class PaperModel(nn.Module):
    """
    Implementation of [Paper Title]
    Paper: [URL]

    Key components:
    - [Component 1]: [Brief description]
    - [Component 2]: [Brief description]
    """

    def __init__(self, config):
        super().__init__()
        # TODO: Initialize layers
        pass

    def forward(self, x):
        # TODO: Implement forward pass
        # Equation (1): ...
        # Equation (2): ...
        pass

# Step 2: Implement each component separately
class NovelAttention(nn.Module):
    """
    Implements Equation (3) from the paper:
    Attention(Q, K, V) = softmax(QK^T / sqrt(d_k)) * V
    With modification: [describe paper's modification]
    """
    pass

# Step 3: Implement the loss function
class PaperLoss(nn.Module):
    """
    Implements the training objective from Section X.X
    L = L_main + lambda * L_aux
    """
    pass

class MultiHeadAttention(nn.Module):
    def __init__(self, d_model: int, n_heads: int, dropout: float = 0.1):
        super().__init__()
        assert d_model % n_heads == 0
        self.d_k = d_model // n_heads
        self.W_q = nn.Linear(d_model, d_model)
        self.W_k = nn.Linear(d_model, d_model)
        self.W_v = nn.Linear(d_model, d_model)
        self.W_o = nn.Linear(d_model, d_model)
        self.dropout = nn.Dropout(dropout)

    def forward(self, q, k, v, mask=None):
        batch_size = q.size(0)
        q = self.W_q(q).view(batch_size, -1, self.n_heads, self.d_k).transpose(1, 2)
        k = self.W_k(k).view(batch_size, -1, self.n_heads, self.d_k).transpose(1, 2)
        v = self.W_v(v).view(batch_size, -1, self.n_heads, self.d_k).transpose(1, 2)
        scores = torch.matmul(q, k.transpose(-2, -1)) / math.sqrt(self.d_k)
        if mask is not None:
            scores = scores.masked_fill(mask == 0, float('-inf'))
        attn = self.dropout(F.softmax(scores, dim=-1))
        out = torch.matmul(attn, v)
        return self.W_o(out.transpose(1, 2).contiguous().view(batch_size, -1, self.d_model))

class SinusoidalPositionalEncoding(nn.Module):
    def __init__(self, d_model: int, max_len: int = 5000):
        super().__init__()
        pe = torch.zeros(max_len, d_model)
        position = torch.arange(0, max_len, dtype=torch.float).unsqueeze(1)
        div_term = torch.exp(torch.arange(0, d_model, 2).float() * (-math.log(10000.0) / d_model))
        pe[:, 0::2] = torch.sin(position * div_term)
        pe[:, 1::2] = torch.cos(position * div_term)
        self.register_buffer('pe', pe.unsqueeze(0))

    def forward(self, x):
        return x + self.pe[:, :x.size(1)]


class RotaryPositionalEmbedding(nn.Module):
    def __init__(self, dim: int, max_len: int = 5000, base: int = 10000):
        super().__init__()
        inv_freq = 1.0 / (base ** (torch.arange(0, dim, 2).float() / dim))
        self.register_buffer('inv_freq', inv_freq)

    def forward(self, x, seq_len: int):
        t = torch.arange(seq_len, device=x.device).type_as(self.inv_freq)
        freqs = torch.einsum('i,j->ij', t, self.inv_freq)
        return torch.cat((freqs, freqs), dim=-1)[None, :, :]

class ContrastiveLoss(nn.Module):
    """InfoNCE / Contrastive loss for representation learning."""
    def __init__(self, temperature: float = 0.07):
        super().__init__()
        self.temperature = temperature

    def forward(self, z_i, z_j):
        z_i = F.normalize(z_i, dim=1)
        z_j = F.normalize(z_j, dim=1)
        batch_size = z_i.size(0)
        representations = torch.cat([z_i, z_j], dim=0)
        similarity = torch.mm(representations, representations.t()) / self.temperature
        labels = torch.cat([torch.arange(batch_size) + batch_size,
                           torch.arange(batch_size)]).to(z_i.device)
        mask = torch.eye(2 * batch_size, device=z_i.device).bool()
        similarity.masked_fill_(mask, float('-inf'))
        return F.cross_entropy(similarity, labels)

def test_attention_shapes():
    attn = MultiHeadAttention(d_model=512, n_heads=8)
    x = torch.randn(2, 10, 512)
    out = attn(x, x, x)
    assert out.shape == x.shape

def test_forward_backward():
    model = PaperModel(config)
    x = torch.randn(2, 3, 224, 224)
    y = model(x)
    loss = y.sum()
    loss.backward()  # Should not error

def compare_with_reference(our_model, ref_model, test_input):
    our_model.eval()
    ref_model.eval()
    with torch.no_grad():
        our_out = our_model(test_input)
        ref_out = ref_model(test_input)
    diff = (our_out - ref_out).abs()
    assert diff.max() < 1e-5, f"Max diff: {diff.max():.6f}"

"""
Implementation of: [Paper Title]
Authors: [Authors]
Paper: [URL]
Official code: [URL or "Not available"]

This implementation covers:
- [x] Core architecture (Section X)
- [x] Training procedure (Section Y)
- [ ] [Optional component not implemented]

Known differences from paper:
- [Difference 1]: [Reason]

Reproduction status:
- Dataset: [name] - [Achieved metric] vs [Paper metric]
"""