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NTT-learning/notebooks/butterfly_mechanics/04_fast_inverse_gs/studio.ipynb

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "meta",
"difficulty": 1,
"kind": "theme",
"title": "Notebook Theme"
}
},
"source": "## META\n\n<style>\n.jp-RenderedHTMLCommon h2 {\n display: none;\n}\n\n.jp-RenderedHTMLCommon .ntt-cell-head {\n position: relative;\n margin: 0 0 0.8rem 0;\n padding: 0.95rem 1rem 0.95rem 1rem;\n border-radius: 16px;\n border: 1px solid rgba(16,42,67,0.12);\n box-shadow: 0 8px 24px rgba(16,42,67,0.06);\n font-family: \"Avenir Next\", \"Trebuchet MS\", sans-serif;\n}\n\n.jp-RenderedHTMLCommon .ntt-cell-row {\n display: flex;\n flex-wrap: wrap;\n gap: 0.45rem;\n align-items: center;\n margin-bottom: 0.55rem;\n}\n\n.jp-RenderedHTMLCommon .ntt-role-pill,\n.jp-RenderedHTMLCommon .ntt-kind-pill,\n.jp-RenderedHTMLCommon .ntt-difficulty-pill {\n display: inline-flex;\n align-items: center;\n padding: 0.18rem 0.58rem;\n border-radius: 999px;\n font-size: 0.72rem;\n font-weight: 800;\n letter-spacing: 0.04em;\n text-transform: uppercase;\n}\n\n.jp-RenderedHTMLCommon .ntt-role-meta {\n background: linear-gradient(135deg, #e2f3ff 0%, #f5fbff 100%);\n}\n\n.jp-RenderedHTMLCommon .ntt-role-mandatory {\n background: linear-gradient(135deg, #fff0b3 0%, #ffd58a 100%);\n}\n\n.jp-RenderedHTMLCommon .ntt-role-facultative {\n background: linear-gradient(135deg, #ffe1d6 0%, #ffc9b9 100%);\n}\n\n.jp-RenderedHTMLCommon .ntt-role-pill {\n color: #102a43;\n background: rgba(16,42,67,0.1);\n}\n\n.jp-RenderedHTMLCommon .ntt-kind-pill {\n color: #486581;\n background: rgba(255,255,255,0.72);\n}\n\n.jp-RenderedHTMLCommon .ntt-difficulty-pill {\n position: absolute;\n top: 0.95rem;\n right: 1rem;\n color: #102a43;\n background: rgba(255,255,255,0.88);\n border: 1px solid rgba(16,42,67,0.08);\n box-shadow: 0 4px 12px rgba(16,42,67,0.08);\n}\n\n.jp-RenderedHTMLCommon .ntt-cell-title {\n font-size: 1.25rem;\n line-height: 1.25;\n font-weight: 850;\n color: #102a43;\n padding-right: 5.3rem;\n}\n\n.jp-RenderedHTMLCommon .ntt-cell-body-hint {\n margin-top: 0.3rem;\n font-size: 0.84rem;\n color: #486581;\n}\n\n.jupyter-widgets.widget-container,\n.jupyter-widgets.widget-box,\n.jupyter-widgets.widget-vbox,\n.jupyter-widgets.widget-hbox {\n width: 100% !important;\n max-width: 100% !important;\n min-width: 0 !important;\n}\n\n.widget-html-content svg {\n display: block !important;\n width: 100% !important;\n max-width: 100% !important;\n height: auto !important;\n}\n</style>\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "meta",
"difficulty": 1,
"kind": "route_nav",
"title": "Route Guardrails"
}
},
"source": "## META\n\n<div class=\"ntt-cell-head ntt-role-meta\">\n <span class=\"ntt-difficulty-pill\">Level 1</span>\n <div class=\"ntt-cell-row\">\n <span class=\"ntt-role-pill\">META</span>\n <span class=\"ntt-kind-pill\">route nav</span>\n </div>\n <div class=\"ntt-cell-title\">Route Guardrails</div>\n</div>\n\nYou are at **step 18 of 27** in the only supported route.\n\nNever choose the next notebook manually from the file tree. Use only the links in this cell and the final handoff cell.