Causal Padding and Look-Ahead Leakage

A convolution layer slides a small kernel across a sequence, and the standard ("same") padding scheme centers that kernel on each output position so the output shape matches the input shape. For images, centering is harmless — there is no "before" or "after" a pixel. For a time series, centering means the kernel's output at time $t$ silently includes inputs from after $t$ too, which is exactly the information a real forecast at time $t$ would never actually have.

The analogy: never read tomorrow's newspaper

A detective solving today's case must never sneak a look at tomorrow's newspaper for clues — that would invalidate the whole investigation, even if the peek happens buried inside some innocuous-looking procedure. Any layer that lets a prediction at time $t$ depend, even partially, on data from after $t$ has done exactly this, whether or not it looks like cheating on the surface.

The mechanics

For a kernel of size $k$ and dilation $d$, "same" padding splits $(k-1) \times d$ padding values evenly across both sides of the sequence, so the kernel window centered at position $t$ reaches both before and after $t$. Causal padding instead places all $(k-1) \times d$ padding on the left (past) side only:

$$\text{output}_t = \sum_{j=0}^{k-1} w_j \, x_{t - j \cdot d}$$

In words: the output at time $t$ is a weighted sum built exclusively from $x_t$ and earlier values — never from $x_{t+1}$ or beyond — because every index in the sum is $t$ minus something non-negative.

Worked example 1: which positions get touched

Kernel size 3, sequence $x_1, \dots, x_6$. Under same padding, the output at position $4$ uses $x_3, x_4, x_5$ — it depends on $x_5$, which lies in the future relative to $t=4$. Under causal padding, the output at position 4 uses $x_2, x_3, x_4$ — entirely past-and-present, never future.

Worked example 2: a value that shouldn't matter but does

Weights $w=(0.2, 0.5, 0.3)$ (oldest to newest in the window), and suppose $x_3=1, x_4=2$. Under causal padding, $\text{output}_4 = 0.2(x_2) + 0.5(x_3) + 0.3(x_4)$ — changing $x_5$ afterward has zero effect on this number, by construction. Under same padding, $\text{output}_4 = 0.2(x_3)+0.5(x_4)+0.3(x_5)$: if $x_5$ later changes from $3$ to $30$, the already computed output at position 4 changes too — a live model, computing this in real time, could never have known $x_5$ yet, so this "prediction" for time 4 was never actually producible at time 4.

What this means in practice

This exact bug is one of the most common ways a backtested time-series model looks excellent in-sample and then fails once deployed live — if any layer touching time-ordered data used symmetric or "same" padding, the reported validation accuracy is contaminated by future information the model would never actually have at prediction time.