Receptive Field & FLOPs

The receptive field (RF) is the region of the original input visible to one output pixel, with recurrence $RF_l = RF_{l-1} + (k_l - 1)\prod_{i=1}^{l-1} s_i$, where $k_l$ is the kernel size of layer $l$ and $s_i$ the stride of layer $i$ — the stride product shows that earlier downsampling amplifies later receptive fields. With all strides 1 it simplifies to $RF_l = RF_{l-1} + k_l - 1$; e.g. three stacked 3×3 (stride 1) layers reach RF 7, and if the first layer has stride 2, the third layer reaches $7 + 2 \times 2 \times 1 = 11$. Conv FLOPs: each output pixel performs $k_h k_w C_{in}$ multiply-adds (1 multiply + 1 add, counted as 2), totalling $2 H_{out} W_{out} k_h k_w C_{in} C_{out}$; e.g. a 3×3 conv with 64→128 channels on 224×224 input: $2 \times 224 \times 224 \times 9 \times 64 \times 128 \approx 7.4 \times 10^9$, i.e. ~7.4 GFLOPs.

hand-computing FLOPs/receptive fields is a core CNN interview staple — estimating model cost, comparing lightweight models (how much MobileNet saves), explaining stacked small kernels and dilated convolution; it is also the baseline against which ViT's global attention is contrasted.

the recurrence quantifies how much of the input a network sees — $l$ stacked 3×3 layers reach $2l+1$, so deep small-kernel networks match the global view of large kernels with fewer parameters; FLOPs measures per-sample multiply-add cost independently of parameter count, giving a unified yardstick for efficient-architecture design and deployment estimation.

Hand-compute receptive fields: three stacked 3×3 stride-1 layers? With the first layer at stride 2? Show the recurrence.

Hand-compute FLOPs: 3×3 conv, 64→128 channels on 224×224 input. Why the factor of 2?

Derive the receptive-field recurrence $RF_l = RF_{l-1} + (k_l-1)\prod_{i=1}^{l-1} s_i$; what does the stride product mean?

Why do two stacked 3×3 convs match a 5×5 receptive field with fewer params and FLOPs? Give numbers.

Which factors does standard-conv FLOPs scale with, and how do you quickly estimate a whole network's FLOPs?