I am given
and
How to find $\left|h_{(w_b,w_t)}(s_i,p_i) \right| \leq $ ?
My attempt
$\left|h_{(w_b,w_t)}(s_i,p_i) \right| \leq {q \cdot \mathcal{C}}^{2}$ [ using cauchy]
Am I wrong? Here w are weights of neural net.
2026-04-09 16:12:53.1775751173
What will be the lower bound of $\left|h_{(w_b,w_t)}(s_i,p_i) \right|$
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Simply use Cauchy-Schwarz
$$\left|h_{(w_b,w_t)}(s_i,p_i) \right| \leq \|B_{w_{b}}(s)\| \cdot \|T_{w_{t}}(p)\| $$
we also know $$\|x\|_\infty \le \|x\|_2 \le \sqrt{n} \|x\|_\infty. $$
So $$\left|h_{(w_b,w_t)}(s_i,p_i) \right| \leq \sqrt{\mathcal{q}} \mathcal{C} \cdot \sqrt{\mathcal{q}} \mathcal{C} $$