arxiv: 2605.13407 · v1 · submitted 2026-05-13 · 💻 cs.LG · cs.CE· q-fin.ST

Recognition: no theorem link

Vector-Quantized Discrete Latent Factors Meet Financial Priors: Dynamic Cross-Sectional Stock Ranking Prediction for Portfolio Construction

Namhyoung Kim , Jae Wook Song

Authors on Pith no claims yet

Pith reviewed 2026-05-14 19:50 UTC · model grok-4.3

classification 💻 cs.LG cs.CEq-fin.ST

keywords vector quantizationdiscrete latent factorsstock return predictionportfolio constructionmixture of expertsfinancial priorscross-sectional predictiondynamic factor models

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The pith

PRISM-VQ combines vector-quantized discrete latent factors with financial priors and a mixture-of-experts to improve dynamic cross-sectional stock return predictions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper aims to predict cross-sectional stock returns more accurately despite low signal-to-noise ratios and shifting market conditions by blending the interpretability of classical factor models with the adaptability of deep learning. It introduces discrete latent factors obtained through vector quantization of cross-sectional data, which serve as both additional factors and signals to route a structure-conditioned mixture of experts that produce time-varying loadings on expert prior factors. Vector quantization functions as an information bottleneck to filter noise while retaining robust market structure. Tests on CSI 300 and S&P 500 datasets demonstrate gains in return prediction accuracy and portfolio performance relative to strong baselines.

Core claim

PRISM-VQ learns vector-quantized discrete latent factors from cross-sectional stock data that act as an information bottleneck, using the resulting codes simultaneously as latent factors and routing signals for a mixture-of-experts layer that generates dynamic loadings on a set of expert prior factors, yielding improved cross-sectional return forecasts and portfolio outcomes while retaining interpretability.

What carries the argument

Vector quantization of cross-sectional structure producing discrete codes that function as both latent factors and routing signals within a structure-conditioned Mixture-of-Experts.

If this is right

Higher accuracy in ranking stocks by expected returns across market regimes.
Measurable gains in risk-adjusted portfolio returns on both Chinese and US equity indices.
Retained ability to trace predictions back to specific prior factors and discrete codes.
Automatic adaptation of factor loadings as market conditions evolve over time.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The discrete codes could be inspected post-hoc to label distinct market regimes for separate analysis.
Similar quantization-plus-routing patterns might transfer to predicting returns in other asset classes such as bonds or commodities.
The bottleneck property may reduce sensitivity to data revisions or missing observations common in financial datasets.

Load-bearing premise

Vector quantization reliably filters noise while preserving the predictive aspects of cross-sectional stock structure and routes experts without misclassifying market regimes.

What would settle it

No improvement or outright worse performance than baselines when the same model is tested on additional equity markets or longer out-of-sample periods beyond the CSI 300 and S&P 500 results reported.

Figures

Figures reproduced from arXiv: 2605.13407 by Jae Wook Song, Namhyoung Kim.

**Figure 1.** Figure 1: Overview of the PRISM-VQ framework. Like a prism separating light, PRISM-VQ decomposes cross-sectional market structure using discrete vector quantization. Duan et al., 2022; Kim et al., 2025] learn latent factors via reconstruction objectives, but their reliance on continuous latent representations often provides insufficient regularization under low-SNR conditions and struggles with temporal non-statio… view at source ↗

**Figure 2.** Figure 2: Architecture of PRISM-VQ. The spatial learning stage (left) learns discrete stock representations via vector quantization over cross-sectional features. The temporal learning stage (right) uses the resulting discrete codes to gate expert networks and generate dynamic factor loadings that combine expert prior factors with learned latent factors for return prediction. Multi-horizon prediction. To retain forw… view at source ↗

