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"""Kernels for ragged attention.""" | ||
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import functools | ||
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import jax | ||
from jax import lax | ||
from jax.experimental import pallas as pl | ||
from jax.experimental.pallas import tpu as pltpu | ||
import jax.numpy as jnp | ||
import numpy as np | ||
import common_types | ||
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from jax.experimental import shard_map | ||
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DEFAULT_MASK_VALUE = -0.7 * float(np.finfo(np.dtype("float32")).max) | ||
BATCH = common_types.BATCH | ||
shard_map = shard_map.shard_map | ||
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@functools.partial(jax.jit, static_argnames=["mask_value"]) | ||
def reference_mqa( | ||
q: jax.Array, | ||
k: jax.Array, | ||
v: jax.Array, | ||
lengths: jax.Array, | ||
*, | ||
mask_value: float = DEFAULT_MASK_VALUE, | ||
) -> tuple[jax.Array, jax.Array, jax.Array]: | ||
"""Multi query attention reference. | ||
Args: | ||
q: A [batch_size, num_heads, head_dim] jax.Array. | ||
k: A [batch_size, seq_len, head_dim] jax.Array. | ||
v: A [batch_size, seq_len, head_dim] jax.Array. | ||
lengths: A i32[batch_size] jax.Array. | ||
mask_value: The value used for padding in attention. By default it is a very | ||
negative floating point number. | ||
Returns: | ||
The output of attention([batch_size, num_heads, head_dim]), along with the | ||
max logit ([batch_size, num_heads]) and softmax denominator ([batch_size, | ||
num_heads]). | ||
""" | ||
logits = jnp.einsum( | ||
"bhd,btd->bht", q.astype(jnp.float32), k.astype(jnp.float32) | ||
) | ||
mask = jnp.arange(k.shape[1])[None] < lengths[:, None] | ||
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logits = logits + jnp.where(mask, 0.0, mask_value)[:, None] | ||
logits_max = logits.max(axis=-1) | ||
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unnormalized = jnp.exp(logits - logits_max[..., None]) | ||
denominator = unnormalized.sum(axis=-1) | ||
o = ( | ||
jnp.einsum("bht,btd->bhd", unnormalized.astype(v.dtype), v) | ||
/ denominator[..., None] | ||
) | ||
return o, logits_max[..., None], denominator[..., None] | ||
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@jax.jit | ||
def reference_mha( | ||
q: jax.Array, | ||
k: jax.Array, | ||
v: jax.Array, | ||
lengths: jax.Array, | ||
*, | ||
mask_value: float = DEFAULT_MASK_VALUE, | ||
) -> tuple[jax.Array, jax.Array, jax.Array]: | ||
"""Multi head attention reference. | ||
Args: | ||
q: A [batch_size, 1, num_heads, head_dim] jax.Array. | ||
k: A [batch_size, seq_len, num_heads, head_dim] jax.Array. | ||
v: A [batch_size, seq_len, num_heads, head_dim] jax.Array. | ||
lengths: A i32[batch_size] jax.Array. | ||
mask_value: The value used for padding in attention. By default it is a very | ||
negative floating point number. | ||
Returns: | ||
The output of attention([batch_size, num_heads, head_dim]), along with the | ||
max logit ([batch_size, num_heads]) and softmax denominator ([batch_size, | ||
num_heads]). | ||
""" | ||
q = jnp.swapaxes(q, 1, 2) | ||
k = jnp.swapaxes(k, 1, 2) | ||
v = jnp.swapaxes(v, 1, 2) | ||
return jax.vmap(functools.partial( | ||
reference_mqa, | ||
mask_value=mask_value), | ||
in_axes=(1, 1, 1, None), | ||
out_axes=2)(q, k, v, lengths) | ||
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def ragged_flash_attention_kernel( | ||
