highest price	Post-adjusted price; positive on eligible rows
low	$L_{i,t}$	Intraday lowest price	Post-adjusted price; positive on eligible rows
close	$P_{i,t}$	Closing price	Post-adjusted price; positive on eligible rows
volume	$V_{i,t}$	Daily trading volume	Source volume unit; nonnegative
vwap	$P^{\mathrm{VWAP}}_{i,t}$	Volume-weighted average price	Same adjusted-price scale

Appendix

Table 13: Fields admissible in factor expressions. All fields are observed at daily frequency. The domain column describes the natural data domain; entries may also be missing.

Variable	Symbol	Definition	Role and scale
industry_id	$g_{i,t}$	Point-in-time industry classification	Categorical operator and preprocessing context
log_mkt_cap	$m_{i,t}$	Natural logarithm of point-in-time market capitalization	Real-valued preprocessing exposure
ret20	$r^{(20)}_{i,t}$	Close-to-close return over the trailing 20 trading days through $t$	Decimal preprocessing exposure
turn20	$\bar{\tau}^{(20)}_{i,t}$	Mean daily turnover over the trailing 20 trading days	Nonnegative preprocessing exposure
vol20	$\sigma^{(20)}_{i,t}$	Sample standard deviation of daily returns over the trailing 20 trading days	Nonnegative preprocessing exposure
Forward return	$y_{i,t}$	One-trading-day forward close-to-close return	Real-valued prediction target

Appendix

Table 14: Context and target variables excluded from factor expressions. All variables are aligned daily and constructed point-in-time.

Signature	Scope	Definition and numerical behavior	Comm.
Non-windowed operators
add(x,y)	Elementwise	$x+y$ for finite inputs	Yes
sub(x,y)	Elementwise	$x-y$ for finite inputs	No
mul(x,y)	Elementwise	$xy$ for finite inputs	Yes
div(x,y)	Elementwise	$x/y$ ; missing when $\|y\|\leq\varepsilon$	No
abs(x)	Elementwise	$\|x\|$	No

Appendix

Table 15: Complete operator catalog. Here

\operatorname{rank}_{t}

is the same-day cross-sectional percentile rank over eligible finite stocks, with average ranks for ties;

\varepsilon=10^{-12}

; and every window argument is an integer

w\in\{5,10,20\}

measured in trading days.

Constraint	Enforced rule
Data frequency	Daily ( 1d ) for every field and operator
Allowed windows	Final integer literal in $\{5,10,20\}$ trading days
Expression length	At most 512 characters at the parser boundary
AST depth	Root counted at depth 1; the run-specific cap appears in Table 5
Operator count	At most 32 call nodes
Field count	At most 6 distinct expression fields and at least 1 field

Appendix

Table 16: Expression-space and validation constraints. Method-specific search budgets and repair limits are reported in Appendix C .

Case	Graph ID	Round/ $d$	$\|\overline{\mathrm{RankIC}}\|$ $\uparrow$	$\sigma(\mathrm{RankIC})$ $\downarrow$	Aligned Top-20 (bp/day) $\uparrow$	AverageDistance $\uparrow$
E1	63d83d	18/5	0.058165	0.073829	13.10	0.5092
E2	835f66	20/7	0.005304	0.057119	4.93	0.8182
E3	1b4d31	21/4	0.054396	0.072582	12.79	0.5040
E4	5a02af	19/7	0.017627	0.063906	3.85	0.8535

Appendix

Table 17: Training-period diagnostics for the representative CSI 300 Graph factors. Direction-aligned Top-20 return is reported in basis points (bp) per trading day.


ID	Round/ $d$	Canonical DSL expression
a6f90c	Init./0	mul(mul(sub(close,low),inv(sub(high,low))),ts_rank(volume,20))
ed54a5	Init./0	rank(mul(sub(div(close,vwap),1),div(turn,div(ts_sum(turn,20),20))))
65260c	0/1	mul(div(turn,div(ts_sum(turn,20),20)),div(sub(vwap,close),sub(high,low)))
4060a1	1/1	rank(mul(div(sub(close,vwap),sub(high,low)),ts_rank(volume,20)))
19f0cc	2/3	mul(div(sub(close,open),open),ts_zscore(free_turn,20))

Appendix

Table 18: Canonical expressions for all 44 factors in terminal search Pareto front 1. The ID is the six-character prefix used in the lineage figure; Round is the generation round and

d

is generation depth.

