Correct why topology changes a result: the data stream is invariant, the arithmetic is not

README.md

@@ -39,26 +39,29 @@ at 20 tokens per parameter, batch 128, base learning rate 2^-8, seed 1337.
 
 ## A seed does not identify a run on its own
 
-The training stream is seeded **per process**:
-
-```python
-train_rng = np.random.default_rng(seed + 1 + process_index * 1_000_003)
-```
-
-Windows are then split rank-disjointly, so the number of processes decides
-which documents each rank draws and in what order. Running the same `--seed`
-on a different process count trains on different data — measured at 0.004 to
-0.023 nats apart on identical configurations, which is the same size as the
-seed effect itself.
-
-Every run therefore records `data_processes` and `devices` in its study's
-`records.jsonl`, alongside `system.process_count` in `result.json`. Reproducing
-a recorded number needs both the seed and the process count.
+The training stream *is* invariant under the process count. The global batch
+sequence is fixed by the seed alone, and each rank takes a slice of it:
+`_prepare_epoch` mixes only the seed and the epoch, and `next_batch` advances a
+global cursor by the whole global batch. Verified directly — 1, 4, and 8
+processes produce byte-identical global batches.
+
+Results still differ across topologies. The same configuration and seed on
+8 chips versus 16 lands 0.004 to 0.023 nats apart, which is the same size as
+the seed effect itself. The data is identical and so is the attention tile
+plan; both were checked. What differs is floating point: gradients are reduced
+across a different number of devices, so the sum is accumulated in a different
+order, and each chip holds a different number of sequences, which changes the
+shapes XLA compiles for. Neither is addressable by seeding, and both are the
+same non-associativity that makes any reduction order-dependent.
+
+So `--seed N` plus the configuration does not pin a number; the topology is
+part of it. Every run records `data_processes` and `devices` in its study's
+`records.jsonl`, alongside `system.process_count` in `result.json`.
 
 All studies here ran at 4 processes over 16 chips except `batch-sweep-500M`,
 whose 20-tokens-per-parameter arm ran at 1 process over 8. Those two arms are
-already separate experiments — their token budgets differ — so the split does
-not cross a comparison that was being made.
+separate experiments — their token budgets differ — so the split does not cross
+a comparison that was being made.
 
 ## The format
 

batch-sweep-250M/README.md

@@ -11,7 +11,7 @@ The 250M rung, extended to batch 512 to see whether the batch optimum keeps movi
 - **learning rates:** 2^-7, 2^-8, 2^-9
 - **seeds:** 1337, 1338, 1339
 - **budget:** 5 tokens per parameter (~1.2B tokens), 2,331-18,650 steps
-- **data processes:** 4 (16 chips) — the training stream is seeded per process (`seed + 1 + process_index * 1000003`) and windows are split rank-disjointly, so the process count is part of what a run is: the same `--seed` on a different count draws different data
+- **data processes:** 4 (16 chips) — the data stream itself is invariant under this, but gradient reduction order and per-chip batch are not, so the same seed on a different count lands 0.004-0.023 nats away
 - **dataset:** FineWeb-Edu, GPT-2 tokenizer (`fineweb-8b-gpt2`)
 - **parameterization:** Complete(d)P
 - **optimizer:** AdamW, beta1 0.9, beta2 0.95, weight decay 0.1, no gradient clipping

batch-sweep-500M/README.md

@@ -12,7 +12,7 @@ Whether the optima found at 5 tokens per parameter survive a four-times-longer h
 - **seeds:** 1337, 1338, 1339 (5 TPP arm); 1337, 1338 (20 TPP arm)
 - **budgets:** 5 and 20 tokens per parameter -- 9,586 to 153,382 steps
 - **note:** the two budgets are different experiments; their losses are not comparable to each other, which is why run names carry the budget
-- **data processes:** 6 runs at 1 (8 chips), 6 runs at 4 (16 chips) — the training stream is seeded per process (`seed + 1 + process_index * 1000003`) and windows are split rank-disjointly, so the process count is part of what a run is: the same `--seed` on a different count draws different data
+- **data processes:** 6 runs at 1 (8 chips), 6 runs at 4 (16 chips) — the data stream itself is invariant under this, but gradient reduction order and per-chip batch are not, so the same seed on a different count lands 0.004-0.023 nats away
 - **dataset:** FineWeb-Edu, GPT-2 tokenizer (`fineweb-8b-gpt2`)
 - **parameterization:** Complete(d)P
 - **optimizer:** AdamW, beta1 0.9, beta2 0.95, weight decay 0.1, no gradient clipping

