Biological synapses transmit signals discretely and with noise, yet biological learners often generalize from few examples. Motivated by this contrast, we study how constraining neural-network weights to discrete grids affects fit and generalization in a controlled rule-learning task. We compare standard float32 training with binary, ternary, and small-integer weight constraints using straight-through estimators (STE), and we include a fine-grained fixed-point grid (Q16.16). We also evaluate a simple pure-integer coordinate-descent baseline to isolate optimization effects when updates are restricted to integer steps. On a 5×5 relational sum-comparison task, coarse discretization substantially reduces the train–test gap but also degrades attainable accuracy under our optimization procedures, indicating that reduced overfitting often coincides with underfitting. In contrast, Q16.16 fixed-point training preserves learnability and, in some settings, matches or exceeds our float32 baseline (e.g., 84% vs. 78% test accuracy at n = 500 in one configuration). We discuss these results in the context of prior work on quantization as regularization and on integer-only training, and we highlight optimization—rather than representational capacity—as the primary bottleneck for very low-bit weights in this setting.