The size of a model has been a strong predictor of its quality, as well as its cost. As such, the trade-off between model cost and quality has been well-studied. Post-training optimizations like quantization and pruning have typically focused on reducing the overall volume of pre-trained models to reduce inference costs while maintaining model quality. However, recent advancements have introduced optimization techniques that, interestingly, expand models post-training, increasing model size to improve quality when reducing volume. For instance, to enable 4-bit weight and activation quantization, incoherence processing often necessitates inserting online Hadamard rotations in the compute graph, and preserving highly sensitive weights often calls for additional higher precision computations. However, if application requirements cannot be met, the prevailing solution is to relax quantization constraints. In contrast, we demonstrate post-training model expansion is a viable strategy to improve model quality within a quantization co-design space, and provide theoretical justification. We show it is possible to progressively and selectively expand the size of a pre-trained large language model (LLM) to improve model quality without end-to-end retraining. In particular, when quantizing the weights and activations to 4 bits for Llama3 1B, we reduce the zero-shot accuracy gap to full precision by an average of 3% relative to both QuaRot and SpinQuant with only 5% more parameters, which is still a 3.8% reduction in volume relative to a BF16 reference model.

Deep learning as a means to inferencing has proliferated thanks to its versatility and ability to approach or exceed human-level accuracy. These computational models have seemingly insatiable appetites for computational resources not only while training, but also when deployed at scales ranging from data centers all the way down to embedded devices. As such, increasing consideration is being made to maximize the computational efficiency given limited hardware and energy resources and, as a result, inferencing with reduced precision has emerged as a viable alternative to the IEEE 754 Standard for Floating-Point Arithmetic. We propose a quantization scheme that allows inferencing to be carried out using arithmetic that is fundamentally more efficient when compared to even half-precision floating-point. Our quantization procedure is significant in that we determine our quantization scheme parameters by calibrating against its reference floating-point model using a single inference batch rather than (re)training and achieve end-to-end post quantization accuracies comparable to the reference model.