{ "schemaVersion": 1, "lessonId": "performance-05", "contentHash": "0ed4e1e9692f1cf9c00068841c968e0f59192c11c421262b792093399bfce201", "executedAt": "2026-10-20T10:47:42.865487+00:00", "environment": { "backend": "cpu", "deviceCount": 1, "python": "3.14.3", "jax": "0.9.2", "numpy": "2.4.4", "matplotlib": "3.10.8" }, "stdout": "Saved residual descriptions:\nplain \nf32[16,16] from a constant\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of sub from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of sub from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of sub from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of sub from :17:20 (layer)\nremat \nf32[16,16] from a constant\nf32[16] from the argument v\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nCompiler memory estimates: [{'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}, {'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}]\nSynchronized gradient samples: [[0.0001016668975353241, 8.600018918514252e-05, 0.00013170810416340828, 5.487492308020592e-05, 3.0375085771083832e-05], [3.7041958421468735e-05, 2.6874709874391556e-05, 1.2292061001062393e-05, 9.582843631505966e-06, 9.292270988225937e-06]]\nIndependent reverse recurrence agrees with both gradients.\nplain \nf32[16,16] from a constant\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of sub from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of sub from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of sub from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of sub from :17:20 (layer)\nremat \nf32[16,16] from a constant\nf32[16] from the argument v\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nf32[16] output of tanh from :17:20 (layer)\nCompiler memory estimates: [{'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}, {'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}]\nSynchronized gradient samples: [[0.0001016668975353241, 8.600018918514252e-05, 0.00013170810416340828, 5.487492308020592e-05, 3.0375085771083832e-05], [3.7041958421468735e-05, 2.6874709874391556e-05, 1.2292061001062393e-05, 9.582843631505966e-06, 9.292270988225937e-06]]\nSaved residual descriptions:\nplain \nf32[16,16] from a constant\nf32[16] output of tanh from :89:20 (layer)\nf32[16] output of sub from :89:20 (layer)\nf32[16] output of tanh from :89:20 (layer)\nf32[16] output of sub from :89:20 (layer)\nf32[16] output of tanh from :89:20 (layer)\nf32[16] output of sub from :89:20 (layer)\nf32[16] output of tanh from :89:20 (layer)\nf32[16] output of sub from :89:20 (layer)\nremat \nf32[16,16] from a constant\nf32[16] from the argument v\nf32[16] output of tanh from :89:20 (layer)\nf32[16] output of tanh from :89:20 (layer)\nf32[16] output of tanh from :89:20 (layer)\nf32[16] output of tanh from :89:20 (layer)\nCompiler memory estimates: [{'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}, {'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}]\nSynchronized gradient samples: [[3.495905548334122e-05, 2.570822834968567e-05, 1.4999881386756897e-05, 1.4166813343763351e-05, 1.6415957361459732e-05], [2.570776268839836e-05, 2.408307045698166e-05, 8.791731670498848e-05, 7.383385673165321e-05, 5.5417418479919434e-05]]\nIndependent reverse recurrence agrees with both gradients.\nWhole-objective residuals: ['f32[16,16] from a constant', 'f32[16] from the argument v']\nWhole-objective memory estimate: CompiledMemoryStats(generated_code_size_in_bytes=0, argument_size_in_bytes=64, output_size_in_bytes=64, alias_size_in_bytes=0, temp_size_in_bytes=256, host_generated_code_size_in_bytes=0, host_argument_size_in_bytes=0, host_output_size_in_bytes=0, host_alias_size_in_bytes=0, host_temp_size_in_bytes=0)\nDirectional derivative finite/automatic: 0.007404538337141275 0.00740453926846385 epsilon 0.001\nHigher-order directional derivatives agree.