Llama 3 8B · Vocabulary projection

Vocabulary projection

learnedself.output(h).float()

Project each normalized feature vector into vocabulary logits.

{\htmlData{light=logits projection}{L}}={\htmlData{light=final-norm}{z}}W_{\mathrm{out}}

in: $z$ [B batch, T positions, 4096 d]
out: $L$ [B batch, T positions, 128256 vocabulary]
parameters: 525,336,576

Cast to float32 before it is returned (model.py 301).

Parameters

525,336,576 parameters per instance.

Exact per-instance accounting
Component	Calculation	Parameters
Weight matrix	$4{,}096 \times 128{,}256$	525,336,576
Per-instance total		525,336,576

This projection owns a separate matrix from the token embedding table.

The reference module holds the weight output by input, [out, in].

Derived from the configured matrix dimensions; checkpoint tensors have not been independently counted.

Explanation

Each entry scores one vocabulary token as the next token for its position. The softmax and the choice of token happen outside the model.

Codemodel.py 266–269, 298–303 · 2 more files

model.py 266–269

        self.norm = RMSNorm(params.dim, eps=params.norm_eps)
        self.output = ColumnParallelLinear(
            params.dim, params.vocab_size, bias=False, init_method=lambda x: x
        )

model.py 298–303

        for layer in self.layers:
            h = layer(h, start_pos, freqs_cis, mask)
        h = self.norm(h)
        output = self.output(h).float()
        return output

layers.py 258–262


        # Parameters.
        # Note: torch.nn.functional.linear performs XA^T + b and as a result
        # we allocate the transpose.
        self.weight = Parameter(torch.Tensor(self.output_size_per_partition, self.in_features))

layers.py 286–290

    def forward(self, input_: torch.Tensor) -> torch.Tensor:  # type: ignore
        # Set up backprop all-reduce.
        input_parallel = copy_to_model_parallel_region(input_)
        # Matrix multiply.
        output_parallel = F.linear(input_parallel, self.weight, self.bias)

layers.py 345–349


        # Parameters.
        # Note: torch.nn.functional.linear performs XA^T + b and as a result
        # we allocate the transpose.
        self.weight = Parameter(torch.Tensor(self.out_features, self.input_size_per_partition))

layers.py 374–380

        # Set up backprop all-reduce.
        if self.input_is_parallel:
            input_parallel = input_
        else:
            input_parallel = scatter_to_model_parallel_region(input_)
        # Matrix multiply.
        output_parallel = F.linear(input_parallel, self.weight)

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,
        ),

Sources3

Direct evidence

Final RMSNorm precedes a separate bias-free vocabulary projection; the returned logits are converted to float32.

model-readout · meta-llama/llama3 / llama/model.py
Pinned revision a0940f9cf706 ↗ · lines 266–303

Read code excerpt

        self.norm = RMSNorm(params.dim, eps=params.norm_eps)
        self.output = ColumnParallelLinear(
            params.dim, params.vocab_size, bias=False, init_method=lambda x: x
        )

… lines 270–297 omitted …

        for layer in self.layers:
            h = layer(h, start_pos, freqs_cis, mask)
        h = self.norm(h)
        output = self.output(h).float()
        return output

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,
        ),

Dependency operation context

FairScale 0.4.13 stores linear weights with output features first and calls F.linear. This is operation-context evidence; the Meta requirements leave the FairScale version unpinned.

linear-storage · facebookresearch/fairscale / fairscale/nn/model_parallel/layers.py
Pinned revision 50b06d251730 ↗ · lines 258–380

Read code excerpt


        # Parameters.
        # Note: torch.nn.functional.linear performs XA^T + b and as a result
        # we allocate the transpose.
        self.weight = Parameter(torch.Tensor(self.output_size_per_partition, self.in_features))

… lines 263–285 omitted …

    def forward(self, input_: torch.Tensor) -> torch.Tensor:  # type: ignore
        # Set up backprop all-reduce.
        input_parallel = copy_to_model_parallel_region(input_)
        # Matrix multiply.
        output_parallel = F.linear(input_parallel, self.weight, self.bias)

… lines 291–344 omitted …


        # Parameters.
        # Note: torch.nn.functional.linear performs XA^T + b and as a result
        # we allocate the transpose.
        self.weight = Parameter(torch.Tensor(self.out_features, self.input_size_per_partition))

… lines 350–373 omitted …

        # Set up backprop all-reduce.
        if self.input_is_parallel:
            input_parallel = input_
        else:
            input_parallel = scatter_to_model_parallel_region(input_)
        # Matrix multiply.
        output_parallel = F.linear(input_parallel, self.weight)