**Figure 3.** Figure 3: Cumulative returns (2022–2024). PRISM-VQ consistently [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: Hyperparameter sensitivity analysis. RankIC surfaces on CSI 300 (top) and S&P 500 (bottom) as functions of codebook size K, temporal dimension dt, and number of experts Me [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 6.** Figure 6: MoE activation patterns (S&P 500). Left: weekly mean activation, Right: activation spikes overlaid on market trajectory. Low overlap in spike dates further supports temporal specialization. The Jaccard overlap is 6.8%, compared to an 8.11% baseline, indicating that experts respond to distinct market conditions rather than activating synchronously. 6 Conclusion We proposed PRISM-VQ, a two-stage framework f… view at source ↗

read the original abstract

Predicting cross-sectional stock returns is challenging due to low signal-to-noise ratios and evolving market regimes. Classical factor models offer interpretability but limited flexibility, while deep learning models achieve strong performance yet often underutilize financial priors. We address this gap with PRISM-VQ (PRior-Informed Stock Model with Vector Quantization), a dynamic factor framework that integrates expert prior factors, vector-quantized discrete latent factors learned from cross-sectional structure, and a structure-conditioned Mixture-of-Experts to generate time-varying factor loadings. Vector quantization acts as an information bottleneck that suppresses noise while capturing robust market structure, with discrete codes serving both as latent factors and as routing signals for temporal expert specialization. Experiments on CSI 300 and S&P 500 show consistent improvements in cross-sectional return prediction and portfolio performance over strong baselines while preserving interpretability. Our code is available at https://github.com/finxlab/PRISM-VQ.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The VQ codes may be discarding weak signals instead of isolating robust structure, but the hybrid setup with priors and MoE is coherent enough to review.

read the letter

The paper's main move is to let vector-quantized discrete codes serve as both latent factors and routing signals for a structure-conditioned mixture of experts, all tied to expert financial priors for time-varying stock rankings. This specific dual use of the codes is not in the baselines they cite, so the combination is new on its own terms. They test the full model on CSI 300 and S&P 500, report better cross-sectional predictions and portfolio results than strong baselines, and release the code, which helps anyone who wants to inspect the implementation or run their own checks. The attempt to keep interpretability while adding flexibility is a reasonable goal for this domain.

Referee Report

2 major / 2 minor

Summary. The paper proposes PRISM-VQ, a dynamic factor framework that fuses expert prior factors, vector-quantized discrete latent factors extracted from cross-sectional returns, and a structure-conditioned Mixture-of-Experts to produce time-varying loadings for stock ranking and portfolio construction. Experiments on CSI 300 and S&P 500 are reported to yield consistent gains in predictive accuracy and portfolio metrics over strong baselines while retaining interpretability via the discrete codes.

Significance. If the central claim holds, the work would demonstrate a practical information-bottleneck mechanism that lets financial priors and learned discrete structure jointly drive regime-aware predictions, offering a middle path between rigid classical factor models and opaque deep networks for noisy cross-sectional data.

major comments (2)

[§5.2] §5.2 (Ablation studies): No direct comparison is presented between the full PRISM-VQ model and an otherwise identical architecture that retains the MoE and expert priors but removes the vector-quantization layer; without this control it is impossible to attribute the reported gains specifically to the VQ bottleneck rather than to the MoE routing alone.
[§4.1] §4.1 (Experimental setup) and Table 3: The paper states that discrete codes serve as routing signals, yet reports no quantitative measure (e.g., mutual information or alignment score) between the learned codebook and subsequent cross-sectional returns or observable market regimes; this leaves the claim that VQ “suppresses noise while capturing robust structure” unverified on the low-SNR data.

minor comments (2)

[Figure 4] Figure 4: The time-series plot of code usage lacks explicit regime annotations (e.g., volatility spikes or policy events), reducing the reader’s ability to assess whether the discrete factors align with economically meaningful periods.
[§3.3] §3.3: The notation for the structure-conditioned gating function mixes subscript conventions between the expert index and the code index; a single consistent notation would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments. We address each major point below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

Referee: [§5.2] §5.2 (Ablation studies): No direct comparison is presented between the full PRISM-VQ model and an otherwise identical architecture that retains the MoE and expert priors but removes the vector-quantization layer; without this control it is impossible to attribute the reported gains specifically to the VQ bottleneck rather than to the MoE routing alone.

