當量化破壞記憶：低精度時間推論中的遞迴狀態寫回

摘要

量化被廣泛用於降低神經網路推論的計算與記憶體需求。然而，在循環網路中，量化後的狀態會被儲存並於下一個時間步返回，因此儲存該狀態所依據的規則可能改變後續的計算。在此，我們引入「循環狀態回寫」（recurrent-state write-back）來指稱此規則，並在一個用於螢光壽命成像的緊湊型 GRU 編碼器－解碼器中隔離其影響；螢光壽命成像是一種用於定量生物成像的分子影像技術。其中一項核心任務是從高噪聲、時間分辨的螢光訊號中估計兩個壽命參數：短壽命成分 τ1 與長壽命成分 τ2。在保持訓練完成的模型不變的條件下，以確定性 4 位元狀態儲存取代連續狀態傳播，會使 τ1 與 τ2 的估計誤差分別增至約 70 倍與 300 倍。失敗發生於重複的小幅更新低於寫入閾值時，此時儲存的狀態幾乎保持不變，而網路仍持續提出變化。誤差回饋、殘差記憶與方向記憶能將這些受抑制的更新所含的資訊跨時間傳遞，並在無需重新訓練的情況下恢復準確度。精度掃描結果顯示，提高狀態精度可能使固定的循環解惡化；而匹配訓練則顯示，與狀態介面的相容性是可以學習的。為測試此行為是否超出 GRU 的範疇，我們在一個獨立訓練的 LSTM 中重複訓練後介入實驗。在該架構中，粗粒度回寫再現了前述失敗，誤差回饋恢復了準確度，而針對特定狀態的介入則顯示細胞狀態比隱藏狀態更為敏感。我們的結果確立循環狀態回寫是低精度循環動態的關鍵決定因素，並指出狀態儲存介面是量化循環推論中的核心設計考量。

English

Quantization is widely used to reduce the computational and memory demands of neural-network inference. In recurrent networks, however, the quantized state is stored and returned at the next time step, so the rule used to store that state can alter subsequent computations. Here, we introduce recurrent-state write-back to denote this rule and isolate its effect in a compact GRU encoder--decoder for fluorescence lifetime imaging, a molecular imaging modality used in quantitative biological imaging. A central task is estimating two lifetime parameters, the short-lived component τ1 and the long-lived component τ2, from high-noise time-resolved fluorescence signals. Holding the trained model fixed, replacing continuous state propagation with deterministic 4-bit state storage increases estimation errors for τ1 and τ2 by approximately 70x and 300x, respectively. Failure occurs when repeated small updates remain below the write threshold, leaving the stored state nearly fixed while the network continues to propose change. Error feedback, residual memory, and direction memory carry information from these suppressed updates across time and recover accuracy without retraining. Precision sweeps show that increasing state precision can worsen a fixed recurrent solution, while matched training shows that compatibility with the state interface can be learned. To test whether this behavior extends beyond the GRU, we repeat the post-training intervention in an independently trained LSTM, where coarse write-back reproduces the failure, error feedback restores accuracy, and state-specific interventions reveal greater sensitivity of the cell state than the hidden state. Our results establish recurrent-state write-back as a key determinant of low-precision recurrent dynamics and identify the state-storage interface as a central design consideration for quantized recurrent inference.