SubLN Module: Quantization-Optimized Normalization

• SubLN module is a submodule-level normalization technique that mitigates training instability in ultra-low bitwidth (1.58-bit) quantized models.
• It is integrated in the BitNet Distillation pipeline to replace conventional normalization layers, preserving feature statistics within attention and feedforward submodules.
• Empirical results show that models using SubLN achieve up to 10x memory savings and 2.65x faster CPU inference, narrowing the gap with full-precision models.

The SubLN (“Submodule Linearity Normalization”; Editor's term) module is a neural network component introduced in the BitNet architecture and further utilized in BitNet Distillation (Wu et al., 15 Oct 2025). It is designed to facilitate robust training and inference for ultra-low bitwidth LLMs, particularly those quantized to ternary weight representations (1.58 bits). The SubLN module is closely linked to advances in quantized model normalization and submodule-wise model merging, as highlighted by recent research in both efficient deep learning systems and practical LLM merging techniques.

1. Definition and Functional Role

The SubLN module is a normalization mechanism applied at the submodule level of neural network architectures. In BitNet and BitNet Distillation pipelines, it acts as a substitute or augmentation to conventional normalization layers (such as LayerNorm, RMSNorm), tailored for the instabilities encountered when weights are aggressively quantized (e.g., to ternary values). Instead of normalizing features globally or per-layer, SubLN performs normalization within each logical submodule (such as multi-head attention blocks or MLP sub-blocks), mitigating the training divergence and performance drop associated with ultra-low bitwidth quantization.

2. Architectural Integration

Within BitNet Distillation, the application of the SubLN module follows a specific pipeline:

• First, a full-precision LLM is fine-tuned or continually pre-trained for the specific downstream task.
• Second, the fine-tuned model is quantized to the 1.58-bit (ternary) format.
• Third, the SubLN module is integrated into the quantized model to replace or supplement standard normalizations, ensuring per-submodule feature statistics are maintained.

The typical locations for SubLN insertion are immediately following the output of submodules such as self-attention heads and feedforward layers in transformer blocks. This design is motivated by the observation that low-bitwidth quantization substantially alters the distribution of activations, which can undermine normalization when performed at the layer or model level.

3. Mathematical Properties

SubLN normalization operates on the output $\mathbf{h}$ of a submodule according to the following form:

$$\mathbf{h}_{\text{SubLN}} = \frac{\mathbf{h} - \mu}{\sigma} \cdot \gamma + \beta$$

where $\mu$ and $\sigma$ are the mean and standard deviation calculated over the submodule's output channel, and $\gamma$, $\beta$ are trainable scale and shift parameters. The distinction from standard LayerNorm lies in the computation domain — $\mu$ and $\sigma$ are computed for each submodule individually, not across the whole layer. This fine-grained normalization is empirically shown to reduce the variance in training dynamics for quantized weights.

4. Empirical Performance

Experimental results from BitNet Distillation demonstrate that the SubLN module is crucial for narrowing the accuracy gap between full-precision and ternary LLMs:

• Using SubLN in quantized models yields performance “comparable to the full-precision counterpart models across model size.”
• Models employing SubLN achieve up to 10x memory savings and 2.65x faster inference on CPU, substantiating the benefit for deployment.
• Without SubLN, finetuned quantized models exhibit unstable gradients and significant performance drops, especially in deep architectures.

This establishes SubLN as essential for practical deployment of ultra-low precision transformers without retraining from scratch or sacrificing downstream effectiveness.

5. Connection to Submodule Linearity and Merging

Submodule normalization is supported by the principle that submodules — such as self-attention blocks and MLPs — exhibit stronger linearity properties than models analyzed globally (Dai et al., 15 Apr 2025). By normalizing at the submodule level, SubLN implicitly supports statistical independence and reduces non-linearity scores, improving the effectiveness of subsequently applied distillation and merging strategies. This is particularly leveraged in scenarios where models are merged for multi-task capabilities or distilled for low-resource inference.

6. Deployment Considerations

The SubLN module is architecture-agnostic but most beneficial in transformer family models subject to aggressive quantization. Its computational cost is negligible compared to the memory and speedup advantages for CPU inference. Integration into existing training frameworks typically requires modifying only the normalization calls per submodule. The BitNet Distillation pipeline (Wu et al., 15 Oct 2025) provides reference implementations illustrating SubLN integration.

7. Ongoing Research and Future Perspectives

Current research focuses on extending SubLN to finer granularity (e.g., head-wise or channel-wise normalization), adaptive SubLN variants for mixed-precision models, and its interaction with emerging submodule-wise model fusion techniques (Dai et al., 15 Apr 2025). The evidence suggests SubLN remains pivotal for keeping deep, quantized models stable and performant across varying deployment contexts. Its modularity enables interoperability with multi-head attention distillation and continual pre-training strategies.

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The SubLN module thus serves as a foundational normalization technique for advanced quantized and merged LLMs, ensuring stable training, efficient inference, and reliable downstream performance.