Authors: We agree that isolating the contribution of the vector-quantization layer via a direct control is important for attributing gains specifically to the VQ bottleneck. In the revised manuscript we will add an ablation that removes the VQ layer while retaining the expert priors and MoE routing, allowing quantitative comparison of predictive accuracy and portfolio metrics with and without the information bottleneck. revision: yes
Referee: [§4.1] §4.1 (Experimental setup) and Table 3: The paper states that discrete codes serve as routing signals, yet reports no quantitative measure (e.g., mutual information or alignment score) between the learned codebook and subsequent cross-sectional returns or observable market regimes; this leaves the claim that VQ “suppresses noise while capturing robust structure” unverified on the low-SNR data.

Authors: We acknowledge that explicit quantitative validation would strengthen the claim that the discrete codes capture robust structure. In the revision we will report mutual information between the learned codebook and observable market regimes (e.g., volatility or return-cluster indicators) as well as alignment scores with cross-sectional return patterns to provide direct verification on the low-SNR data. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained with external empirical grounding

full rationale

The paper defines PRISM-VQ as a composite architecture combining expert prior factors, vector-quantized discrete latents, and a structure-conditioned MoE for time-varying loadings. The abstract and description present the VQ component as an information bottleneck whose value is assessed via out-of-sample performance on CSI 300 and S&P 500 benchmarks. No equations are shown that reduce a reported prediction or ranking metric to a fitted parameter by algebraic identity, nor are any load-bearing claims justified solely by self-citation chains. The reported improvements are therefore not forced by the model's own definitions or by renaming of inputs; they rest on independent dataset evaluation.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The framework relies on the assumption that vector quantization forms an effective information bottleneck for noisy cross-sectional data and introduces several model hyperparameters whose values are not reported in the abstract.

free parameters (2)

number of discrete codes in VQ
Hyperparameter controlling the size of the discrete latent space; value not stated in abstract.
number of experts in MoE
Hyperparameter determining the number of specialized sub-models; value not stated in abstract.

axioms (1)

domain assumption Vector quantization acts as an information bottleneck that suppresses noise while capturing robust market structure
Invoked in the model description to justify the use of discrete codes.

pith-pipeline@v0.9.0 · 5468 in / 1285 out tokens · 68462 ms · 2026-05-14T19:50:45.200203+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

37 extracted references · 5 canonical work pages · 3 internal anchors

[1]

Hypergraph neural networks to predict stock movements by exploring higher-order relationships

[Alaygut and Sefer, 2025] Tuna Alaygut and Emre Sefer. Hypergraph neural networks to predict stock movements by exploring higher-order relationships. InProceedings of the 6th ACM International Conference on AI in Finance, pages 700–708,

2025
[2]

Matcc: A novel approach for ro- bust stock price prediction incorporating market trends and cross-time correlations

[Caoet al., 2024 ] Zhiyuan Cao, Jiayu Xu, Chengqi Dong, Peiwen Yu, and Tian Bai. Matcc: A novel approach for ro- bust stock price prediction incorporating market trends and cross-time correlations. InProceedings of the 33rd ACM International Conference on Information and Knowledge Management, pages 187–196,

2024
[3]

Xgboost: A scalable tree boosting system

[Chen and Guestrin, 2016] Tianqi Chen and Carlos Guestrin. Xgboost: A scalable tree boosting system. InProceedings of the 22nd acm sigkdd international conference on knowl- edge discovery and data mining, pages 785–794,

2016
[4]

A simple framework for contrastive learning of visual representations

[Chenet al., 2020 ] Ting Chen, Simon Kornblith, Moham- mad Norouzi, and Geoffrey Hinton. A simple framework for contrastive learning of visual representations. InIn- ternational conference on machine learning, pages 1597–

2020
[5]

