Where does vanish collide?

In the geometry of linear perspective, a vanishing point is the point on the picture plane at which the projected images of a set of parallel lines receding from the viewer appear to meet, giving a flat image its illusion of depth. Kemp's The science of art traces how Renaissance painters from Brunelleschi onward formalized the single central vanishing point and its construction. The referent is a convergence point of projected parallels in a perspective image, a feature of optics and geometry, not a disappearing object or a numerical quantity falling to zero.[1]

Unit

The image location where a pencil of parallel lines converges

Recovery means

Not applicable

Measured by

Located geometrically as the intersection of the images of parallel lines on the picture plane

In machine learning the vanishing-gradient problem is the tendency, when training deep or recurrent neural networks by backpropagation, for error gradients to shrink multiplicatively as they propagate back through many layers until they become too small to update the earliest weights. Bengio, Simard, and Frasconi's Learning long-term dependencies with gradient descent is difficult showed formally why gradient-based learning struggles to capture long-range dependencies for exactly this reason. The referent is the decay of a gradient signal toward zero across depth, a numerical training pathology, unrelated to a stage disappearance or a perspective point save for the meaning of something fading away.[2]

Unit

The magnitude of the error gradient at early layers during training

Recovery means

Mitigated by gated architectures, residual connections, normalization, and careful initialization that keep gradients from decaying

Measured by

Diagnosed by the norm of backpropagated gradients across layers and by failure to learn long-range dependencies