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@@ -251,9 +251,9 @@ So the takeaway is that **dot-product attention FLOPs only become dominant durin
 
 ### Sparsity and Mixture-of-Experts
 
-We'd be remiss not to briefly discuss Mixture of Experts (MoE) models<d-cite key="moe"></d-cite>, which replace the single dense MLP blocks in a standard Transformer with a set of independent MLPs that can be dynamically routed between. To a first approximation, **an MoE is a dense model with E MLP blocks per layer**, instead of just one. Each token activates k of these experts, typically k=2. This increases the parameter count by O(E), while keeping the total number of activated parameters roughly the same as the dense model.
+We'd be remiss not to briefly discuss Mixture of Experts (MoE) models<d-cite key="moe"></d-cite>, which replace the single dense MLP blocks in a standard Transformer with a set of independent MLPs that can be dynamically routed between. To a first approximation, **an MoE is a dense model with E MLP blocks per layer**, instead of just one. Each token activates $k$ of these experts, typically $k=2$. This increases the parameter count by $O(E)$, while multiplying the total number of activated parameters per token by $k$, compared with the dense version.
 
-{% include figure.liquid path="assets/img/moe.png" class="img-fluid img-small" caption="<b>Figure:</b> an example MoE layer with n experts. The gating expert routes each token to k of them, and the output of those k MLPs get summed. Our parameter count is n times the size of each expert, but only k are used for each token. <a href=\"https://deepgram.com/learn/mixture-of-experts-ml-model-guide\">Source</a>." %}
+{% include figure.liquid path="assets/img/moe.png" class="img-fluid img-small" caption="<b>Figure:</b> an example MoE layer with $n$ experts. The gating expert routes each token to $k$ of them, and the output of those $k$ MLPs get summed. Our parameter count is $n$ times the size of each expert, but only $k$ are used for each token. <a href=\"https://deepgram.com/learn/mixture-of-experts-ml-model-guide\">Source</a>." %}
 
 Compared to a dense model, an MoE introduces new comms, primarily two AllToAlls (one before and one after the MoE block) that route tokens to the correct expert and bring them back to their home device.<d-footnote>Technically, this only happens if we are data or sequence sharded along the same axis as our experts.</d-footnote> However as we saw in the previous section, the cost of each AllToAll is only 1/4 that of a comparable AllGather along a single axis (for a bidirectional ring).