\n\n**Immediate navigation**\n- Next notebook: [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Lecture](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb)\n- Previous notebook: [Butterfly Mechanics / 04 Fast Inverse GS / Problems](problems.ipynb)\n- Restart route: [Start Here](../../START_HERE.ipynb)\n\n**Official route chain**\n1. [Start Here](../../START_HERE.ipynb)\n2. [Course Blueprint](../../COURSE_BLUEPRINT.ipynb)\n3. [Foundations / 01 Convolution To Toy NTT / Lecture](../../foundations/01_convolution_to_toy_ntt/lecture.ipynb)\n4. [Foundations / 01 Convolution To Toy NTT / Lab](../../foundations/01_convolution_to_toy_ntt/lab.ipynb)\n5. [Foundations / 01 Convolution To Toy NTT / Problems](../../foundations/01_convolution_to_toy_ntt/problems.ipynb)\n6. [Foundations / 01 Convolution To Toy NTT / Studio](../../foundations/01_convolution_to_toy_ntt/studio.ipynb)\n7. [Foundations / 02 Negative Wrapped NTT / Lecture](../../foundations/02_negative_wrapped_ntt/lecture.ipynb)\n8. [Foundations / 02 Negative Wrapped NTT / Lab](../../foundations/02_negative_wrapped_ntt/lab.ipynb)\n9. [Foundations / 02 Negative Wrapped NTT / Problems](../../foundations/02_negative_wrapped_ntt/problems.ipynb)\n10. [Foundations / 02 Negative Wrapped NTT / Studio](../../foundations/02_negative_wrapped_ntt/studio.ipynb)\n11. [Butterfly Mechanics / 03 Fast Forward CT / Lecture](../03_fast_forward_ct/lecture.ipynb)\n12. [Butterfly Mechanics / 03 Fast Forward CT / Lab](../03_fast_forward_ct/lab.ipynb)\n13. [Butterfly Mechanics / 03 Fast Forward CT / Problems](../03_fast_forward_ct/problems.ipynb)\n14. [Butterfly Mechanics / 03 Fast Forward CT / Studio](../03_fast_forward_ct/studio.ipynb)\n15. [Butterfly Mechanics / 04 Fast Inverse GS / Lecture](lecture.ipynb)\n16. [Butterfly Mechanics / 04 Fast Inverse GS / Lab](lab.ipynb)\n17. [Butterfly Mechanics / 04 Fast Inverse GS / Problems](problems.ipynb)\n18. **Butterfly Mechanics / 04 Fast Inverse GS / Studio** <- you are here\n19. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Lecture](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb)\n20. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Lab](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/lab.ipynb)\n21. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Problems](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/problems.ipynb)\n22. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Studio](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/studio.ipynb)\n23. [Professional / 06 Debugging NTT Failures / Lecture](../../professional/06_debugging_ntt_failures/lecture.ipynb)\n24. [Professional / 06 Debugging NTT Failures / Lab](../../professional/06_debugging_ntt_failures/lab.ipynb)\n25. [Professional / 06 Debugging NTT Failures / Problems](../../professional/06_debugging_ntt_failures/problems.ipynb)\n26. [Professional / 06 Debugging NTT Failures / Studio](../../professional/06_debugging_ntt_failures/studio.ipynb)\n27. [Course Complete](../../COURSE_COMPLETE.ipynb)\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "meta",
"difficulty": 1,
"kind": "orientation",
"title": "Studio Goals"
}
},
"source": "## META\n\n<div class=\"ntt-cell-head ntt-role-meta\">\n <span class=\"ntt-difficulty-pill\">Level 1</span>\n <div class=\"ntt-cell-row\">\n <span class=\"ntt-role-pill\">META</span>\n <span class=\"ntt-kind-pill\">orientation</span>\n </div>\n <div class=\"ntt-cell-title\">Studio Goals</div>\n</div>\n\nThe studio puts CT and GS next to each other and treats ordering as a first-class object, not a side note.\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "mandatory",
"difficulty": 3,
"kind": "explanation",
"title": "Forward And Inverse Need To Meet In The Middle Cleanly"