lengths_ref, | ||
q_ref, | ||
k_ref, | ||
v_ref, | ||
o_ref, | ||
m_ref, | ||
l_ref, | ||
*, | ||
block_size: int, | ||
mask_value: float, | ||
): | ||
"""Pallas kernel for flash attention.""" | ||
b, i = pl.program_id(0), pl.program_id(1) | ||
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@pl.when(i == 0) | ||
def init(): | ||
m_ref[...] = jnp.full_like(m_ref, -jnp.inf) | ||
l_ref[...] = jnp.zeros_like(l_ref) | ||
o_ref[...] = jnp.zeros_like(o_ref) | ||
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length = lengths_ref[b] | ||
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@pl.when(i * block_size < length) | ||
def run(): | ||
q = q_ref[...].astype(jnp.float32) | ||
k = k_ref[...].astype(jnp.float32) | ||
v = v_ref[...].astype(jnp.float32) | ||
m_prev, l_prev = m_ref[...], l_ref[...] | ||
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qk = lax.dot_general( | ||
q, k, (((1,), (1,)), ((), ())), preferred_element_type=jnp.float32 | ||
) | ||
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mask = i * block_size + jax.lax.broadcasted_iota(jnp.int32, qk.shape, 1) < length | ||
qk = qk + jnp.where(mask, 0.0, mask_value) | ||
m_curr = qk.max(axis=-1) | ||
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s_curr = jnp.exp(qk - m_curr[..., None]) | ||
l_curr = jax.lax.broadcast_in_dim(s_curr.sum(axis=-1), l_prev.shape, (0,)) | ||
o_curr_times_l_curr = jnp.dot(s_curr, v) | ||
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m_curr = jax.lax.broadcast_in_dim(m_curr, m_prev.shape, (0,)) | ||
m_next = jnp.maximum(m_prev, m_curr) | ||
alpha = jnp.exp(m_prev - m_next) | ||
beta = jnp.exp(m_curr - m_next) | ||
l_next = alpha * l_prev + beta * l_curr | ||
l_next_safe = jnp.where(l_next == 0.0, 1.0, l_next) | ||
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m_ref[...], l_ref[...] = m_next, l_next_safe | ||
o_ref[...] = ( | ||
(l_prev * alpha * o_ref[...] + beta * o_curr_times_l_curr) / l_next_safe | ||
).astype(o_ref.dtype) | ||
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def ragged_mqa( | ||
q: jax.Array, | ||
k: jax.Array, | ||
v: jax.Array, | ||
lengths: jax.Array, | ||
*, | ||
block_size: int = 256, | ||
mask_value: float = DEFAULT_MASK_VALUE, | ||
cost_estimate: pltpu.CostEstimate | None = None, | ||
) -> tuple[jax.Array, jax.Array, jax.Array]: | ||
"""Ragged multi query attention. | ||
Args: | ||
q: A [batch_size, 1, head_dim] jax.Array. | ||
k: A [batch_size, seq_len, head_dim] jax.Array. | ||
v: A [batch_size, seq_len, head_dim] jax.Array. | ||
lengths: A i32[batch_size] jax.Array. | ||
mask_value: The value used for padding in attention. By default it is a very | ||
negative floating point number. | ||
cost_estimate: A Pallas TPU cost estimate based on a reference implementation | ||
Returns: | ||
The output of attention([batch_size, num_heads, head_dim]), along with the | ||
max logit ([batch_size, num_heads, 1]) and softmax denominator ([batch_size, | ||
num_heads, 1]). | ||
""" | ||
batch_size, num_heads, head_dim = q.shape | ||
assert lengths.shape == (batch_size,) | ||
assert lengths.dtype == jnp.int32 | ||
seq_len = k.shape[1] | ||
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def compute_ragged_block_indices(b, i, lengths_ref): | ||
length = lengths_ref[b] | ||
not_done = i * block_size < length | ||
am_last_batch = b == batch_size - 1 | ||
last_good_block = lax.div(length, block_size) - 1 | ||
b_next = jnp.where(not_done, b, jnp.where(am_last_batch, b, b + 1)) | ||
