Parameter-Efficient Fine-Tuning (PEFT) methods for Transformers are designed for floating-point weights. When applied to extremely low-bit models (e.g., ternary {-1,0,1) they convert the base weights to floating point (dequantization) to add the update and then quantize again, which can diminish the benefits of aggressive quantization. We introduce a multiplicative ternary adapter that enables in-domain fine-tuning by applying an element-wise ternary mask to the base ternary Transformer weights, avoiding any dequantization to floating point and allowing direct merging back into the model. Constructed as the Kronecker product of two small trainable matrices and applied via a Hadamard product, the adapter preserves the ternary domain and merges with zero inference overhead. On a ternarized Llama-3.2-1B model, our method recovers substantial accuracy and surpasses stronger 2-bit baselines on most tasks, while retaining the efficiency advantages of ternary weights.

Binary Neural Networks (BNNs) are compact and efficient by using binary weights instead of real-valued weights. Current BNNs use latent real-valued weights during training, where several training hyper-parameters are inherited from real-valued networks. The interpretation of several of these hyperparameters is based on the magnitude of the real-valued weights. For BNNs, however, the magnitude of binary weights is not meaningful, and thus it is unclear what these hyperparameters actually do. One example is weight-decay, which aims to keep the magnitude of real-valued weights small. Other examples are latent weight initialization, the learning rate, and learning rate decay, which influence the magnitude of the real-valued weights. The magnitude is interpretable for real-valued weights, but loses its meaning for binary weights.
In this paper we offer a new interpretation of these magnitude-based hyperparameters based on higher-order gradient filtering during network optimization. Our analysis makes it possible to understand how magnitude-based hyperparameters influence the training of binary networks which allows for new optimization filters specifically designed for binary neural networks that are independent of their real-valued interpretation. Moreover, our improved understanding reduces the number of hyperparameters, which in turn eases the hyperparameter tuning effort which may lead to better hyperparameter values for improved accuracy.