diff --git a/dist/index.html b/dist/index.html index 634f030..6ef4c51 100644 --- a/dist/index.html +++ b/dist/index.html @@ -214,10 +214,6 @@ all constraints. $\text{Feasible@}K$ is then the fraction of problems where model $m$ produces a feasible design in $K$ attempts:

-
- $$\text{feasible}(d, p) = \mathbf{1}[\text{correct}(d, p)] \cdot \mathbf{1}[\text{synth}(d)] \cdot - \prod_{j=1}^{N_c} \mathbf{1}[d \text{ meets constraint } c_p(j)]$$ -
$$\text{Feasible@}K = \frac{1}{|P|} \sum_{p \in P} \max_{1 \le i \le K} \text{feasible}(d^{(i)}, p)$$
@@ -229,35 +225,12 @@ PPA Optimization Index

- $\text{Feasible@}K$ measures whether a model can produce a usable design, but not how well that design - optimises the target hardware. To quantify synthesis quality among feasible designs, we define the - Maximum Objective Quality (MOQ). -

-

- For each problem $p$, let $f_p^*$ denote the objective value achieved by the reference implementation. For a - feasible generated design $d$, define its normalised quality $q_p(d)$: + For a feasible design $d$, the quality ratio $q_p(d)$ measures performance relative to the reference design ($q_p(d) > 1$ improves on the reference, while $q_p(d) < 1$ underperforms). $\text{MOQ@}K$ is the geometric mean of the best quality ratio found within $K$ attempts:

- $$q_p(d) = \begin{cases} \frac{f(d)}{f_p^*} & \text{if } \text{dir}_p = \;\uparrow (F_{\text{max}}) \\ - \frac{f_p^*}{f(d)} & \text{if } \text{dir}_p = \;\downarrow (\text{LUTs}) \end{cases}$$ + $$\text{MOQ@}K = \left( \prod_{p \in P} \max_{\substack{1 \le i \le K \\ \text{feasible}(d^{(i)}, p) = + 1}} q_p(d^{(i)}) \right)^{\frac{1}{|P|}}$$
-

- Here, $q_p(d) = 1$ means the generated design matches the reference, $q_p(d) > 1$ means it improves on the - reference, and $q_p(d) < 1$ indicates underperformance.

-

- Across a benchmark set $P$, $\text{MOQ@}K$ is defined as the geometric mean, over all problems, of the - best feasible objective ratio found within the first $K$ attempts: -

-
- $$\text{MOQ@}K = \left( \prod_{p \in P} \max_{\substack{1 \le i \le K \\ \text{feasible}(d^{(i)}, p) = - 1}} q_p(d^{(i)}) \right)^{\frac{1}{|P|}}$$ -
-

- The geometric mean is the natural aggregator for ratio-valued scores: a design $2\times$ better and one - $0.5\times$ worse correctly average to $1.0$ ($\sqrt{2 \times 0.5} = 1.0$), whereas the arithmetic mean - would incorrectly report a net gain of $1.25$. $\text{MOQ@}K$ is conditional on feasibility and must be - interpreted alongside $\text{Feasible@}K$. -

diff --git a/index.html b/index.html index 9782115..eed6a2f 100644 --- a/index.html +++ b/index.html @@ -213,10 +213,6 @@ all constraints. $\text{Feasible@}K$ is then the fraction of problems where model $m$ produces a feasible design in $K$ attempts:

-
- $$\text{feasible}(d, p) = \mathbf{1}[\text{correct}(d, p)] \cdot \mathbf{1}[\text{synth}(d)] \cdot - \prod_{j=1}^{N_c} \mathbf{1}[d \text{ meets constraint } c_p(j)]$$ -
$$\text{Feasible@}K = \frac{1}{|P|} \sum_{p \in P} \max_{1 \le i \le K} \text{feasible}(d^{(i)}, p)$$
@@ -228,35 +224,12 @@ PPA Optimization Index

- $\text{Feasible@}K$ measures whether a model can produce a usable design, but not how well that design - optimises the target hardware. To quantify synthesis quality among feasible designs, we define the - Maximum Objective Quality (MOQ). -

-

- For each problem $p$, let $f_p^*$ denote the objective value achieved by the reference implementation. For a - feasible generated design $d$, define its normalised quality $q_p(d)$: + For a feasible design $d$, the quality ratio $q_p(d)$ measures performance relative to the reference design ($q_p(d) > 1$ improves on the reference, while $q_p(d) < 1$ underperforms). $\text{MOQ@}K$ is the geometric mean of the best quality ratio found within $K$ attempts:

- $$q_p(d) = \begin{cases} \frac{f(d)}{f_p^*} & \text{if } \text{dir}_p = \;\uparrow (F_{\text{max}}) \\ - \frac{f_p^*}{f(d)} & \text{if } \text{dir}_p = \;\downarrow (\text{LUTs}) \end{cases}$$ + $$\text{MOQ@}K = \left( \prod_{p \in P} \max_{\substack{1 \le i \le K \\ \text{feasible}(d^{(i)}, p) = + 1}} q_p(d^{(i)}) \right)^{\frac{1}{|P|}}$$
-

- Here, $q_p(d) = 1$ means the generated design matches the reference, $q_p(d) > 1$ means it improves on the - reference, and $q_p(d) < 1$ indicates underperformance.

-

- Across a benchmark set $P$, $\text{MOQ@}K$ is defined as the geometric mean, over all problems, of the - best feasible objective ratio found within the first $K$ attempts: -

-
- $$\text{MOQ@}K = \left( \prod_{p \in P} \max_{\substack{1 \le i \le K \\ \text{feasible}(d^{(i)}, p) = - 1}} q_p(d^{(i)}) \right)^{\frac{1}{|P|}}$$ -
-

- The geometric mean is the natural aggregator for ratio-valued scores: a design $2\times$ better and one - $0.5\times$ worse correctly average to $1.0$ ($\sqrt{2 \times 0.5} = 1.0$), whereas the arithmetic mean - would incorrectly report a net gain of $1.25$. $\text{MOQ@}K$ is conditional on feasibility and must be - interpreted alongside $\text{Feasible@}K$. -