Optical neural networks (ONNs) are promising hardware platforms for next-generation artificial intelligence acceleration with ultrafast speed and low-energy consumption. However, previous ONN designs are bounded by one multiply–accumulate operation per device, showing unsatisfying scalability. In this work, we propose a scalable ONN architecture, dubbed SqueezeLight. We propose a nonlinear optical neuron based on multioperand ring resonators (MORRs) to squeeze vector dot-product into a single device with low wavelength usage and built-in nonlinearity. A block-level squeezing technique with structured sparsity is exploited to support higher scalability. We adopt a robustness-aware training algorithm to guarantee variation tolerance. To enable a truly scalable ONN architecture, we extend SqueezeLight to a separable optical CNN architecture that further squeezes in the layer level. Two orthogonal convolutional layers are mapped to one MORR array, leading to order-of-magnitude higher software training scalability. We further explore augmented representability for SqueezeLight by introducing parametric MORR neurons with trainable nonlinearity, together with a nonlinearity-aware initialization method to stabilize convergence. Experimental results show that SqueezeLight achieves one-order-of-magnitude better compactness and efficiency than previous designs with high fidelity, trainability, and robustness. Our open-source codes are available at https://github.com/JeremieMelo/SqueezeLight.