Dynamic Thresholding Block (DTB)

• Dynamic Thresholding Block (DTB) is an adaptive mechanism that replaces static thresholds with values based on input statistics, historical data, or learned parameters.
• It is applied in digital logic, binary neural networks, anomaly detection, and non-volatile memories to enhance resilience, efficiency, and accuracy.
• DTBs enable dynamic calibration with low computational overhead, yielding improvements such as energy savings, reduced detection delays, and higher model performance.

A Dynamic Thresholding Block (DTB) is an architectural or algorithmic construct that adaptively determines decision boundaries or quantization thresholds based on local, recent, or learned statistics, rather than relying on static (fixed) thresholds. DTBs have been formulated across several domains, including digital logic, binary neural networks (BNNs), anomaly detection, and non-volatile memory (NVM) readout. Dynamic thresholding enables higher resilience to distributional drift, maximizes representational capacity in quantized systems, and accelerates or improves model performance under real-world nonstationarity and class imbalance.

1. Core Principles and Definitions

The core principle of a DTB is to replace a static threshold $\theta$ by a quantity $T$ that reflects either (a) input-dependent statistics (e.g., per-sample features in DL systems), (b) recent activity history (e.g., rolling statistics of errors), or (c) population-level adaptation (e.g., class-conditional confidence), driven by explicit modules or meta-learners.

• In digital logic, a DTB physically realizes threshold logic (weighted sum and comparison) using dynamic, stateful devices for fast, energy-efficient operation (Sharad et al., 2013).
• In BNNs and binarized transformers, a DTB (often called "DySign") computes a per-channel, per-sample threshold $\tau_c$ via learned mappings from layer activations, drastically reducing information loss from binarization (Zhang et al., 2022).
• In sequential anomaly detection, a DTB adaptively maintains $T_t$ blending global and recent reconstruction error statistics, increasing detection accuracy and timeliness (Bell1 et al., 2022).
• In NVM readout, a DTB updates sense thresholds based on NN inferences, minimizing bit errors by online calibration to channel conditions (Mei et al., 2019).

2. Fundamental Mathematical Formulations

Digital Logic

A threshold logic gate implemented as a DTB operates:

$$S = \sum_{i=1}^N w_i x_i, \quad y = \begin{cases} 1 & S \geq \theta \ 0 & S < \theta \end{cases}$$

In dynamic resistive threshold logic, weights $w_i$ and threshold $\theta$ are realized as conductances in a dynamic CMOS latch (Sharad et al., 2013).

Binary Neural Networks

For an activation block $X \in \mathbb{R}^{C \times H \times W}$,

• Compute channel-wise summary $s = \text{GAP}(X) \in \mathbb{R}^C$
• Learn dynamic thresholds as:

$$\tau = W_2\,\phi(W_1 s + b_1) + b_2 \in \mathbb{R}^C$$

• Binarize using:

$$B_{c}(i,j) = \text{Sign}\left(X_c(i,j) - \tau_c\right)$$

where $W_1, W_2$ are weights, $\phi$ is a nonlinearity (ReLU/GELU) (Zhang et al., 2022).

Anomaly Detection

With windowed error statistics $M_t$ (mean) and $S_t$ (stdev) computed over $j$ timesteps, and static baseline $L = \mu_{\text{train}} + \sigma_{\text{train}}$,

$T_t = W_y L + W_z (M_t + S_t)$

with $W_y, W_z$ experimentally chosen (Bell1 et al., 2022).

NVM Readout

Given hard NN estimates $\hat x^{(i)}$ and raw reads $y^{(i)}$,

$$T^{(k)} = \arg \min_T \sum_{i=1}^M d(\hat x^{(i)}, \bar x^{(i)}(T))$$

where $d(\cdot,\cdot)$ is Hamming distance of hard decisions after thresholding (Mei et al., 2019).

3. Representative Implementations

Dynamic Resistive Threshold Logic (DRTL)

A DTB in DRTL is a dynamic, small-fan-in gate in which weights and threshold are stored in programmable resistive elements (e.g., spin-torque MTJs or memristors) embedded in a CMOS dynamic comparator. Each DTB includes:

• Pull-down branches encoding both sign and magnitude of weights
• Dynamic latching (evaluate/hold phases), allowing pipelining at GHz rates
• Sub-femtojoule switching energy and per-gate delay $<1$ ns
• Low-swing programmable memristor interconnects for system-level energy reduction Fully pipelined DRTL networks show $>100\times$ reduction in energy-delay product compared to LUT-based FPGAs (Sharad et al., 2013).

DTB for Binary Quantization in Deep Learning

The "DySign" DTB module interposes between convolutional activations and the binarization step:

1. Apply global average pooling per channel ($s$).
2. Pass $s$ through two FC layers with bottleneck and nonlinearity to yield adaptive thresholds $\tau$.
3. Use $\tau$ in lieu of static thresholds in the sign operation. This structure is fully differentiable and parameter-efficient, adding only $C + C^2/\gamma$ float ops per block, and provides 1.5–1.8% top-1 ImageNet accuracy lift for binarized MobileNetV1/ResNet18, with similar boosts for binarized transformers (Zhang et al., 2022).