Figure 3: Factor lineage and terminal search Pareto-front assignments for the finalized CSI 300 Graph run. Node fill color marks the front; the legend reports the number of nodes in each front. Edges show direct generation links, and each node lists its shortened ID, generation depth

d

, and front index.

Mode	LLM	Predictive Performance				Portfolio Performance
		IC $\uparrow$	ICIR $\uparrow$	RankIC $\uparrow$	RankICIR $\uparrow$	ARR (%) $\uparrow$	IR $\uparrow$	MDD (%) $\uparrow$
Chain	DeepSeek-V4-Flash	0.0241	0.2731	0.0373	0.4260	3.94	0.2223	-35.33
	GPT-5.6-Sol	0.0280	0.2892	0.0411	0.4519	4.16	0.2599	-29.11
	Kimi K3	0.0299	0.3156	0.0401	0.3932	4.28	0.2810	-33.60
MCTS	DeepSeek-V4-Flash	0.0281	0.3238	0.0409	0.5145	5.68	0.3296	-31.56
	GPT-5.6-Sol	0.0259	0.2868	0.0419	0.4590	5.95	0.3361	-33.81

Appendix

Table 19: LLM and search-mode sensitivity on CSI 300 under the main factor-pool integration protocol. ARR and signed MDD are percentages; higher values are better for every displayed metric because a signed MDD closer to zero denotes a smaller drawdown.

Mode	Run	Predictive Performance				Portfolio Performance
		IC $\uparrow$	ICIR $\uparrow$	RankIC $\uparrow$	RankICIR $\uparrow$	ARR (%) $\uparrow$	IR $\uparrow$	MDD (%) $\uparrow$
Chain	Run 1	0.0230	0.2606	0.0369	0.4087	3.49	0.1839	-39.27
	Run 2	0.0234	0.2732	0.0371	0.4261	4.06	0.2399	-33.13
	Run 3	0.0242	0.2912	0.0352	0.4332	4.48	0.2631	-36.60
	Mean	0.0235	0.2750	0.0364	0.4227	4.01	0.2290	-36.33
	Std.	0.0005	0.0126	0.0009	0.0103	0.41	0.0332	2.51

Appendix

Table 20: Three-run stability of CosmosAlpha-Graph, CosmosAlpha-MCTS, and CosmosAlpha-Chain with DeepSeek-V4-Flash on CSI 300 under the main integration protocol. The table uses the same predictive and portfolio metric groups and metric directions as Tables 1 and 2 . ARR and signed MDD are percentages. The Mean and Std. rows are computed across the three independent runs for each method; Std. uses the population standard deviation.

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Automated alpha mining has increasingly adopted large language model (LLM) agents for factor generation and iterative discovery. However, existing LLM-based systems often delegate both factor construction and search decisions to the agent itself, without an explicit exploration space or a principled mechanism for navigating that space. As a result, exploration remains largely implicit and difficult to control or optimize systematically. We introduce AlphaSchema, which constructs and explores a structured space of trading semantics for alpha mining. Each point in this space is a schema plan composed of Event, Context, Qualities, Direction, and Output, specifying the semantics of a candidate factor before implementation. AlphaSchema decouples exploration from implementation: an LLM translates selected schema plans into executable factors, while evaluated rewards are accumulated to learn a surrogate model over the semantic space. An iterative selection mechanism uses this model to balance global exploration, surrogate-guided exploitation, and local mutation. Experiments on the Chinese stock market show that AlphaSchema discovers factor pools with strong predictive and portfolio performance. Further analyses show that the semantic search process navigates diverse regions while increasingly allocating evaluations toward high-reward regions, and that implementations of the same schema plans by different LLMs exhibit comparable predictive quality, suggesting that alpha mining quality is largely robust to the choice of LLM within our framework.

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