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While Conformer-Transducers offer state-of-the-art ASR performance, their excessive memory footprints create a bottleneck for on-device deployment. Conventional integer quantization is fundamentally constrained by a discrete grid, imposing a structural lower bound of 1 bit per parameter. To address this challenge, we propose LittleASR, a mixed-precision framework based on variable-rank binary decomposition. Guided by a gradient-aware sensitivity metric, LittleASR identifies and compresses non-critical layers to the sub-1-bit regime, pushing the limits of compression beyond the boundaries of standard quantization while maintaining a favorable trade-off between extreme memory reduction and recognition accuracy.