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Cross-Sectional Asset Retrieval via Future-Aligned Soft Contrastive Learning

The paper proposes Future-Aligned Soft Contrastive Learning (FASCL), a representation learning framework that improves asset retrieval by using pairwise future return correlations as continuous supervision targets to ensure retrieved assets exhibit similar future trajectories.

Original authors: Hyeongmin Lee, Chanyeol Choi, Jihoon Kwon, Yoon Kim, Alejandro Lopez-Lira, Wonbin Ahn, Yongjae Lee

Published 2026-02-12

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CC BY 4.0

Original authors: Hyeongmin Lee, Chanyeol Choi, Jihoon Kwon, Yoon Kim, Alejandro Lopez-Lira, Wonbin Ahn, Yongjae Lee

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are a talent scout for a professional sports league. You are looking for the next superstar.

Most scouts use "Backward-Looking" methods. They look at a player's stats from last year: "He scored 20 goals last season, so he’s a good striker." This works, but it’s risky. What if that player was just lucky, or what if they are about to get injured? You are basing your future bets on what already happened.

This paper introduces a new way of scouting called FASCL, which is "Future-Aligned." Instead of just looking at how players played in the past, this method tries to find players who are likely to move and react to the game in the same way in the future.

Here is the breakdown of how it works using everyday analogies:

1. The Problem: The "Look-Alike" Trap

In the stock market, many companies look similar on paper. Two companies might both sell electronics and have similar stock prices today. Traditional computer models see them and say, "These are twins! They are similar."

But in the stock market, "looking alike" doesn't mean "acting alike." One company might soar tomorrow while the other crashes. Traditional models are like a person who thinks two people are "similar" just because they are wearing the same outfit. They miss the fact that one person is a marathon runner and the other is a couch potato.

2. The Solution: The "Dance Partner" Method (FASCL)

The researchers created FASCL. Instead of teaching the computer to find companies that look the same (the outfit), they teach it to find companies that dance the same way (the movement).

Imagine you are watching a ballroom dance. You see a dancer performing a specific, complex tango. You want to find their perfect partner. You don't look for someone wearing the same sequins; you look for someone whose rhythm, timing, and energy match the tango perfectly.

FASCL does this with stocks:

The Training: The computer looks at a group of stocks. It doesn't just look at their prices; it looks at how they actually behaved over the next few weeks.
The "Soft" Connection: Instead of saying "Stock A and Stock B are identical" (which is rarely true), it uses "Soft Contrastive Learning." This is like saying, "Stock A and B are close dance partners, Stock A and C are just casual acquaintances, and Stock A and D are total strangers who move to different music." It recognizes the subtle degrees of similarity.

3. The Result: Better "Predictive Teams"

The researchers tested this on over 4,000 US stocks, and the results were impressive. They measured success in three ways:

Direction (The Compass): If the main stock goes up, do the "similar" stocks also go up? (Yes, FASCL was much better at this).
Trajectory (The Path): Do the stocks follow the same wavy line on a graph? (FASCL was the winner here).
The Consensus (The Group Vote): If you take the top 10 "similar" stocks and average them out, does that group give you a reliable hint about where the main stock is going? (FASCL provided a much clearer "signal" than any other method).

4. Why does this matter? (The "Basket" Advantage)

The most cool part is what happens when you build a "basket" of stocks.

If you use old methods to pick a group of 20 "similar" stocks, the group becomes a mess—the similarity disappears as you add more stocks. It’s like trying to pick a 20-person dance troupe where only the first two people actually know the steps.

But with FASCL, the more stocks you add to the basket, the stronger and more reliable the signal becomes. It’s like finding a whole troupe of dancers who all move in perfect synchronization. For investors, this means they can build much more stable and predictable portfolios.

Summary in one sentence:

Instead of teaching computers to find stocks that look the same, this paper teaches them to find stocks that behave the same, making them much better at predicting future market movements.

Technical Summary: Cross-Sectional Asset Retrieval via Future-Aligned Soft Contrastive Learning (FASCL)

1. Problem Statement

In quantitative finance, asset retrieval—identifying assets that behave similarly to a query asset—is critical for portfolio construction, pairs trading, and risk management. Traditional retrieval methods rely on backward-looking criteria, such as historical Pearson correlation, Dynamic Time Warping (DTW) of past price patterns, or static sector classifications (e.g., GICS).