i_next = jnp.where(not_done, i, jnp.where(am_last_batch, last_good_block, 0)) | ||
return b_next, i_next, 0 | ||
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out, m, l = pl.pallas_call( | ||
functools.partial( | ||
ragged_flash_attention_kernel, | ||
block_size=block_size, | ||
mask_value=mask_value, | ||
), | ||
grid_spec=pltpu.PrefetchScalarGridSpec( | ||
num_scalar_prefetch=1, | ||
in_specs=[ | ||
pl.BlockSpec( | ||
(None, num_heads, head_dim), | ||
lambda b, i, _: (b, 0, 0)), | ||
pl.BlockSpec( | ||
(None, block_size, head_dim), | ||
compute_ragged_block_indices), | ||
pl.BlockSpec( | ||
(None, block_size, head_dim), | ||
compute_ragged_block_indices), | ||
], | ||
out_specs=[ | ||
pl.BlockSpec( | ||
(None, num_heads, head_dim), | ||
lambda b, i, _: (b, 0, 0)), | ||
pl.BlockSpec( | ||
(None, num_heads, head_dim), | ||
lambda b, i, _: (b, 0, 0)), | ||
pl.BlockSpec( | ||
(None, num_heads, head_dim), | ||
lambda b, i, _: (b, 0, 0)), | ||
], | ||
grid=(batch_size, seq_len // block_size), | ||
), | ||
compiler_params=dict( | ||
mosaic=dict( | ||
dimension_semantics=("parallel", "arbitrary"), | ||
cost_estimate=cost_estimate, | ||
) | ||
), | ||
out_shape=[ | ||
jax.ShapeDtypeStruct((batch_size, num_heads, head_dim), jnp.float32), | ||
jax.ShapeDtypeStruct((batch_size, num_heads, head_dim), jnp.float32), | ||
jax.ShapeDtypeStruct((batch_size, num_heads, head_dim), jnp.float32), | ||
], | ||
)(lengths, q, k, v) | ||
return out, m[..., 0], l[..., 0] | ||
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@functools.partial( | ||
jax.jit, | ||
static_argnames=[ | ||
"block_size", | ||
"mask_value", | ||
], | ||
) | ||
def ragged_mha( | ||
query: jax.Array, | ||
key: jax.Array, | ||
value: jax.Array, | ||
lengths: jax.Array, | ||
*, | ||
block_size: int = 256, | ||
mask_value: float = DEFAULT_MASK_VALUE, | ||
) -> tuple[jax.Array, jax.Array, jax.Array]: | ||
"""Ragged multi head attention. | ||
Args: | ||
q: A [batch_size, 1, num_heads, head_dim] jax.Array. | ||
k: A [batch_size, seq_len, num_heads, head_dim] jax.Array. | ||
v: A [batch_size, seq_len, num_heads, head_dim] jax.Array. | ||
lengths: A i32[batch_size] jax.Array. | ||
block_size: Value defining the Pallas block length in the seq_len dimension | ||
mask_value: The value used for padding in attention. By default it is a very | ||
negative floating point number. | ||
Returns: | ||
The output of attention([batch_size, num_heads, head_dim]), along with the | ||
max logit ([batch_size, num_heads, 1]) and softmax denominator ([batch_size, | ||
num_heads, 1]). | ||
""" | ||
cost_analysis = ( | ||
reference_mha.lower( | ||
query, | ||
key, | ||
value, | ||
lengths, | ||
mask_value=mask_value, | ||
) | ||
.compile() | ||
.cost_analysis()[0] | ||
) | ||
cost_estimate = pltpu.CostEstimate( | ||
flops=int(cost_analysis["flops"]), | ||
transcendentals=int(cost_analysis["transcendentals"]), | ||
bytes_accessed=int(cost_analysis["bytes accessed"]), | ||
) | ||
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query = jnp.swapaxes(query, 1, 2) | ||
key = jnp.swapaxes(key, 1, 2) | ||
value = jnp.swapaxes(value, 1, 2) | ||
o, m, l = jax.vmap( | ||
functools.partial( | ||
ragged_mqa, | ||
block_size=block_size, | ||
mask_value=mask_value, | ||
cost_estimate=cost_estimate, | ||
), | ||
in_axes=(1, 1, 1, None), | ||
out_axes=2, | ||
)(query, key, value, lengths) | ||
m = jnp.expand_dims(m, axis=-1) | ||
l = jnp.expand_dims(l, axis=-1) | ||
o = o * l | ||
return o, m, l |
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