\nPASS: performance-05\n", "notebookCells": [ { "sourceHash": "57e3485ff6aa5c2b1aa70671f229e497b67cf54fb951473eacd0083fd62c7f02", "outputs": [] }, { "sourceHash": "43544ad80e4be3dc6e61b8a2eef37d82225602fdf68520a3721319d3fb4c6c87", "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Saved residual descriptions:\n", "plain \n", "f32[16,16] from a constant\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "remat \n", "f32[16,16] from a constant\n", "f32[16] from the argument v\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "Compiler memory estimates: [{'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}, {'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}]\n", "Synchronized gradient samples: [[7.233396172523499e-05, 5.825003609061241e-05, 4.295911639928818e-05, 4.370789974927902e-05, 3.420887514948845e-05], [3.1833071261644363e-05, 2.4416949599981308e-05, 1.1249911040067673e-05, 2.16667540371418e-05, 1.39591284096241e-05]]\n", "Independent reverse recurrence agrees with both gradients.\n" ] } ] }, { "sourceHash": "51b8b10143846649e63ccaaf3f1c959995b8026ef0880e7528669ad6185eaff7", "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "plain \n", "f32[16,16] from a constant\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "remat \n", "f32[16,16] from a constant\n", "f32[16] from the argument v\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-1:14:20 (layer)\n", "Compiler memory estimates: [{'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}, {'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}]\n", "Synchronized gradient samples: [[7.233396172523499e-05, 5.825003609061241e-05, 4.295911639928818e-05, 4.370789974927902e-05, 3.420887514948845e-05], [3.1833071261644363e-05, 2.4416949599981308e-05, 1.1249911040067673e-05, 2.16667540371418e-05, 1.39591284096241e-05]]\n" ] } ] }, { "sourceHash": "4bd2918cc50d5113ff5f9870e570f02f1feca8126ff31bb3bd0b639ba4c85b9c", "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Saved residual descriptions:\n", "plain \n", "f32[16,16] from a constant\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "f32[16] output of sub from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "remat \n", "f32[16,16] from a constant\n", "f32[16] from the argument v\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "f32[16] output of tanh from /Users/tahabsn/Documents/ChatGPT/jaxpathways/phases/08-performance/05-memory-rematerialization-and-optimization-tradeoffs/notebooks/exercise.ipynb:cell-4:14:20 (layer)\n", "Compiler memory estimates: [{'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}, {'argument_size_in_bytes': 64, 'output_size_in_bytes': 64, 'temp_size_in_bytes': 256, 'alias_size_in_bytes': 0}]\n", "Synchronized gradient samples: [[3.591692075133324e-05, 2.550007775425911e-05, 1.5667174011468887e-05, 1.3167038559913635e-05, 1.5125144273042679e-05], [7.28340819478035e-05, 5.0833914428949356e-05, 6.554229184985161e-05, 6.400002166628838e-05, 6.479164585471153e-05]]\n", "Independent reverse recurrence agrees with both gradients.\n" ] } ] }, { "sourceHash": "54fce560951da0ffcbfd8272e2733e3b97301ad31e7fa81541977853898d8cfb", "outputs": [] }, { "sourceHash": "25df6d662f9d3f0c4e984c6a201f79fa0cfd7a2633dc4b0773dfba6c2dd4ee6c", "outputs": [ { "output_type": "display_data", "metadata": {}, "data": { "image/png": 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"text/plain": [ "Executed Matplotlib figure" ] } } ] }, { "sourceHash": "730935d55298ebb37724df089127f78550d329a6796e2bd234c055055a62dc15", "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Whole-objective residuals: ['f32[16,16] from a constant', 'f32[16] from the argument v']\n", "Whole-objective memory estimate: CompiledMemoryStats(generated_code_size_in_bytes=0, argument_size_in_bytes=64, output_size_in_bytes=64, alias_size_in_bytes=0, temp_size_in_bytes=256, host_generated_code_size_in_bytes=0, host_argument_size_in_bytes=0, host_output_size_in_bytes=0, host_alias_size_in_bytes=0, host_temp_size_in_bytes=0)\n" ] } ] }, { "sourceHash": "d28ff535e6ee96d5a865a9dd504e849a980a4fc2ddf30300792badc9d0964abf", "outputs": [] }, { "sourceHash": "646c965fae06c29640a51598f680d6c65931b4a98a0394f015d81283f070f949", "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Directional derivative finite/automatic: 0.007404538337141275 0.00740453926846385 epsilon 0.001\n" ] } ] }, { "sourceHash": "e9a5f64ebb099a5643344492eebf418640502937383042fb0c2a293dce2b2035", "outputs": [] }, { "sourceHash": "50a06dcbc3f8e14a7c262cd55e2b859687cc1426c345fd77f877f42ac36dae44", "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "Higher-order directional derivatives agree.\n" ] } ] } ], "scope": "Recorded instructor reference run; all script assertions and notebook code cells passed. No accelerator performance claim." }