Sign-Aware Loss

How to use loss functions that focus on getting the direction of the forecast right rather than the precision of its absolute magnitude.

Application examples

• Trading — what matters is predicting whether the price will go up or down, not guessing every cent.
• Demand forecasting — what matters is whether there will be growth or decline, even if specific numbers are off.
• Inventory management — the trend direction matters in order to adjust the strategy.

The problem with classical loss functions

Standard regression loss functions (MSE, MAE) penalize the model for deviation in magnitude but do not account for the fact that in real-world tasks the sign of the prediction may be more critical than the magnitude itself.

Example:
Reality:    +5.0 (growth)
Forecast 1: +1.0 (magnitude error: 4.0, but direction is correct)
Forecast 2: -0.5 (magnitude error: 5.5, but direction is wrong)

How Sign-Aware Loss works

Step-by-step process:

• Take the sign of the forecast (+ or -) and the sign of the true value
• Convert them into a binary format: 1 — growth, 0 — decline
• Compute binary cross-entropy (BCE) so that only the wrong direction is penalized

Mathematical formula

Sign-Aware Loss: L_sign = BCE(σ(ŷ), (sign(y_true) + 1) / 2)

where:
• σ(ŷ) — sigmoid of the prediction (probability of growth)
• (sign(y_true) + 1) / 2 — the true direction encoded as 0 or 1

Intuitive explanation

You can imagine that we are training a classifier for the direction of movement:

This turns regression on time series into a two-part task:

• If the model guessed "up" or "down" — it is rewarded
• If it confused the directions — it is penalized, regardless of how close the predicted magnitude was

Two-part task

• Determine the direction
• Optionally — refine the magnitude (with a separate loss)

Advantages of the approach

• Focus on strategy — the model learns to make forecasts that are useful for decision-making, not just to minimize average error.
• Reduced impact of outliers — extreme values disturb optimization less because the sign is what matters.
• Flexibility — can be combined with other losses (e.g. Huber or MSE) to balance magnitude accuracy with directional correctness.

When to apply

• Algorithmic trading — the direction of the trade matters more than the absolute magnitude of the predicted return.
• Forecasting macro indicators — knowing whether GDP will grow or decline is often more important than the exact figure.
• Trend analysis in data — for example, in medicine for assessing improvement or deterioration of a patient's condition.

Comparison with classical loss functions

• MSE — focus: magnitude accuracy; advantages: simplicity, differentiability; drawbacks: ignores direction
• MAE — focus: absolute error; advantages: robustness to outliers; drawbacks: does not consider direction
• Sign-Aware Loss — focus: forecast direction; advantages: strategic usefulness; drawbacks: implementation complexity
• Combined — focus: direction + magnitude; advantages: best of both worlds; drawbacks: tuning complexity

Practical implementation

Step-by-step rollout plan:

• Define priorities — what matters more: direction or magnitude accuracy?
• Choose a base model — a regression architecture (LSTM, CNN, Transformer)
• Implement Sign-Aware Loss — add a loss function that accounts for the sign
• Tune the balancing — combine with other losses if needed
• Evaluate results — separately for direction and magnitude

Key takeaways

• Sign-Aware Loss — a tool that shifts the emphasis from "how precisely we hit" to "how correctly we identified the direction of motion"
• In tasks where direction matters more than magnitude, it lets you train models aligned with practical business or strategic goals
• Can be combined with classical loss functions to achieve balance
• Especially effective in financial tasks, forecasting, and trend analysis

Practical recommendations

• Start with simple problems — try it on basic regression tasks
• Use validation — evaluate direction and magnitude accuracy separately
• Consider a combined approach — Sign-Aware Loss + a traditional loss
• Adapt to the task — tune the weights based on priorities
• Monitor results — track how directional forecast quality changes