}
},
"source": "## MANDATORY\n\n<div class=\"ntt-cell-head ntt-role-mandatory\">\n <span class=\"ntt-difficulty-pill\">Level 3</span>\n <div class=\"ntt-cell-row\">\n <span class=\"ntt-role-pill\">MANDATORY</span>\n <span class=\"ntt-kind-pill\">explanation</span>\n </div>\n <div class=\"ntt-cell-title\">Forward And Inverse Need To Meet In The Middle Cleanly</div>\n</div>\n\nThe whole point of the pair is:\n\n- CT gets you into the transform domain efficiently\n- GS gets you back out efficiently\n- the two only meet cleanly if you respect BO/NO and the final scaling\n"
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"pedagogy": {
"role": "mandatory",
"difficulty": 3,
"kind": "demo",
"title": "See CT Output Feed GS Input"
}
},
"outputs": [],
"source": "# MANDATORY\n# title: See CT Output Feed GS Input\n# kind: demo | level: 3\n\nfrom IPython.display import display\n\nfrom ntt_learning.toy_ntt import fast_intt_psi_gs_trace, fast_ntt_psi_ct_trace\nfrom ntt_learning.visuals import plot_vector_comparison\n\nsignal = [5, 6, 7, 8]\nforward_trace = fast_ntt_psi_ct_trace(signal, 7681, 1925)\ninverse_trace = fast_intt_psi_gs_trace(forward_trace.raw_output, 7681, 1925)\n\nprint(\"CT BO output:\", forward_trace.raw_output)\nprint(\"GS scaled output:\", inverse_trace.scaled_output)\ndisplay(\n plot_vector_comparison(\n signal,\n inverse_trace.scaled_output,\n left_label=\"start\",\n right_label=\"after_CT_then_GS\",\n title=\"CT output cleanly feeds GS input\",\n )\n)\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "mandatory",
"difficulty": 2,
"kind": "exercise",
"title": "Debug Checklist"
}
},
"source": "## MANDATORY\n\n<div class=\"ntt-cell-head ntt-role-mandatory\">\n <span class=\"ntt-difficulty-pill\">Level 2</span>\n <div class=\"ntt-cell-row\">\n <span class=\"ntt-role-pill\">MANDATORY</span>\n <span class=\"ntt-kind-pill\">exercise</span>\n </div>\n <div class=\"ntt-cell-title\">Debug Checklist</div>\n</div>\n\nIf the inverse output is wrong, inspect:\n\n1. whether the input was BO\n2. whether the zetas were inverse-stage zetas\n3. whether the final `n^-1` scaling was applied\n4. whether you compared the correct order against the direct reference\n"
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"pedagogy": {
"role": "mandatory",
"difficulty": 2,
"kind": "exercise",
"title": "See A Missing-Scale Failure"
}
},
"outputs": [],
"source": "# MANDATORY\n# title: See A Missing-Scale Failure\n# kind: exercise | level: 2\n\nfrom IPython.display import display\n\nfrom ntt_learning.toy_ntt import fast_intt_psi_gs_trace\nfrom ntt_learning.visuals import plot_vector_comparison\n\ntrace = fast_intt_psi_gs_trace([1467, 3471, 2807, 7621], 7681, 1925)\nprint(\"unscaled:\", trace.raw_output)\nprint(\"scaled:\", trace.scaled_output)\ndisplay(\n plot_vector_comparison(\n trace.raw_output,\n trace.scaled_output,\n left_label=\"missing_scale\",\n right_label=\"correct\",\n title=\"Missing n^-1 scale vs correct output\",\n )\n)\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "mandatory",
"difficulty": 2,
"kind": "reflection",
"title": "Reflection"
}
},
"source": "## MANDATORY\n\n<div class=\"ntt-cell-head ntt-role-mandatory\">\n <span class=\"ntt-difficulty-pill\">Level 2</span>\n <div class=\"ntt-cell-row\">\n <span class=\"ntt-role-pill\">MANDATORY</span>\n <span class=\"ntt-kind-pill\">reflection</span>\n </div>\n <div class=\"ntt-cell-title\">Reflection</div>\n</div>\n\nExplain why \u201cthe inverse looked almost right\u201d is a dangerous debugging sentence unless you say what happened with ordering and scaling.\n"
