GPT-2 Small · Masked multi-head self-attention

in: $x$ [B batch, 1, 768 d]
out: $\Delta_{\mathrm{attn}}$ [B batch, 1, 768 d]
parameters: 2,362,368 · × 12 blocks = 28,348,416
mode: decode · P = 1,000 cached positions · L = P + 1 = 1,001 keys read
state: KV cache: appends position 1,000, reads positions 0–1,000 · training-only steps off

Parameters

2,362,368 parameters per instance, across its learned components

Exact per-instance accounting
Component	Calculation	Parameters
Fused Q, K, V projection	$768 \times 2{,}304 + 2{,}304$	1,771,776
Attention output projection	$768 \times 768 + 768$	590,592
Per-instance total		2,362,368

Across 12 independent blocks: $2{,}362{,}368 \times 12 = 28{,}348{,}416$ parameters.

In numbers

KV cache per token · all layers

GPT-2 small · float3272 KiB

GPT-2 medium · float32192 KiB

GPT-2 large · float32360 KiB

GPT-2 XL · float32600 KiB

2 (K, V) × 12 layers × 12 heads × 64 × 4 bytes. After this call, at 1,001 positions: 70.4 MiB in use per sequence. At the full 1,024 positions: 72 MiB per sequence.

Float32: the released code creates its weights without a dtype.

model.py 102–108 model.py 132–133 model.py 152–155 gpt2/config.json gpt2-medium/config.json gpt2-large/config.json gpt2-xl/config.json

Codemodel.py 69–112 · modeling_gpt2.py 185–191, 204–224

model.py 69–112

def attn(x, scope, n_state, *, past, hparams):
    assert x.shape.ndims == 3  # Should be [batch, sequence, features]
    assert n_state % hparams.n_head == 0
    if past is not None:
        assert past.shape.ndims == 5  # Should be [batch, 2, heads, sequence, features], where 2 is [k, v]

    def split_heads(x):
        # From [batch, sequence, features] to [batch, heads, sequence, features]
        return tf.transpose(split_states(x, hparams.n_head), [0, 2, 1, 3])

    def merge_heads(x):
        # Reverse of split_heads
        return merge_states(tf.transpose(x, [0, 2, 1, 3]))

    def mask_attn_weights(w):
        # w has shape [batch, heads, dst_sequence, src_sequence], where information flows from src to dst.
        _, _, nd, ns = shape_list(w)
        b = attention_mask(nd, ns, dtype=w.dtype)
        b = tf.reshape(b, [1, 1, nd, ns])
        w = w*b - tf.cast(1e10, w.dtype)*(1-b)
        return w

    def multihead_attn(q, k, v):
        # q, k, v have shape [batch, heads, sequence, features]
        w = tf.matmul(q, k, transpose_b=True)
        w = w * tf.rsqrt(tf.cast(v.shape[-1].value, w.dtype))

        w = mask_attn_weights(w)
        w = softmax(w)
        a = tf.matmul(w, v)
        return a

    with tf.variable_scope(scope):
        c = conv1d(x, 'c_attn', n_state*3)
        q, k, v = map(split_heads, tf.split(c, 3, axis=2))
        present = tf.stack([k, v], axis=1)
        if past is not None:
            pk, pv = tf.unstack(past, axis=1)
            k = tf.concat([pk, k], axis=-2)
            v = tf.concat([pv, v], axis=-2)
        a = multihead_attn(q, k, v)
        a = merge_heads(a)
        a = conv1d(a, 'c_proj', n_state)
        return a, present

modeling_gpt2.py 185–191

            query_states, key_states, value_states = self.c_attn(hidden_states).split(self.split_size, dim=2)
            shape_kv = (*key_states.shape[:-1], -1, self.head_dim)
            key_states = key_states.view(shape_kv).transpose(1, 2)
            value_states = value_states.view(shape_kv).transpose(1, 2)

        shape_q = (*query_states.shape[:-1], -1, self.head_dim)
        query_states = query_states.view(shape_q).transpose(1, 2)

modeling_gpt2.py 204–224

        )

        if using_eager and self.reorder_and_upcast_attn:
            attn_output, attn_weights = self._upcast_and_reordered_attn(
                query_states, key_states, value_states, attention_mask
            )
        else:
            attn_output, attn_weights = attention_interface(
                self,
                query_states,
                key_states,
                value_states,
                attention_mask,
                dropout=self.attn_dropout.p if self.training else 0.0,
                scaling=self.scaling,
                **kwargs,
            )

        attn_output = attn_output.reshape(*attn_output.shape[:-2], -1).contiguous()
        attn_output = self.c_proj(attn_output)
        attn_output = self.resid_dropout(attn_output)