DTB in Sequential Anomaly Detection

The DTB maintains and updates a window buffer of recent losses; at every timestep, it interpolates between a static baseline and empirical rolling statistics, flagging anomalies when the reconstruction error exceeds the adaptive threshold. Weighted MSE during training sharpens the learned definition of "normal," further improving detection specificity (Bell1 et al., 2022).

Dynamic Threshold Detection in NVM

Upon ECC failure or on a timer, the DTB module runs an NN (MLP/RNN) detector, computes hard decision vectors, and then adjusts the read threshold $T$ so that conventional hard detection best matches NN outputs. Normal, latency-critical read operations use the last-compensated scalar threshold, thus maintaining high throughput with rare, rapid recalibration. DTD built with an RNN achieves BER indistinguishable from the optimum MAP detector with perfect channel knowledge (Mei et al., 2019).

4. Comparative Analysis Across Domains

A summary of DTB roles, mechanisms, and outcomes:

Domain	DTB Mechanism	Benefit/Outcome
Digital logic (DRTL)	Resistively-weighted dynamic latch	$>100\times$ EDP reduction
BNN/transformers	Per-channel, sample-adaptive threshold	$+1.5$–$+8.4\%$ accuracy, very low overhead
Anomaly detection	Rolling error buffer, adaptive blend	+6 pp accuracy, 80% reduction in detection delay
NVM readout	NN-guided, error-minimizing threshold	Optimal BER, negligible throughput penalty

These results suggest that data- or context-driven adjustment of decision boundaries yields significant advantages over static thresholds, especially where input statistics, drift, or distributions are nonstationary.

5. Learning, Optimization, and Practical Considerations

DTB parameters (e.g., weights in DySign, window sizes and blending constants in anomaly detection) are typically learned or tuned end-to-end with the primary task loss. Notably:

• Binary neural network DTBs are trained via standard backprop; the non-differentiable sign is handled with straight-through estimators, and no bespoke loss term is required for thresholds (Zhang et al., 2022).
• Anomaly detection DTBs use a small buffer and simple scalar computations, requiring negligible computational overhead (Bell1 et al., 2022).
• NVM DTBs (DTD) update only on rare triggers, so latency and power impact are negligible even when employing relatively heavy neural inference for threshold selection (Mei et al., 2019).
• In DRTL, the static nature of resistive weights is offset by their rapid, low-energy programmability and inherent pipeline synchronization (Sharad et al., 2013).

6. Empirical Results and Performance Metrics

Specific empirical findings:

• DRTL-based DTBs outperform 4-input-LUT FPGAs (ISCAS-85 benchmarks): $>99.8\%$ energy savings, $>100\times$ EDP reduction; sub-nanosecond per-gate latency (Sharad et al., 2013).
• DySign-equipped BNNs (DyBCNN): MobileNetV1 (71.2% Top-1, +1.8%), ResNet-18 (67.4%, +1.5%), DyBinaryCCT ViT ($+8.4\%$ Top-1) (Zhang et al., 2022).
• Anomaly detection: LSTM-AE + DTB (dynamic): mean accuracy $0.809\pm0.10$ (+6 pp over static), detection delay $0.5$ s ($<25\%$ of static threshold) (Bell1 et al., 2022).
• NVM: DTD at 15 dB SNR achieves $9\times10^{-6}$ BER (RNN-based), versus $1\times10^{-2}$ with mid-point threshold; matches optimum detector curve, negligible throughput penalty (Mei et al., 2019).

7. Extensions and Future Directions

Extensions for DTB modules include:

• For anomaly detection, adaptively tuning the window size $j$ or incorporating higher-order statistics of reconstruction loss; exponential smoothing for robust threshold evolution; per-group or multimodal thresholding as in multi-sensor systems (Bell1 et al., 2022).
• In NVM DTBs, additional context (e.g., temperature, wear-level) could inform NN threshold predictions, and hardware-aware optimizations (accelerator power gating, adaptive update frequency) further reduce overhead (Mei et al., 2019).
• For BNN DTBs, expanding to weight quantization or more complex activation summary (e.g., higher moments, token- or spatial-wise thresholds) can further close the gap to full-precision networks (Zhang et al., 2022).
• For DRTL, scaling to higher fan-in and more complex logic or integrating with neuromorphic architectures expands applicability (Sharad et al., 2013).

• "Ultra-low Energy, High-Performance Dynamic Resistive Threshold Logic" (Sharad et al., 2013)
• "Boosting Binary Neural Networks via Dynamic Thresholds Learning" (Zhang et al., 2022)
• "Anomaly Detection for Unmanned Aerial Vehicle Sensor Data Using a Stacked Recurrent Autoencoder Method with Dynamic Thresholding" (Bell1 et al., 2022)
• "Neural Network-Based Dynamic Threshold Detection for Non-Volatile Memories" (Mei et al., 2019)