Title:Compute-in-Memory Attention: A Time-Domain Analog Softmax Circuit with RC-Tunable Temperature

Abstract:Softmax is a key operation in Transformer attention, but its exponentiation and normalization add significant overhead in compute-in-memory (CIM) accelerators, especially when analog attention scores must first be converted to the digital domain. This work presents a tunable-temperature analog softmax circuit in GlobalFoundries 22-nm fully depleted silicon-on-insulator (FDSOI) technology that operates directly on CIM-generated score voltages without intermediate analog-to-digital conversion. Each input score is converted into a time-domain event using a shared falling ramp. The corresponding comparator transition samples an RC-decaying reference to generate an exponential weight, which is then processed by an in-circuit normalization stage. In contrast to analog softmax circuits that rely on transistor weak-inversion behavior for exponentiation, the proposed architecture controls the softmax response through the ramp slope and RC time constant, enabling programmable effective temperature. The 128-element architecture is evaluated using transistor-level and post-layout extracted simulations, including multi-level input vectors, capacitance variation and mismatch, process and temperature variation, monte carlo analysis, and shared-interconnect parasitics. The complete 128-element implementation occupies 9453.42~$\mu\mathrm{m}^{2}$ including the shared global ramp circuitry, while each replicated softmax element occupies 70.2~$\mu\mathrm{m}^{2}$. The circuit achieves a 242.97-ns evaluation latency at 13.44~mW total power, corresponding to 25.5~pJ per output element. The simultaneous 128-element evaluation achieves an RMSE of 24.46~mV relative to the ideal softmax response. The extracted circuit characteristics are further incorporated into a MemTorch-based hardware-aware Transformer model, where the proposed softmax achieves a validation loss within 2.5\% of the ideal-softmax baseline.

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