On Orthogonal Recurrent Neural Networks Quantization

Quantized orthogonal fine-tuning (qoft) enables parameter-efficient adaptation of low-bit language models by learning structured activation rotations before frozen quantized weights. However, its task-specific updates remain constrained to linear orthogonal transformations, limiting input-dependent nonlinear corrections. We introduce AuroOFT, which keeps qoft as a stable quantization-compatible branch while attaching a zero-start gated low-rank nonlinear residual to each adapted linear layer. AuroOFT maps activations into an RMS-normalized compact latent space and uses adaptive nonlinear bases with bounded or token-dependent gating. The zero-initialized up projection makes AuroOFT functionally identical to qoft at initialization, while orthogonality remains a branch-level stability property rather than a property of the combined nonlinear layer. Under matched data, optimization, decoding, and parser protocols, AuroOFT improves Macro-6 over matched qoft by 1.30-2.70% on the 1.5B/3B Qwen2.5 settings, exceeds QLoRA by 6.52-10.62%, and saves 32.3-44.7% trainable parameters relative to QLoRA in representative scales. The small exam-style multiple-choice math set is treated only as a protocol-sensitivity diagnostic. Our code is available at the anonymous repository: https://anonymous.4open.science/r/AuroOFT-F3FD.

Serving large language models (LLMs) under diverse deployment constraints requires flexible trade-offs between accuracy, memory footprint, and throughput. However, conventional quantization methods typically require a separate checkpoint for each target bit-width. We introduce Recurrent Residual Quantization (RRQ), a post-training quantization (PTQ) framework that represents weights as a low-bit quantized base together with a sequence of quantized residual corrections, enabling multiple effective precisions from a single checkpoint. Starting from a 2-bit model obtained via post-training quantization (PTQ) or round-to-nearest (RTN), RRQ progressively adds lightweight 2-bit residuals generated via RTN to construct 4-, 6-, and 8-bit representations. The method is calibration-free and avoids joint multi-bit optimization. In our Qwen3-8B setup, the full all-RTN 2-/4-/6-/8-bit package is constructed in 1,293 seconds, 3.3 times faster than the measured MatGPTQ construction. Experiments on six recent LLMs show competitive accuracy at 6 and 8 bits, with model-dependent behavior at 4 bits. The code will be made publicly available upon publication.

We introduce a lightweight Quantum Prototypical Recurrent Unit (QPRU) that requires significantly fewer parameters than both classical recurrent architectures, such as Long Short- Term Memory (LSTM) and Gated Recurrent Unit (GRU), and quantum variants, including Quantum LSTM (QLSTM) and Quantum GRU (QGRU). Despite its compact design, the QPRU achieves competitive forecasting performance, matching state-of-the-art baselines while offering important structural and practical advantages, including enhanced scalability and a reduced number of trainable parameters.