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"pedagogy": {
"role": "facultative",
"difficulty": 4,
"kind": "exploration",
"title": "Optional: Another bit-reversal map"
}
},
"outputs": [],
"source": "# FACULTATIVE\n# title: Optional: Another bit-reversal map\n# kind: exploration | level: 4\n\nfrom IPython.display import display\n\nfrom ntt_learning.visuals import plot_bit_reversal_mapping\n\ndisplay(plot_bit_reversal_mapping(16, title=\"Bit-reversal for n=16\"))\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "meta",
"difficulty": 1,
"kind": "handoff",
"title": "Next Notebook"
}
},
"source": "## META\n\n<div class=\"ntt-cell-head ntt-role-meta\">\n <span class=\"ntt-difficulty-pill\">Level 1</span>\n <div class=\"ntt-cell-row\">\n <span class=\"ntt-role-pill\">META</span>\n <span class=\"ntt-kind-pill\">handoff</span>\n </div>\n <div class=\"ntt-cell-title\">Next Notebook</div>\n</div>\n\nYou finished **Butterfly Mechanics / 04 Fast Inverse GS / Studio**.\n\n**Primary next action**\n- Next notebook: [Step 19 of 27 - Kyber Mapping / 05 Kyber NTT And Base Multiplication / Lecture](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb)\n\n**Recovery links if you get lost**\n- Previous notebook: [Butterfly Mechanics / 04 Fast Inverse GS / Problems](problems.ipynb)\n- Restart route: [Start Here](../../START_HERE.ipynb)\n"
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"name": "python"
},
"ntt_learning": {
"title": "Studio: Fast Inverse GS",
"contract_version": "0.2",
"sequence": [
"notebooks/START_HERE.ipynb",
"notebooks/COURSE_BLUEPRINT.ipynb",
"notebooks/foundations/01_convolution_to_toy_ntt/lecture.ipynb",
"notebooks/foundations/01_convolution_to_toy_ntt/lab.ipynb",
"notebooks/foundations/01_convolution_to_toy_ntt/problems.ipynb",
"notebooks/foundations/01_convolution_to_toy_ntt/studio.ipynb",
"notebooks/foundations/02_negative_wrapped_ntt/lecture.ipynb",
"notebooks/foundations/02_negative_wrapped_ntt/lab.ipynb",
"notebooks/foundations/02_negative_wrapped_ntt/problems.ipynb",
"notebooks/foundations/02_negative_wrapped_ntt/studio.ipynb",
"notebooks/butterfly_mechanics/03_fast_forward_ct/lecture.ipynb",
"notebooks/butterfly_mechanics/03_fast_forward_ct/lab.ipynb",
"notebooks/butterfly_mechanics/03_fast_forward_ct/problems.ipynb",
"notebooks/butterfly_mechanics/03_fast_forward_ct/studio.ipynb",
"notebooks/butterfly_mechanics/04_fast_inverse_gs/lecture.ipynb",
"notebooks/butterfly_mechanics/04_fast_inverse_gs/lab.ipynb",
"notebooks/butterfly_mechanics/04_fast_inverse_gs/problems.ipynb",
"notebooks/butterfly_mechanics/04_fast_inverse_gs/studio.ipynb",
"notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb",
"notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/lab.ipynb",
"notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/problems.ipynb",
"notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/studio.ipynb",
"notebooks/professional/06_debugging_ntt_failures/lecture.ipynb",
"notebooks/professional/06_debugging_ntt_failures/lab.ipynb",
"notebooks/professional/06_debugging_ntt_failures/problems.ipynb",
"notebooks/professional/06_debugging_ntt_failures/studio.ipynb",
"notebooks/COURSE_COMPLETE.ipynb"
]
}
},
"nbformat": 4,
"nbformat_minor": 5
}
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