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A multilayer perceptron usually connects every input unit of a layer to every output unit. For $n$ inputs and $m$ outputs its dense affine layer has $nm+m$ parameters, including biases. A convolutional layer instead applies small local filters with weight sharing across positions. A two-dimensional filter of size $k_h\times k_w$, with $C_{\mathrm{in}}$ input channels and $C_{\mathrm{out}}$ output channels, has $k_h{k}_w{C}_{\mathrm{in}}{C}_{\mathrm{out}}+C_{\mathrm{out}}$ parameters. The count does not increase with spatial height and width, although the activation storage and arithmetic do.

Local receptive fields and repeated layers capture increasingly extended patterns. translation equivariance follows from shared filters under compatible boundary conventions; pooling or global aggregation can help build invariance but a convolution alone is not generally translation-invariant. Flattening a large convolutional output into a dense head can reintroduce many parameters. For an unordered descriptor vector, a convolutional locality assumption must be justified rather than imposed merely because convolutional layers have fewer weights.

Reuse of one learnable parameter in multiple computational positions. In a convolution this reduces parameter count and imposes translation equivariance away from boundary effects.