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

{
  "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 16 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: [Butterfly Mechanics / 04 Fast Inverse GS / Problems](problems.ipynb)\n- Previous notebook: [Butterfly Mechanics / 04 Fast Inverse GS / Lecture](lecture.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** <- you are here\n17. [Butterfly Mechanics / 04 Fast Inverse GS / Problems](problems.ipynb)\n18. [Butterfly Mechanics / 04 Fast Inverse GS / Studio](studio.ipynb)\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": "Lab 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\">Lab Goals</div>\n</div>\n\nPredict the BO input and the final scaling before you run the stage explorer.\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 3,
          "kind": "exercise",
          "title": "Exercise 1"
        }
      },
      "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\">exercise</span>\n  </div>\n  <div class=\"ntt-cell-title\">Exercise 1</div>\n</div>\n\nExplain before running the next cell:\n\n- why the GS input must be BO in the standard schedule\n- why the unscaled output is not yet the original signal\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 3,
          "kind": "exercise",
          "title": "Prediction Check"
        }
      },
      "outputs": [],
      "source": "# MANDATORY\n# title: Prediction Check\n# kind: exercise | level: 3\n\nfrom IPython.display import display\n\nfrom ntt_learning.toy_ntt import fast_intt_psi_gs_trace\nfrom ntt_learning.visuals import interactive_trace\n\ntrace = fast_intt_psi_gs_trace([1467, 3471, 2807, 7621], 7681, 1925)\ndisplay(interactive_trace(trace, title=\"Check your GS prediction\"))\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 3,
          "kind": "exercise",
          "title": "Exercise 2"
        }
      },
      "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\">exercise</span>\n  </div>\n  <div class=\"ntt-cell-title\">Exercise 2</div>\n</div>\n\nPredict the bit-reversal of `[0,1,2,3,4,5,6,7]` before running the next cell.\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 3,
          "kind": "exercise",
          "title": "Prediction Check For Ordering"
        }
      },
      "outputs": [],
      "source": "# MANDATORY\n# title: Prediction Check For Ordering\n# kind: exercise | level: 3\n\nfrom ntt_learning.toy_ntt import bit_reversed_order\n\nprint(bit_reversed_order([0, 1, 2, 3, 4, 5, 6, 7]))\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\nReflection prompt:\n\n- Which part of GS felt like a true inverse to you?\n- Which part felt like pure bookkeeping?\n- Why is the ordering story impossible to ignore?\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "facultative",
          "difficulty": 4,
          "kind": "exploration",
          "title": "Optional: Explore Another BO Input"
        }
      },
      "outputs": [],
      "source": "# FACULTATIVE\n# title: Optional: Explore Another BO Input\n# kind: exploration | level: 4\n\nimport ipywidgets as widgets\nfrom IPython.display import display\n\nfrom ntt_learning.toy_ntt import fast_intt_psi_gs_trace\nfrom ntt_learning.visuals import interactive_trace\n\ndef preview(x0=1467, x1=3471, x2=2807, x3=7621):\n    trace = fast_intt_psi_gs_trace([x0, x1, x2, x3], 7681, 1925)\n    display(interactive_trace(trace, title=\"Interactive GS trace\"))\n\ndisplay(\n    widgets.interact(\n        preview,\n        x0=(0, 7680),\n        x1=(0, 7680),\n        x2=(0, 7680),\n        x3=(0, 7680),\n    )\n)\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 / Lab**.\n\n**Primary next action**\n- Next notebook: [Step 17 of 27 - Butterfly Mechanics / 04 Fast Inverse GS / Problems](problems.ipynb)\n\n**Recovery links if you get lost**\n- Previous notebook: [Butterfly Mechanics / 04 Fast Inverse GS / Lecture](lecture.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": "Lab: 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
}