batch-sweep-60M/README.md

@@ -11,7 +11,7 @@ The widest grid in the collection: every batch size against every learning rate,
 - **learning rates:** 2^-6, 2^-7, 2^-8, 2^-9, 2^-10
 - **seeds:** 1337, 1338, 1339
 - **budget:** 5 tokens per parameter (~300M tokens), 571-9,143 steps depending on batch
-- **data processes:** 4 (16 chips) — the training stream is seeded per process (`seed + 1 + process_index * 1000003`) and windows are split rank-disjointly, so the process count is part of what a run is: the same `--seed` on a different count draws different data
+- **data processes:** 4 (16 chips) — the data stream itself is invariant under this, but gradient reduction order and per-chip batch are not, so the same seed on a different count lands 0.004-0.023 nats away
 - **dataset:** FineWeb-Edu, GPT-2 tokenizer (`fineweb-8b-gpt2`)
 - **parameterization:** Complete(d)P
 - **optimizer:** AdamW, beta1 0.9, beta2 0.95, weight decay 0.1, no gradient clipping

lr-batch-sweep-125M/README.md

@@ -11,7 +11,7 @@ The 125M rung of the batch/learning-rate grid. The same product read either way:
 - **learning rates:** 2^-7, 2^-8, 2^-9
 - **seeds:** 1337, 1338, 1339
 - **budget:** 5 tokens per parameter (~617M tokens), 2,355-9,419 steps
-- **data processes:** 4 (16 chips) — the training stream is seeded per process (`seed + 1 + process_index * 1000003`) and windows are split rank-disjointly, so the process count is part of what a run is: the same `--seed` on a different count draws different data
+- **data processes:** 4 (16 chips) — the data stream itself is invariant under this, but gradient reduction order and per-chip batch are not, so the same seed on a different count lands 0.004-0.023 nats away
 - **dataset:** FineWeb-Edu, GPT-2 tokenizer (`fineweb-8b-gpt2`)
 - **parameterization:** Complete(d)P
 - **optimizer:** AdamW, beta1 0.9, beta2 0.95, weight decay 0.1, no gradient clipping

lr-sweep-8k-60M/README.md

@@ -11,7 +11,7 @@ Whether the learning-rate optimum moves when the context length grows eight-fold
 - **learning rates:** 2^-6, 2^-7, 2^-8, 2^-9, 2^-10
 - **seeds:** 1337, 1338, 1339
 - **budget:** 5 tokens per parameter, 2,286 steps -- identical to the 1,024-context ladder
-- **data processes:** 4 (16 chips) — the training stream is seeded per process (`seed + 1 + process_index * 1000003`) and windows are split rank-disjointly, so the process count is part of what a run is: the same `--seed` on a different count draws different data
+- **data processes:** 4 (16 chips) — the data stream itself is invariant under this, but gradient reduction order and per-chip batch are not, so the same seed on a different count lands 0.004-0.023 nats away
 - **dataset:** FineWeb-Edu, GPT-2 tokenizer (`fineweb-8b-gpt2`)
 - **parameterization:** Complete(d)P
 - **optimizer:** AdamW, beta1 0.9, beta2 0.95, weight decay 0.1, no gradient clipping

lr-transfer-250M/README.md

@@ -11,7 +11,7 @@ Run to settle a 250M result that a single seed had gotten wrong, and the evidenc
 - **learning rates:** 2^-6, 2^-7, 2^-8, 2^-9
 - **seeds:** 1337, 1338, 1339
 - **budget:** 5 tokens per parameter, 9,325 steps
-- **data processes:** 4 (16 chips) — the training stream is seeded per process (`seed + 1 + process_index * 1000003`) and windows are split rank-disjointly, so the process count is part of what a run is: the same `--seed` on a different count draws different data
+- **data processes:** 4 (16 chips) — the data stream itself is invariant under this, but gradient reduction order and per-chip batch are not, so the same seed on a different count lands 0.004-0.023 nats away
 - **dataset:** FineWeb-Edu, GPT-2 tokenizer (`fineweb-8b-gpt2`)
 - **parameterization:** Complete(d)P
 - **optimizer:** AdamW, beta1 0.9, beta2 0.95, weight decay 0.1, no gradient clipping

moe-lr-sweep-8k/README.md

@@ -17,7 +17,7 @@ dropped — actually does.
 - **learning rates:** 2^-6, 2^-7, 2^-8, 2^-9, 2^-10 at 60M; 2^-7, 2^-8, 2^-9 at 125M
 - **batch size:** 16 sequences — 131,072 tokens per step, matching the dense ladder
 - **budget:** 5 tokens per parameter, sized by *active* parameters
-- **data processes:** 4 (16 chips) — the training stream is seeded per process (`seed + 1 + process_index * 1000003`) and windows are split rank-disjointly, so the process count is part of what a run is: the same `--seed` on a different count draws different data
+- **data processes:** 4 (16 chips) — the data stream itself is invariant under this, but gradient reduction order and per-chip batch are not, so the same seed on a different count lands 0.004-0.023 nats away
 - **dataset:** FineWeb-Edu, GPT-2 tokenizer (`fineweb-8b-gpt2`)
 - **parameterization:** Complete(d)P
 - **optimizer:** AdamW, beta1 0.9, beta2 0.95, weight decay 0.1, no gradient clipping