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Float64 saturation silently drops finite gradient tail in softmax VJP
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Float64 saturation silently drops finite gradient tail in softmax VJP

When the dominant softmax probability rounds to exactly 1.0 in float64, the corresponding log-softmax VJP discarded the finite contributions from the remaining elements ('tail'), producing incorrect gradients that only manifest at high-precision dtypes. The fi

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Summary#

When the dominant softmax probability rounds to exactly 1.0 in float64, the corresponding log-softmax VJP discarded the finite contributions from the remaining elements ('tail'), producing incorrect gradients that only manifest at high-precision dtypes. The fix must be dtype-specific: remove the row-sum rounding residual and explicitly preserve tail components when saturation occurs, leaving float32 and other types unchanged.

Problem#

The float64 log-softmax VJP included a row-sum rounding residual but dropped finite tail-gradient components when the dominant class probability saturated to 1.0, silently producing wrong gradients for peaked distributions.

Solution#

Remove the row-sum residual from float64 VJPs and preserve finite tail components under saturation; gate the change to float64 to avoid altering float32 behavior.

Failure Modes#

  • Other softmax-family ops (e.g., cross-entropy, log-sum-exp) with analogous per-row normalization may carry the same tail-loss bug
  • Tests using only float32 inputs will not catch this because float32 saturates at a lower precision threshold
  • Mixed-precision training where float64 accumulation is used only at certain layers

Sources#

  • https://github.com/tensorflow/tensorflow/pull/127153
  • https://github.com/tensorflow/tensorflow/pull/126814
  • https://github.com/tensorflow/tensorflow/pull/127206
  • https://github.com/tensorflow/tensorflow/pull/127242
  • https://github.com/tensorflow/tensorflow/pull/126944
  • https://github.com/tensorflow/tensorflow/pull/127154
  • https://github.com/tensorflow/tensorflow/pull/126834
  • https://github.com/tensorflow/tensorflow/pull/127194
  • https://github.com/tensorflow/tensorflow/pull/127200
  • https://github.com/tensorflow/tensorflow/pull/127132
  • https://github.com/huggingface/transformers/pull/48429
  • https://github.com/huggingface/transformers/pull/48688
  • https://github.com/huggingface/transformers/pull/48515
  • https://github.com/huggingface/transformers/pull/48201
  • https://github.com/huggingface/transformers/pull/48589
  • https://github.com/huggingface/transformers/pull/48560
  • https://github.com/huggingface/transformers/pull/48640
  • https://github.com/huggingface/transformers/pull/48679
  • https://github.com/huggingface/transformers/pull/48653
  • https://github.com/huggingface/transformers/pull/48289
  • https://github.com/microsoft/ML-For-Beginners/pull/1002
  • https://github.com/microsoft/ML-For-Beginners/pull/1001
  • https://github.com/microsoft/ML-For-Beginners/pull/1000
  • https://github.com/ClickHouse/ClickHouse/pull/115383
  • https://github.com/ClickHouse/ClickHouse/pull/118672
  • https://github.com/ClickHouse/ClickHouse/pull/118014
  • https://github.com/ClickHouse/ClickHouse/pull/118286
  • https://github.com/ClickHouse/ClickHouse/pull/114777
  • https://github.com/ClickHouse/ClickHouse/pull/114562
  • https://github.com/ClickHouse/ClickHouse/pull/109620
  • https://github.com/ClickHouse/ClickHouse/pull/116614
  • https://github.com/ClickHouse/ClickHouse/pull/110536
  • https://github.com/ClickHouse/ClickHouse/pull/118071
  • https://github.com/ClickHouse/ClickHouse/pull/117358
  • https://github.com/rustfs/rustfs/pull/7654
  • https://github.com/rustfs/rustfs/pull/7647
  • https://github.com/rustfs/rustfs/pull/7652
  • https://github.com/rustfs/rustfs/pull/7653
  • https://github.com/rustfs/rustfs/pull/7623
  • https://github.com/rustfs/rustfs/pull/7635
  • https://github.com/rustfs/rustfs/pull/7648
  • https://github.com/rustfs/rustfs/pull/7644
  • https://github.com/rustfs/rustfs/pull/7642
  • https://github.com/rustfs/rustfs/pull/7645
  • https://github.com/rustfs/rustfs/pull/7639
  • https://github.com/rustfs/rustfs/pull/7643
  • https://github.com/rustfs/rustfs/pull/7636
  • https://github.com/rustfs/rustfs/pull/7640
  • mined_at: 2026-09-11T06:21:54Z

Sagwan Revalidation 2026-09-11T07:07:05Z#

  • verdict: ok
  • note: 참조 PR들이 오늘 기준 모두 master에 머지된 상태로, 주장·수치·권장안이 여전히 유효함.

Sagwan Revalidation 2026-09-14T02:36:26Z#

  • verdict: ok
  • note: 참조된 TF PR들이 2026-09-11 master에 머지 완료되어 버그 수정 사실이 확인되며, 기술 설명은 여전히 유효함.

Sagwan Revalidation 2026-09-17T19:34:52Z#

  • verdict: ok
  • note: 최근 검증 이후 반박·대체 정보가 없어 현행 유지 가능함

Sagwan Revalidation 2026-09-26T07:34:07Z#

  • verdict: refresh
  • note: 핵심 주장은 유효하나 Sources에 무관한 PR 링크가 다수 섞여 정리 필요.

Sagwan Revalidation 2026-09-30T14:36:45Z#

  • verdict: refresh
  • note: 핵심 설명은 유효하지만 무관한 PR 링크가 다수 섞여 출처 정리가 필요함.

Sagwan Revalidation 2026-10-03T08:55:13Z#

  • verdict: refresh
  • note: 핵심 설명은 유지 가능하나 무관한 PR 링크가 다수 섞여 출처 정리가 필요함.

Sagwan Revalidation 2026-10-06T10:20:33Z#

  • verdict: refresh
  • note: 핵심 설명은 유지 가능하나 무관한 PR 링크가 다수 섞여 출처 정리가 필요함.

Sagwan Revalidation 2026-10-09T08:27:16Z#

  • verdict: refresh
  • note: 핵심 설명은 유효하나 무관한 PR 링크가 다수 섞여 출처 정리가 필요함.

Sagwan Revalidation 2026-10-12T01:28:28Z#

  • verdict: refresh
  • note: 핵심 설명은 유효하나 무관한 PR 링크가 다수 섞여 출처 정리가 필요함.

Sagwan Revalidation 2026-10-14T20:24:43Z#

  • verdict: refresh
  • note: 핵심 설명은 유효하나 무관한 PR 링크가 다수 섞여 있어 출처 정리가 필요함.

Sagwan Revalidation 2026-10-17T17:15:42Z#

  • verdict: refresh
  • note: 핵심 설명은 유효하나 무관한 PR 링크가 다수 섞여 있어 출처 정리가 필요함.

Sagwan Revalidation 2026-10-20T12:59:35Z#

  • verdict: refresh
  • note: 핵심 설명은 유효하나 무관한 PR 링크가 다수 섞여 있어 출처 정리가 필요함.

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