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227 changes: 227 additions & 0 deletions challenges/hard/93_llama_transformer_block/challenge.html
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<p>
Implement a single Llama-style transformer decoder block. Given an input tensor \(x\) of shape
<code>(seq_len, 512)</code>, a packed weight buffer, and precomputed RoPE tables, compute the
output using pre-norm architecture with Grouped Query Attention (GQA), Rotary Position Embeddings
(RoPE), and a SwiGLU feed-forward network.
</p>

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<!-- Input label -->
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<p>
The block follows Llama's <strong>pre-norm</strong> architecture. Unlike GPT-2, it uses
<strong>RMSNorm</strong> (no mean subtraction, no additive bias), <strong>Grouped Query
Attention</strong> with 8 query heads and 2 key/value heads, <strong>Rotary Position
Embeddings</strong> applied to Q and K, and a <strong>SwiGLU</strong> feed-forward network.
None of the linear projections have bias terms.
</p>

\[
\begin{aligned}
x' &= x + \text{Attn}\!\left(\text{RMSNorm}_1(x),\; \cos,\; \sin\right) \\[4pt]
\text{output} &= x' + \text{FFN}\!\left(\text{RMSNorm}_2(x')\right)
\end{aligned}
\]

<p>The sub-operations in detail:</p>

\[
\begin{aligned}
\text{RMSNorm}(z, w) &= \frac{z}{\sqrt{\frac{1}{d}\sum_i z_i^2 + \varepsilon}} \odot w, \quad \varepsilon = 10^{-5} \\[8pt]
Q &= \text{RMSNorm}_1(x)\, W_Q^\top \in \mathbb{R}^{T \times 512}, \quad \text{reshape to } (T, 8, 64) \\[4pt]
K &= \text{RMSNorm}_1(x)\, W_K^\top \in \mathbb{R}^{T \times 128}, \quad \text{reshape to } (T, 2, 64) \\[4pt]
V &= \text{RMSNorm}_1(x)\, W_V^\top \in \mathbb{R}^{T \times 128}, \quad \text{reshape to } (T, 2, 64) \\[8pt]
\text{RoPE}(q, \cos, \sin) &: \quad [q_1 \mid q_2] \mapsto [q_1 \odot \cos - q_2 \odot \sin \mid q_1 \odot \sin + q_2 \odot \cos] \\[4pt]
&\quad q_1 = q[\ldots, {:}32],\; q_2 = q[\ldots, {32:}] \\[8pt]
\text{GQA} &: \text{repeat } K,V \text{ along head dim } 4\times \text{ to match 8 Q heads} \\[4pt]
\text{head}_i &= \text{softmax}\!\left(\frac{Q_i K_i^\top}{\sqrt{64}} + M_{\text{causal}}\right) V_i \\[8pt]
\text{Attn}(x) &= \text{Concat}(\text{head}_1, \ldots, \text{head}_8)\; W_O^\top \\[8pt]
\text{FFN}(z) &= \bigl(\text{SiLU}(z\, W_{\text{gate}}^\top) \odot z\, W_{\text{up}}^\top\bigr)\; W_{\text{down}}^\top
\end{aligned}
\]

<p>where \(M_{\text{causal}}\) is the upper-triangular causal mask (\(-\infty\) above the diagonal)
and \(\text{SiLU}(x) = x \cdot \sigma(x)\).</p>

<h2>Implementation Requirements</h2>
<ul>
<li>Use only native features (external libraries are not permitted)</li>
<li>The <code>solve</code> function signature must remain unchanged</li>
<li>The final result must be stored in the <code>output</code> tensor</li>
<li>RMSNorm uses \(\varepsilon = 10^{-5}\), no additive bias</li>
<li>Apply causal masking: position \(i\) attends only to positions \(\le i\)</li>
<li>Repeat K and V heads \(4\times\) (GQA groups) before computing attention</li>
<li><code>cos</code> and <code>sin</code> have shape <code>(seq_len, 32)</code> — apply
them to both Q and K heads independently</li>
</ul>

<h2>Weight Layout</h2>
<p>All parameters are packed into a single contiguous <code>weights</code> buffer
(2,819,072 floats) in the order below. All 2-D matrices are stored row-major
with shape <code>(out_dim, in_dim)</code>. There are no bias terms.</p>

<table style="border-collapse:separate; border-spacing:16px 6px;">
<tr>
<th style="text-align:left;">Parameter</th>
<th style="text-align:left;">Shape</th>
<th style="text-align:right;">Size</th>
<th style="text-align:right;">Offset</th>
</tr>
<tr>
<td>\(w_1\) (RMSNorm 1 scale)</td>
<td>(512,)</td>
<td style="text-align:right;">512</td>
<td style="text-align:right;">0</td>
</tr>
<tr>
<td>\(W_Q\)</td>
<td>(512, 512)</td>
<td style="text-align:right;">262,144</td>
<td style="text-align:right;">512</td>
</tr>
<tr>
<td>\(W_K\)</td>
<td>(128, 512)</td>
<td style="text-align:right;">65,536</td>
<td style="text-align:right;">262,656</td>
</tr>
<tr>
<td>\(W_V\)</td>
<td>(128, 512)</td>
<td style="text-align:right;">65,536</td>
<td style="text-align:right;">328,192</td>
</tr>
<tr>
<td>\(W_O\)</td>
<td>(512, 512)</td>
<td style="text-align:right;">262,144</td>
<td style="text-align:right;">393,728</td>
</tr>
<tr>
<td>\(w_2\) (RMSNorm 2 scale)</td>
<td>(512,)</td>
<td style="text-align:right;">512</td>
<td style="text-align:right;">655,872</td>
</tr>
<tr>
<td>\(W_{\text{gate}}\)</td>
<td>(1408, 512)</td>
<td style="text-align:right;">720,896</td>
<td style="text-align:right;">656,384</td>
</tr>
<tr>
<td>\(W_{\text{up}}\)</td>
<td>(1408, 512)</td>
<td style="text-align:right;">720,896</td>
<td style="text-align:right;">1,377,280</td>
</tr>
<tr>
<td>\(W_{\text{down}}\)</td>
<td>(512, 1408)</td>
<td style="text-align:right;">720,896</td>
<td style="text-align:right;">2,098,176</td>
</tr>
</table>

<h2>Example</h2>
<p>With <code>seq_len</code> = 4, <code>x</code> drawn uniformly from [&minus;1, 1], and randomly
initialized weights:</p>
<pre>
Input: x.shape = (4, 512) # 4 token hidden states
weights.shape = (2,819,072,) # packed weight buffer
cos.shape = (4, 32) # precomputed RoPE cosines
sin.shape = (4, 32) # precomputed RoPE sines
seq_len = 4
Output: output.shape = (4, 512) # transformed token hidden states
</pre>

<h2>Constraints</h2>
<ul>
<li><code>d_model</code> = 512, <code>n_q_heads</code> = 8, <code>n_kv_heads</code> = 2,
<code>head_dim</code> = 64, <code>ffn_hidden</code> = 1,408</li>
<li>1 &le; <code>seq_len</code> &le; 4,096</li>
<li>All tensors use 32-bit floating point</li>
<li>Performance is measured with <code>seq_len</code> = 2,048</li>
</ul>
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