Automatic de- biased temporal-relational modeling for stock investment recommendation

[Chenet al., 2024 ] Weijun Chen, Shun Li, Xipu Yu, Heyuan Wang, Wei Chen, and Tengjiao Wang. Automatic de- biased temporal-relational modeling for stock investment recommendation. InProceedings of the Thirty-Third Inter- national Joint Conference on Artificial Intelligence, pages 1999–2008,

2024
[6]

Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling

[Chunget al., 2014 ] Junyoung Chung, Caglar Gulcehre, KyungHyun Cho, and Yoshua Bengio. Empirical evalua- tion of gated recurrent neural networks on sequence mod- eling.arXiv preprint arXiv:1412.3555,

work page internal anchor Pith review Pith/arXiv arXiv 2014
[7]

Presidential address: Discount rates.The Journal of finance, 66(4):1047–1108,

[Cochrane, 2011] John H Cochrane. Presidential address: Discount rates.The Journal of finance, 66(4):1047–1108,

2011
[8]

Explainable stock price movement pre- diction using contrastive learning

[Duet al., 2024 ] Kelvin Du, Rui Mao, Frank Xing, and Erik Cambria. Explainable stock price movement pre- diction using contrastive learning. InProceedings of the 33rd ACM International Conference on Information and Knowledge Management, pages 529–537,

2024
[9]

Factorvae: A probabilistic dynamic fac- tor model based on variational autoencoder for predicting cross-sectional stock returns

[Duanet al., 2022 ] Yitong Duan, Lei Wang, Qizhong Zhang, and Jian Li. Factorvae: A probabilistic dynamic fac- tor model based on variational autoencoder for predicting cross-sectional stock returns. InProceedings of the AAAI conference on artificial intelligence, volume 36, pages 4468–4476,

2022
[10]

Factorgcl: A hypergraph-based factor model with tempo- ral residual contrastive learning for stock returns predic- tion

[Duanet al., 2025 ] Yitong Duan, Weiran Wang, and Jian Li. Factorgcl: A hypergraph-based factor model with tempo- ral residual contrastive learning for stock returns predic- tion. InProceedings of the AAAI Conference on Artificial Intelligence, volume 39, pages 173–181,

2025
[11]

The cross-section of expected stock returns.the Journal of Finance, 47(2):427–465,

[Fama and French, 1992] Eugene F Fama and Kenneth R French. The cross-section of expected stock returns.the Journal of Finance, 47(2):427–465,

1992
[12]

Common risk factors in the returns on stocks and bonds.Journal of financial economics, 33(1):3–56,

[Fama and French, 1993] Eugene F Fama and Kenneth R French. Common risk factors in the returns on stocks and bonds.Journal of financial economics, 33(1):3–56,

1993
[13]

Autoencoder asset pricing models.Journal of Economet- rics, 222(1):429–450,

[Guet al., 2021 ] Shihao Gu, Bryan Kelly, and Dacheng Xiu. Autoencoder asset pricing models.Journal of Economet- rics, 222(1):429–450,

2021
[14]

Simstock: Representation model for stock similari- ties

[Hwanget al., 2023 ] Yoontae Hwang, Junhyeong Lee, Da- ham Kim, Seunghwan Noh, Joohwan Hong, and Yongjae Lee. Simstock: Representation model for stock similari- ties. InProceedings of the Fourth ACM International Con- ference on AI in Finance, pages 533–540,

2023
[15]

Can machines’ learn’finance?Journal of Investment Management,

[Israelet al., 2020 ] Ronen Israel, Bryan T Kelly, and To- bias J Moskowitz. Can machines’ learn’finance?Journal of Investment Management,

2020
[16]

Is there a replication crisis in finance?The Journal of Finance, 78(5):2465–2518,

[Jensenet al., 2023 ] Theis Ingerslev Jensen, Bryan Kelly, and Lasse Heje Pedersen. Is there a replication crisis in finance?The Journal of Finance, 78(5):2465–2518,

2023
[17]

