operational definitions
the lines we draw, the boundaries we set
Definition: In deep neural networks, the reduction of error signals as they propagate backward through layers, making it difficult for early (shallow) layers to learn. It also describes the tendency for transformative insights to lose strength as they travel back through our own beliefs, rarely reaching and reshaping our foundational assumptions.
A neural network learns by listening to its mistakes.
You show it something, it guesses, it’s wrong. That wrongness becomes a signal—a whisper that travels backward through the architecture, asking each layer: how did you contribute to this error? How should you change?
But signals decay over distance.
By the time the whisper reaches the earliest layers—the ones forming the most primitive representations, the foundations upon which everything else is built—it has faded to silence. The gradient has vanished. The deep layers learn. The shallow layers remain strangers to the truth that passed through them.
I named this blog after the phenomenon because I keep noticing it.
The insight arrives. It’s vivid, urgent. But by the time it propagates back to our foundations—to the premises we forgot we chose, the assumptions that calcified into identity—it’s too faint to disturb anything. We update our conclusions while our origins stay frozen in place.
We mistake this for growth.
The fix in neural networks is almost philosophical: create shortcuts. Residual connections. Pathways that let the signal skip across depth, arriving at the beginning with enough force to matter.
The fix in ourselves is the same, and harder.
It means building deliberate channels back to first principles. It means treating settled questions as open questions. It means accepting that the deepest error might live in the shallowest layer—in something you decided so long ago you no longer experience it as a decision.
The gradient wants to vanish. Depth wants to forget.
Remembering is architectural.