Understanding when quantization is effective — and when it becomes a liability — requires synthesizing theoretical insights about model scale, task sensitivity, and the boundaries of precision. As you have seen in previous chapters, quantization introduces noise and constraints, but the impact of these changes depends heavily on the size of the model and the nature of the task at hand.

Larger neural networks often exhibit greater robustness to quantization. Theoretical results discussed earlier, such as error accumulation and redundancy in over-parameterized models, suggest that as model scale increases, individual quantization errors are less likely to cause catastrophic failures. This is partly due to the distributed representation of information: when many parameters contribute to each prediction, the effect of quantizing any single parameter is diluted. Furthermore, large models can absorb quantization noise due to their higher capacity, maintaining accuracy even as precision is reduced. In contrast, small models have fewer parameters and less redundancy, so quantization noise can have a disproportionately large effect, sometimes leading to rapid accuracy degradation.

The sensitivity of a task to quantization is equally crucial. Some tasks, like image classification on large, diverse datasets, are more tolerant of quantization noise because the underlying patterns are robust and the models can compensate for minor inaccuracies. On the other hand, tasks requiring fine-grained precision — such as speech recognition, medical diagnosis, or regression tasks with tight error margins — are much less forgiving. In these cases, even small quantization errors can lead to significant performance drops, as the model's outputs may cross critical thresholds or lose subtle distinctions essential for the task.

The boundaries where quantization fails are most apparent as you approach extremely low precision, such as INT4 or below. At these levels, the representational capacity of each parameter is severely restricted, and quantization noise can overwhelm the signal. Theoretical limits — such as the minimum number of bits required to represent meaningful information in weights and activations — become binding constraints. In practice, you may observe that while some large models can tolerate INT8 or even INT6 quantization with modest accuracy loss, moving to INT4 or binary representations often results in abrupt performance collapse. This collapse is not always gradual; instead, there is often a sharp threshold where the model transitions from "good enough" to "completely broken," reflecting the non-linear effects of information loss at extreme quantization.