[Relay][PRNG] Add uniform distribution generator wrt threefry PRNG by zhuzilin · Pull Request #8041 · apache/tvm

zhuzilin · 2021-05-14T04:17:04Z

This PR adds a uniform distribution generator using the threefry PRNG introduced in #7083. We would need uniform to develop the training phase dropout as the following roadmap:

uniform -> bernoulli -> dropout

The algorithm used is basically the same as the one used in jax: using the random bits generated from threefry_generate as the fraction section of the float32 or float64. To be specific, I use the last 23 bits of the random bits for float32 and last 52 for float64. There is one different from the jax implementation. In jax, they used a bitcast to turn uint into float:

# jax implementation
def _uniform(key, shape, dtype, minval, maxval) -> jnp.ndarray:
  ...
  bits = _random_bits(key, nbits, shape)

  # The strategy here is to randomize only the mantissa bits with an exponent of
  # 1 (after applying the bias), then shift and scale to the desired range. The
  # bit-level transformation we use relies on Numpy and XLA having bit-for-bit
  # equivalent float representations, which might not be true on all platforms.
  float_bits = lax.bitwise_or(
      lax.shift_right_logical(bits, np.array(nbits - nmant, lax.dtype(bits))),
      np.array(1., dtype).view(_UINT_DTYPES[nbits]))
  floats = lax.bitcast_convert_type(float_bits, dtype) - np.array(1., dtype)
  return lax.max(
      minval,
      lax.reshape(floats * (maxval - minval) + minval, shape.positional))

However, as I haven't found the bitcast in te or topi, I use a divide to cast the type, which may be slower:

    def uniform_scalar(bits):
        bits = bits >> (nbits - nfraction)
        standard_uniform = bits.astype(out_dtype) / float(1 << nfraction)
        return standard_uniform

Thank you for your time on reviewing this PR. I may not be familiar enough with the tvm codebase at the moment, so I'm sorry for breaking any conventions in the community and I'd love to fix them :).

Gently ping @tqchen @altanh @tkonolige

FrozenGene · 2021-05-14T09:19:42Z

+
+    Parameters
+    ----------
+    gen : Tensor[10, uint64]


What is the meaning of 10?

This is the ThreefryKeyType introduced in #7083. Please refer to:

tvm/src/relay/op/random/kernel.cc

Line 28 in c999a84

static TensorType ThreefryKeyType() { return TensorType({10}, tvm::DataType::UInt(64)); }

If so, let us add comment describe what is the meaning of 10.

You could probably say ThreefryKey instead of Tensor[10, uint64]

FrozenGene · 2021-05-14T09:20:29Z

+        less than high.
+
+    out_shape : Sequence[int]
+        Output shape of the random numbers. Product of all dimensions must be a multiple of 4.


What is the reason of product must be a multiple of 4?

It's the property of the threefry key. Please refer to this comment: #7083 (comment)

Sorry, I just rethink about this problem. There should not be any restriction to the output shape... We could change the input restriction of the threefry_generate in other PR.

do you mind sending a PR for updating the threefry_generate output, or rather what approach do you have in mind? I tried to avoid this problem by truncating output buffer but this required an extra copy, wonder if you have something else

@altanh Sorry that I'm not familiar with the threefry algorithm. Is it possible to call _threefry twice in threefry_generate in the following form? something like:

out_array = irb.buffer_ptr(out_array_ptr) # deal with most of the array _threefry(irb, tmp, 0, tmp, 4, out_array, 0, out_len // 4) if out_len % 4 != 0: # generate remainders in a small tmp buffer tmp_array = irb.allocate(gen.dtype, 4, name="tmp", scope="global") # may need to update the tmp key in between # ... _threefry(irb, tmp, 0, tmp, 4, tmp_array, 0, out_len // 4) # only copy the tmp buffer for i in range(out_len // 4 * 4, out_len): out_array[i] = tmp_array[i%4]

In this way, we coud avoid copying the whole generated tensor.

Yeah, you could do that. Maybe submit it in a new PR?

@tkonolige Sure, I will submit one. Could you tell me what kind of update on key tmp we need before the second _threefry? I can only think of updating increment counter (tmp[7]).

You'll need to update the counter buffer to be equal to out_len

FrozenGene · 2021-05-14T09:23:13Z


+def test_uniform_infer():
+    oshape = (12,)
+    odtype = "float32"


Should cover more types. For example float64 you have implemented

tkonolige · 2021-05-14T16:18:35Z

+
+    standard_uniform_values = tvm.te.compute(out_shape, lambda *i: uniform_scalar(random_bits(*i)))
+
+    uniform_values = tvm.topi.add(tvm.topi.multiply(standard_uniform_values, high - low), low)


How well does this approach work when we have a large range (high - low)? It seems like we would be loosing a lot of potential randomness.

altanh · 2021-05-14T18:54:41Z

Thanks for this PR! I will be reading it soon, and just wanted to point you to a branch I worked on a while ago where I hacked a uniform op + dropout support: https://github.com/altanh/tvm/commits/prng (just in case it might be useful for you to check and compare).

