Llama 3 8B · Generate RoPE coefficients

Generate RoPE coefficients

no parameterstorch.polar(torch.ones_like(freqs), freqs)

Construct the position-dependent rotations used by attention.

{\htmlData{light=model-rotations frequencies}{{\htmlClass{vl-stream-context}{R_{t,j}}}}}=e^{\mathrm i t\omega_j}

in: $p$ [T positions]
out: $R$ [T positions, 64 pairs]

Computed once, when the model is built, for 2 × max_seq_len positions in float32 and stored as complex64 (model.py 49–54, 271–275); each forward pass takes its T rows (282).

Explanation

Here $\omega_j=500000^{-2j/128}$ , with 500000 the configured rope_theta (model.py 50; sku_list.py 203, 221).

Codemodel.py 49–54, 271–282 · sku_list.py 19, 188–207

model.py 49–54

def precompute_freqs_cis(dim: int, end: int, theta: float = 10000.0):
    freqs = 1.0 / (theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim))
    t = torch.arange(end, device=freqs.device, dtype=torch.float32)
    freqs = torch.outer(t, freqs)
    freqs_cis = torch.polar(torch.ones_like(freqs), freqs)  # complex64
    return freqs_cis

model.py 271–282

        self.freqs_cis = precompute_freqs_cis(
            params.dim // params.n_heads,
            params.max_seq_len * 2,
            params.rope_theta,
        )

    @torch.inference_mode()
    def forward(self, tokens: torch.Tensor, start_pos: int):
        _bsz, seqlen = tokens.shape
        h = self.tok_embeddings(tokens)
        self.freqs_cis = self.freqs_cis.to(h.device)
        freqs_cis = self.freqs_cis[start_pos : start_pos + seqlen]

sku_list.py 19

LLAMA3_VOCAB_SIZE = 128256

sku_list.py 188–207

def llama3_base_models() -> list[Model]:
    return [
        Model(
            core_model_id=CoreModelId.llama3_8b,
            description="Llama 3 8b model",
            huggingface_repo="meta-llama/Llama-3-8B",
            arch_args={
                "dim": 4096,
                "n_layers": 32,
                "n_heads": 32,
                "n_kv_heads": 8,
                "vocab_size": LLAMA3_VOCAB_SIZE,
                "ffn_dim_multiplier": 1.3,
                "multiple_of": 1024,
                "norm_eps": 1e-05,
                "rope_theta": 500000.0,
                "use_scaled_rope": False,
            },
            pth_file_count=1,
        ),

Sources2

Direct evidence

RoPE precomputation uses position indices; the forward call selects coefficients using the supplied offset and token sequence length.

model-positions · meta-llama/llama3 / llama/model.py
Pinned revision a0940f9cf706 ↗ · lines 49–282

Read code excerpt

def precompute_freqs_cis(dim: int, end: int, theta: float = 10000.0):
    freqs = 1.0 / (theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim))
    t = torch.arange(end, device=freqs.device, dtype=torch.float32)
    freqs = torch.outer(t, freqs)
    freqs_cis = torch.polar(torch.ones_like(freqs), freqs)  # complex64
    return freqs_cis

… lines 55–270 omitted …

        self.freqs_cis = precompute_freqs_cis(
            params.dim // params.n_heads,
            params.max_seq_len * 2,
            params.rope_theta,
        )

    @torch.inference_mode()
    def forward(self, tokens: torch.Tensor, start_pos: int):
        _bsz, seqlen = tokens.shape
        h = self.tok_embeddings(tokens)
        self.freqs_cis = self.freqs_cis.to(h.device)
        freqs_cis = self.freqs_cis[start_pos : start_pos + seqlen]

Direct evidence

Meta’s original Llama 3 8B base catalogue entry supplies dimensions, head counts, vocabulary, MLP rounding settings, epsilon and unscaled RoPE settings.

config · meta-llama/llama-models / models/sku_list.py
Pinned revision 0e0b8c519242 ↗ · lines 19–207

Read code excerpt

LLAMA3_VOCAB_SIZE = 128256

… lines 20–187 omitted …

def llama3_base_models() -> list[Model]:
    return [
        Model(
            core_model_id=CoreModelId.llama3_8b,
            description="Llama 3 8b model",
            huggingface_repo="meta-llama/Llama-3-8B",
            arch_args={
                "dim": 4096,
                "n_layers": 32,
                "n_heads": 32,
                "n_kv_heads": 8,
                "vocab_size": LLAMA3_VOCAB_SIZE,
                "ffn_dim_multiplier": 1.3,
                "multiple_of": 1024,
                "norm_eps": 1e-05,
                "rope_theta": 500000.0,
                "use_scaled_rope": False,
            },
            pth_file_count=1,
        ),