Photonic processors are described. The photonic processors described herein are configured to perform matrix-matrix (e.g., matrix-vector) multiplication. Some embodiments relate to photonic processors arranged according to a dual-rail architecture, in which numeric values are encoded in the difference between a pair optical signals (e.g., in the difference between the powers of the optical signals). Relative to other architectures, these photonic processors exhibit increased immunity to noise. Some embodiments relate to photonic processors including modulatable detector-based multipliers. Modulatable detectors are detectors designed so that the photocurrent can be modulated according to an electrical control signal. Photonic processors designed using modulatable detector-based multipliers are significantly more compact than other types of photonic processors.