However, as I haven't found the bitcast in te or topi, I use a divide to cast the type, which may be slower:

Perhaps this is the operation you're looking for? https://github.com/altanh/tvm/blob/2d9ac7710ab055d4f20e8b5a0a3580836723efac/python/tvm/topi/generic/algorithm.py#L465

Thanks!

zhuzilin · 2021-05-15T17:06:22Z

@FrozenGene @tkonolige @altanh Thank you for your reviews. I've updated this PR based on them.

I think there are 2 options: 1. Ref Conv2DRel. 2. You could restrict the type here and raise exception. I prefer option 1.

@FrozenGene Thank you for the clue! However, I haven't find how to restrict the dtype attributes in Conv2DRel or Conv2DAttrs... Should I add the type restriction to the UniformAttrs, or raise error in the MakeUniform and UniformRel?

How well does this approach work when we have a large range (high - low)? It seems like we would be loosing a lot of potential randomness.

@tkonolige As this approach is only using the fraction bits to represent float, there will be loss of randomness for all floats, at least (2^nexp-1) / 2^nexp of the float (nexp stands for the number of exponential digits). However, it's a little tricky to use all 64 digits of the random bit to represent a uniform distributed float number... Do you have any idea on that?

Perhaps this is the operation you're looking for? https://github.com/altanh/tvm/blob/2d9ac7710ab055d4f20e8b5a0a3580836723efac/python/tvm/topi/generic/algorithm.py#L465

@altanh Thank you for your references! The reinterpret is exactly what I was looking for. I've updated the algorithm and right now it is the same as the one used in jax.

FrozenGene · 2021-05-17T01:35:40Z

@FrozenGene Thank you for the clue! However, I haven't find how to restrict the dtype attributes in Conv2DRel or Conv2DAttrs... Should I add the type restriction to the UniformAttrs, or raise error in the MakeUniform and UniformRel?

Suggest UniformRel

zhuzilin · 2021-05-17T15:10:41Z

Suggest UniformRel

@FrozenGene Thank you. I've added the type restriction.

tkonolige

Looks pretty good to me. Just a couple of minor fixes.

altanh

Overall LGTM with some minor comments. I did want to request that we keep the output shape restriction in the documentation for now until a follow up PR is merged which relaxes it. Thanks for the work!

zhuzilin · 2021-05-18T08:24:47Z

@FrozenGene @altanh @tkonolige I've updated the PR upon the reviews. Could you take another look? Thank you~

tkonolige

Looks good to me. Just some small comments

altanh

LGTM! I'm a bit uneasy about introducing a nondeterministic test based on averaging the random numbers but I imagine it will almost never fail. Also left a comment about comparing the min/max of the generated numbers - can we always guarantee <= or >= on the output or will there be some floating point inaccuracy cases where this might be violated?

zhuzilin · 2021-05-19T03:48:59Z

@FrozenGene Could you take another look of this PR? Thank you~

zhuzilin · 2021-05-21T02:36:18Z

@FrozenGene Could you have another look at this PR? Thank you!

FrozenGene · 2021-05-21T03:15:39Z

Thanks @zhuzilin @altanh @tkonolige merged now

…pache#8041) * Add uniform distribution generator wrt threefry PRNG * fix lint * remove the redundant print * modifications based on review * update docs * update uniform algorithm to use bit operations only * add type restrictions * minor fix upon review * update test and error information

Add uniform distribution generator wrt threefry PRNG

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zhuzilin force-pushed the prng_uniform branch 2 times, most recently from 2f831ea to 78bc8b7 Compare May 14, 2021 04:28

fix lint

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zhuzilin force-pushed the prng_uniform branch from 78bc8b7 to fd68ff4 Compare May 14, 2021 04:44

FrozenGene reviewed May 14, 2021

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FrozenGene reviewed May 14, 2021

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Comment thread tests/python/topi/python/test_topi_prng.py Outdated

remove the redundant print

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zhuzilin requested a review from FrozenGene May 14, 2021 05:04

FrozenGene reviewed May 14, 2021

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tqchen assigned FrozenGene May 14, 2021

tqchen added the status: need review label May 14, 2021

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zhuzilin added 2 commits May 16, 2021 00:09

modifications based on review

cbaec73

update docs

024e176

update uniform algorithm to use bit operations only

fd1368b

zhuzilin requested a review from FrozenGene May 16, 2021 02:33

add type restrictions

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tkonolige approved these changes May 17, 2021

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zhuzilin force-pushed the prng_uniform branch from 7e4e0bc to 49383a7 Compare May 18, 2021 09:24

minor fix upon review

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zhuzilin force-pushed the prng_uniform branch from 49383a7 to aa372d4 Compare May 18, 2021 09:26

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update test and error information

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FrozenGene merged commit e438a73 into apache:main May 21, 2021

FrozenGene added status: accepted and removed status: need review labels May 21, 2021


		standard_uniform_values = tvm.te.compute(out_shape, lambda i: uniform_scalar(random_bits(i)))

		uniform_values = tvm.topi.add(tvm.topi.multiply(standard_uniform_values, high - low), low)

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zhuzilin commented May 14, 2021

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