Re- versible instance normalization for accurate time-series forecasting against distribution shift

[Kimet al., 2021 ] Taesung Kim, Jinhee Kim, Yunwon Tae, Cheonbok Park, Jang-Ho Choi, and Jaegul Choo. Re- versible instance normalization for accurate time-series forecasting against distribution shift. InInternational con- ference on learning representations,

2021
[18]

Factorvqvae: Discrete latent factor model via vector quantized variational autoencoder.Knowledge- Based Systems, 318:113460,

[Kimet al., 2025 ] Namhyoung Kim, Seung Eun Ock, and Jae Wook Song. Factorvqvae: Discrete latent factor model via vector quantized variational autoencoder.Knowledge- Based Systems, 318:113460,

2025
[19]

Temporal convolu- tional networks for action segmentation and detection

[Leaet al., 2017 ] Colin Lea, Michael D Flynn, Rene Vidal, Austin Reiter, and Gregory D Hager. Temporal convolu- tional networks for action segmentation and detection. In proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pages 156–165,

2017
[20]

Master: Market- guided stock transformer for stock price forecasting

[Liet al., 2024 ] Tong Li, Zhaoyang Liu, Yanyan Shen, Xue Wang, Haokun Chen, and Sen Huang. Master: Market- guided stock transformer for stock price forecasting. In Proceedings of the AAAI Conference on Artificial Intelli- gence, volume 38, pages 162–170,

2024
[21]

Decoupled Weight Decay Regularization

[Loshchilov and Hutter, 2017] Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization.arXiv preprint arXiv:1711.05101,

work page internal anchor Pith review Pith/arXiv arXiv 2017
[22]

Pytorch: An imperative style, high- performance deep learning library.Advances in neural in- formation processing systems, 32,

[Paszkeet al., 2019 ] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high- performance deep learning library.Advances in neural in- formation processing systems, 32,

2019
[23]

Film: Visual reasoning with a general conditioning layer

[Perezet al., 2018 ] Ethan Perez, Florian Strub, Harm De Vries, Vincent Dumoulin, and Aaron Courville. Film: Visual reasoning with a general conditioning layer. InPro- ceedings of the AAAI conference on artificial intelligence, volume 32,

2018
[24]

Capital asset prices: A theory of market equilibrium under conditions of risk.The journal of finance, 19(3):425–442,

[Sharpe, 1964] William F Sharpe. Capital asset prices: A theory of market equilibrium under conditions of risk.The journal of finance, 19(3):425–442,

1964
[25]

Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer

[Shazeeret al., 2017 ] Noam Shazeer, Azalia Mirhoseini, Krzysztof Maziarz, Andy Davis, Quoc Le, Geoffrey Hin- ton, and Jeff Dean. Outrageously large neural net- works: The sparsely-gated mixture-of-experts layer.arXiv preprint arXiv:1701.06538,

work page internal anchor Pith review Pith/arXiv arXiv 2017
[26]

Multi-scale temporal neural net- work for stock trend prediction enhanced by temporal hyepredge learning.Proceedings of the IJCAI, Montreal, QC, Canada, pages 16–22,

[Songet al., 2025 ] Lingyun Song, Haodong Li, Siyu Chen, Xinbiao Gan, Binze Shi, Jie Ma, Yudai Pan, Xiaoqi Wang, and Xuequn Shang. Multi-scale temporal neural net- work for stock trend prediction enhanced by temporal hyepredge learning.Proceedings of the IJCAI, Montreal, QC, Canada, pages 16–22,

2025
[27]

Roformer: En- hanced transformer with rotary position embedding.Neu- rocomputing, 568:127063,

[Suet al., 2024 ] Jianlin Su, Murtadha Ahmed, Yu Lu, Shengfeng Pan, Wen Bo, and Yunfeng Liu. Roformer: En- hanced transformer with rotary position embedding.Neu- rocomputing, 568:127063,

2024
[28]