The authors argue that these methods are fundamentally flawed because they do not guarantee future alignment. An asset that moved similarly to a query in the past is not necessarily one that will move similarly in the future. The core challenge is to learn a representation space where similarity is grounded in future co-movement rather than historical pattern matching.

2. Methodology

The paper proposes Future-Aligned Soft Contrastive Learning (FASCL), a representation learning framework designed to map assets into an embedding space where cosine similarity directly reflects future return correlations.

Encoder Architecture: The model uses a patch-based Transformer encoder. It takes multivariate financial time series (Open, High, Low, Close, Volume, and Trading Value) as input. The series are normalized, split into non-overlapping patches, and processed through Transformer blocks. The final asset embedding is obtained via mean-pooling over the patch tokens.
Future-Aligned Soft Contrastive Loss (LSC): This is the central innovation. Unlike standard contrastive learning (e.g., InfoNCE) which uses binary "positive/negative" labels, FASCL uses continuous supervision:
1. Target Distribution ( $p_{ij}$ ): For a batch of assets, the model calculates the pairwise Pearson correlation of their actual future returns over a horizon $H$ . These correlations are transformed into a probability distribution using a temperature-scaled softmax.
2. Predicted Distribution ( $q_{ij}$ ): The model calculates the cosine similarity between the learned embeddings of the assets, also transformed via softmax.
3. Optimization: The model minimizes the Kullback-Leibler (KL) Divergence between the target distribution (future reality) and the predicted distribution (embedding similarity). This allows the model to learn a graded ranking: assets with 80% future correlation are pulled together more strongly than those with 30% correlation.
Inference: At test time, retrieval is performed via a fast nearest-neighbor search in the embedding space.

3. Key Contributions

New Objective Function: The introduction of a soft contrastive loss that uses pairwise future return correlations as continuous targets, moving beyond binary or observation-aligned supervision.
Comprehensive Evaluation Protocol: The authors propose three new metrics to measure "future alignment":
- Trend Consistency (TC@K): Measures if retrieved assets move in the same direction as the query.
- Future Return Correlation (FRC@K): Measures the average Pearson correlation of future daily returns.
- Information Coefficient (IC@K): Measures the ability of the retrieved "consensus" to rank assets cross-sectionally.
Standardized Benchmark: A rigorous experimental setup using 4,229 US equities with strict temporal splits to prevent look-ahead bias, comparing FASCL against 13 diverse baselines.

4. Results

The experiments demonstrate that FASCL significantly outperforms all 13 baselines (including statistical methods, self-supervised models like TS2Vec, forecasting models like PatchTST, and foundation models like Chronos).

Superior Future Alignment: FASCL achieved state-of-the-art results across all metrics. Notably, it achieved a much higher FRC@K (0.3837 at $K=1$ ) compared to the second-best (Pearson correlation at 0.3425).
Emergent Structure: t-SNE visualizations showed that even without being trained on labels, the embeddings naturally clustered by GICS sectors and thematic ETFs (e.g., the "Magnificent 7"), proving the model captures fundamental economic drivers.
Scalability in Trading: In a stylized spread trading backtest, while most models' performance (Sharpe ratio) degraded as the number of retrieved assets ( $K$ ) increased, FASCL's Sharpe ratio actually improved as $K$ increased from 5 to 20. This indicates that its similarity ranking is robust and reliable even for assets further down the list.
Efficiency: The model is highly efficient, capable of embedding and retrieving assets in milliseconds, making it suitable for real-time production environments.

5. Significance

This work shifts the paradigm of financial representation learning from forecasting (predicting exact values) to alignment (learning structural similarity). By proving that embeddings can be optimized to predict future co-movement, the authors provide a powerful tool for quantitative investors to build more robust, diversified, and statistically sound portfolios. The ability of the model to maintain high signal quality in larger baskets ( $K=20$ ) makes it particularly valuable for institutional-scale portfolio construction.