The Label Horizon Paradox: Rethinking Supervision Targets in Financial Forecasting

TL;DR

The paper tackles the problem that the training target in financial forecasting need not match the inference horizon, revealing a dynamic Label Horizon Paradox driven by a signal-noise trade-off. It formulates a time-varying factor-model framework and derives a log-performance decomposition showing how information gain and noise accumulation determine the optimal proxy horizon $δ^*$. To operationalize this, it introduces a bi-level optimization framework that learns horizon weights $\boldsymbol{λ}$ to automatically select the best supervision signal within a single training run, with a warm-up phase to stabilize optimization. Empirical results on CSI 300/500/1000 data across diverse architectures show consistent improvements over standard baselines, and the learned horizon distribution aligns with empirically optimal horizons, indicating practical benefits for label-centric approaches in noisy financial forecasting.

Abstract

While deep learning has revolutionized financial forecasting through sophisticated architectures, the design of the supervision signal itself is rarely scrutinized. We challenge the canonical assumption that training labels must strictly mirror inference targets, uncovering the Label Horizon Paradox: the optimal supervision signal often deviates from the prediction goal, shifting across intermediate horizons governed by market dynamics. We theoretically ground this phenomenon in a dynamic signal-noise trade-off, demonstrating that generalization hinges on the competition between marginal signal realization and noise accumulation. To operationalize this insight, we propose a bi-level optimization framework that autonomously identifies the optimal proxy label within a single training run. Extensive experiments on large-scale financial datasets demonstrate consistent improvements over conventional baselines, thereby opening new avenues for label-centric research in financial forecasting.

Figures (4)

• Figure 1: Training and Inference Pipeline. The leftmost panel shows historical input features $X_t$, which are processed by a neural network model $f_\theta^\delta$. The right panel illustrates unfolding future price paths with different time horizons ($r_t^1, r_t^\delta, r_t^{\Delta}$). The arrows highlight a central premise of this study: during training (top arrow), the model may be optimized against an intermediate proxy label $r_t^\delta$; however, during inference (bottom arrow), the model's performance is strictly evaluated on its ability to forecast the final target return ($r_t^{\Delta}$). Our goal is not to change the evaluation target, but to question and improve the choice of training label that best serves this fixed objective.
• Figure 2: Performance Curves across Different Scenarios. The x-axis is the training horizon $\delta$, and the y-axis is the out-of-sample IC on the fixed final target $\mathbf{r}^\Delta$. The curves are obtained by training LSTM models on the CSI 500 dataset, with 5 independent models per horizon. The blue line shows the raw results, and the red line shows the Gaussian-smoothed trend.
• Figure 3: Decomposition Validation. The x-axis represents the training horizon $\delta$, and the y-axis represents the Out-of-Sample IC on the fixed final target $\mathbf{r}^\Delta$. We performed a dense experimental sweep to rigorously verify the theoretical decomposition, training distinct LSTM models for every minute-level horizon across 5 random seeds. The red lines depict the empirical Test IC on the inference target ($\Delta$), while the blue lines illustrate the theoretical values derived from the product term in Corollary \ref{['corollary']}. For both metrics, lighter shades correspond to raw measurements from individual trials, while solid darker curves indicate the Gaussian-smoothed trends.
• Figure 4: Visualization of Learned Horizon Weights ($\boldsymbol{\lambda}$). We illustrate the final distribution of $\boldsymbol{\lambda}$ learned by an LSTM model on the CSI500 dataset. The panels correspond to Scenario 1 (top), Scenario 2 (second), Scenario 3 (third), and Scenario 3 without warm-up (bottom).

Theorems & Definitions (3)

• Theorem 3.2
• Corollary 3.3
• Remark 3.4