Neural discrete representation learning

[Van Den Oordet al., 2017 ] Aaron Van Den Oord, Oriol Vinyals, et al. Neural discrete representation learning. Advances in neural information processing systems, 30,

2017
[29]

Attention is all you need.Advances in neural information processing systems, 30,

[Vaswaniet al., 2017 ] Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin. Attention is all you need.Advances in neural information processing systems, 30,

2017
[30]

Rsap-dfm: Regime-shifting adaptive posterior dynamic factor model for stock returns predic- tion

[Xianget al., 2024 ] Quanzhou Xiang, Zhan Chen, Qi Sun, and Rujun Jiang. Rsap-dfm: Regime-shifting adaptive posterior dynamic factor model for stock returns predic- tion. InProceedings of the Thirty-Third International Joint Conference on Artificial Intelligence, IJCAI-24. Interna- tional Joint Conferences on Artificial Intelligence Organi- zation,

2024
[31]

Qlib: An ai-oriented quantitative investment platform.arXiv:2009.11189, 2020

[Yanget al., 2020 ] Xiao Yang, Weiqing Liu, Dong Zhou, Jiang Bian, and Tie-Yan Liu. Qlib: An ai- oriented quantitative investment platform.arXiv preprint arXiv:2009.11189,

work page arXiv 2020
[32]

Accurate multivariate stock movement pre- diction via data-axis transformer with multi-level contexts

[Yooet al., 2021 ] Jaemin Yoo, Yejun Soun, Yong-chan Park, and U Kang. Accurate multivariate stock movement pre- diction via data-axis transformer with multi-level contexts. InProceedings of the 27th ACM SIGKDD Conference on Knowledge Discovery & Data Mining, pages 2037–2045,

2021
[33]

Major issues in high-frequency financial data analysis: A survey of so- lutions.Mathematics, 13(3):347,

[Zhang and Hua, 2025] Lu Zhang and Lei Hua. Major issues in high-frequency financial data analysis: A survey of so- lutions.Mathematics, 13(3):347,

2025
[34]

Storm: A spatio-temporal factor model based on dual vec- tor quantized variational autoencoders for financial trad- ing.arXiv preprint arXiv:2412.09468,

[Zhaoet al., 2024 ] Yilei Zhao, Wentao Zhang, Tingran Yang, Yong Jiang, Fei Huang, and Wei Yang Bryan Lim. Storm: A spatio-temporal factor model based on dual vec- tor quantized variational autoencoders for financial trad- ing.arXiv preprint arXiv:2412.09468,

work page arXiv 2024
[35]

The GELU nonlinearity pro- vides smooth activation and empirically improves optimiza- tion stability in Transformers

+b 2, W1 ∈R d×dff , W 2 ∈R dff ×d,(A.4) whered ff denotes the intermediate expansion dimension, typ- ically chosen as a multiple ofd. The GELU nonlinearity pro- vides smooth activation and empirically improves optimiza- tion stability in Transformers. Encoder block structure.Each Transformer encoder block combines the above components with residual connec...

2024
[36]

Each expertξ j is a lightweight MLP mappingu i ∈R dt toR dmoe, with hidden sized moe=64and dropout 0.1. Expert outputs are aggregated as mi = MeX j=1 Gi,j ξj(ui)∈R dmoe .(A.12) We useM e=2experts with top-1 routing for CSI 300, and Me=8experts with top-4 routing for S&P 500, reflecting dif- ferences in market complexity and signal heterogeneity. Dynamic l...

2023
[37]

Unless otherwise specified, portfolios are equal- weighted, i.e.,w i,t = 1/|Pt|

At each datet, letP t denote the set of held stocks after ranking and filtering, and letw i,t be the portfolio weight assigned to stock i∈ P t. Unless otherwise specified, portfolios are equal- weighted, i.e.,w i,t = 1/|Pt|. Daily portfolio return.Given realized stock returnsy i,t, the portfolio log return is computed as gp,t = log 1 + X i∈Pt wi,t yi,t ! ...

2005