Llama 3.1 8B · Generate RoPE coefficients

Generate RoPE coefficients

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

Construct the position-dependent rotations used by attention, from frequencies scaled for long context.

{\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; the frequencies are scaled before the rotations are built when use_scaled_rope is set, as the 3.1 catalogue sets it (llama-models model.py 65–69). Llama 3 builds the same table unscaled.

Explanation

Here $\omega_j=500000^{-2j/d_h}$ , with 500000 the configured rope_theta, and $\omega'_j$ is $\omega_j$ scaled by its wavelength $\lambda_j=2\pi/\omega_j$ : kept where $\lambda_j<8192/4$ , divided by 8 where $\lambda_j>8192$ , and between the two blended, $\omega'_j=(1-s_j)\,\omega_j/8+s_j\,\omega_j$ with $s_j=(8192/\lambda_j-1)/3$ (llama-models model.py 45–62).

Codemodel.py 45–69, 271–282 · sku_list.py 19, 231–248

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]

model.py 45–69

def apply_scaling(freqs: torch.Tensor) -> torch.Tensor:
    # Values obtained from grid search
    scale_factor = 8
    low_freq_factor = 1
    high_freq_factor = 4
    old_context_len = 8192  # original llama3 length

    low_freq_wavelen = old_context_len / low_freq_factor
    high_freq_wavelen = old_context_len / high_freq_factor

    wavelen = 2 * torch.pi / freqs
    new_freqs = torch.where(wavelen > low_freq_wavelen, freqs / scale_factor, freqs)
    smooth = (old_context_len / wavelen - low_freq_factor) / (high_freq_factor - low_freq_factor)
    return torch.where(
        (wavelen >= high_freq_wavelen) & (wavelen <= low_freq_wavelen),
        (1 - smooth) * new_freqs / scale_factor + smooth * new_freqs,
        new_freqs,
    )


def precompute_freqs_cis(dim: int, end: int, theta: float = 10000.0, use_scaled: bool = False):
    freqs = 1.0 / (theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim))
    t = torch.arange(end, device=freqs.device, dtype=torch.float32)
    if use_scaled:
        freqs = apply_scaling(freqs)

sku_list.py 19

LLAMA3_VOCAB_SIZE = 128256

sku_list.py 231–248

        Model(
            core_model_id=CoreModelId.llama3_1_8b,
            description="Llama 3.1 8b model",
            huggingface_repo="meta-llama/Llama-3.1-8B",
            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": True,
            },
            pth_file_count=1,
        ),

Sources3

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 Llama 3.1 8B base catalogue entry supplies dimensions, head counts, the vocabulary (LLAMA3_VOCAB_SIZE, line 19), MLP rounding, epsilon, rope_theta and use_scaled_rope: True.

config · meta-llama/llama-models / models/sku_list.py
Pinned revision 0e0b8c519242 ↗ · lines 19–248

Read code excerpt

LLAMA3_VOCAB_SIZE = 128256

… lines 20–230 omitted …

        Model(
            core_model_id=CoreModelId.llama3_1_8b,
            description="Llama 3.1 8b model",
            huggingface_repo="meta-llama/Llama-3.1-8B",
            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": True,
            },
            pth_file_count=1,
        ),

Direct evidence

apply_scaling: scale_factor 8, low_freq_factor 1, high_freq_factor 4, old_context_len 8192; precompute_freqs_cis applies it when use_scaled is set (68–69). Apart from this and device placement, the file computes as the pinned Llama 3 model.py.

scaling · meta-llama/llama-models / models/llama3/model.py
Pinned revision 0e0b8c519242 ↗ · lines 45–69

Read code excerpt

def apply_scaling(freqs: torch.Tensor) -> torch.Tensor:
    # Values obtained from grid search
    scale_factor = 8
    low_freq_factor = 1
    high_freq_factor = 4
    old_context_len = 8192  # original llama3 length

    low_freq_wavelen = old_context_len / low_freq_factor
    high_freq_wavelen = old_context_len / high_freq_factor

    wavelen = 2 * torch.pi / freqs
    new_freqs = torch.where(wavelen > low_freq_wavelen, freqs / scale_factor, freqs)
    smooth = (old_context_len / wavelen - low_freq_factor) / (high_freq_factor - low_freq_factor)
    return torch.where(
        (wavelen >= high_freq_wavelen) & (wavelen <= low_freq_wavelen),
        (1 - smooth) * new_freqs / scale_factor + smooth * new_freqs,
        new_freqs,
    )


def precompute_freqs_cis(dim: int, end: int, theta: float = 10000.0, use_scaled: bool = False):
    freqs = 1.0 / (theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim))
    t = torch.arange(end, device=freqs.device, dtype=torch.float32)
    if use_scaled:
        freqs = apply_scaling(freqs)