Sources2

Direct evidence

Original fused QKV projection, causal mask, head split, and output projection.

openai · openai/gpt-2 / src/model.py
Pinned revision 9b63575ef427 ↗ · lines 69–112

Read code excerpt

def attn(x, scope, n_state, *, past, hparams):
    assert x.shape.ndims == 3  # Should be [batch, sequence, features]
    assert n_state % hparams.n_head == 0
    if past is not None:
        assert past.shape.ndims == 5  # Should be [batch, 2, heads, sequence, features], where 2 is [k, v]

    def split_heads(x):
        # From [batch, sequence, features] to [batch, heads, sequence, features]
        return tf.transpose(split_states(x, hparams.n_head), [0, 2, 1, 3])

    def merge_heads(x):
        # Reverse of split_heads
        return merge_states(tf.transpose(x, [0, 2, 1, 3]))

    def mask_attn_weights(w):
        # w has shape [batch, heads, dst_sequence, src_sequence], where information flows from src to dst.
        _, _, nd, ns = shape_list(w)
        b = attention_mask(nd, ns, dtype=w.dtype)
        b = tf.reshape(b, [1, 1, nd, ns])
        w = w*b - tf.cast(1e10, w.dtype)*(1-b)
        return w

    def multihead_attn(q, k, v):
        # q, k, v have shape [batch, heads, sequence, features]
        w = tf.matmul(q, k, transpose_b=True)
        w = w * tf.rsqrt(tf.cast(v.shape[-1].value, w.dtype))

        w = mask_attn_weights(w)
        w = softmax(w)
        a = tf.matmul(w, v)
        return a

    with tf.variable_scope(scope):
        c = conv1d(x, 'c_attn', n_state*3)
        q, k, v = map(split_heads, tf.split(c, 3, axis=2))
        present = tf.stack([k, v], axis=1)
        if past is not None:
            pk, pv = tf.unstack(past, axis=1)
            k = tf.concat([pk, k], axis=-2)
            v = tf.concat([pv, v], axis=-2)
        a = multihead_attn(q, k, v)
        a = merge_heads(a)
        a = conv1d(a, 'c_proj', n_state)
        return a, present

Direct evidence

Transformers can select an optimized attention backend while retaining the same projections and causal contract.

transformers · huggingface/transformers / src/transformers/models/gpt2/modeling_gpt2.py
Pinned revision 71c6f699ac9b ↗ · lines 185–224

Read code excerpt

            query_states, key_states, value_states = self.c_attn(hidden_states).split(self.split_size, dim=2)
            shape_kv = (*key_states.shape[:-1], -1, self.head_dim)
            key_states = key_states.view(shape_kv).transpose(1, 2)
            value_states = value_states.view(shape_kv).transpose(1, 2)

        shape_q = (*query_states.shape[:-1], -1, self.head_dim)
        query_states = query_states.view(shape_q).transpose(1, 2)

… lines 192–203 omitted …

        )

        if using_eager and self.reorder_and_upcast_attn:
            attn_output, attn_weights = self._upcast_and_reordered_attn(
                query_states, key_states, value_states, attention_mask
            )
        else:
            attn_output, attn_weights = attention_interface(
                self,
                query_states,
                key_states,
                value_states,
                attention_mask,
                dropout=self.attn_dropout.p if self.training else 0.0,
                scaling=self.scaling,
                **kwargs,
            )

        attn_output = attn_output.reshape(*attn_output.shape[:-2], -1).contiguous()
        attn_output = self.c_proj(attn_output)
        attn_output = self.resid_dropout(attn_output)

GPT-2

GPT-2 attention computation flow

KV cache per token · all layers