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

{
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    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "orientation",
          "title": "Studio Goals"
        }
      },
      "source": "## META | difficulty 1 | Studio Goals\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 | difficulty 3 | Forward And Inverse Need To Meet In The Middle Cleanly\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 | difficulty 3 | See CT Output Feed GS Input\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 | difficulty 2 | Debug Checklist\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 | difficulty 2 | See A Missing-Scale Failure\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 | difficulty 2 | Reflection\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 | difficulty 4 | Optional: Another bit-reversal map\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 | difficulty 1 | Next Notebook\n\nNext notebook: `../../../kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb`\n"
    }
  ],
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    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
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    "language_info": {
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    "ntt_learning": {
      "title": "Studio: Fast Inverse GS",
      "contract_version": "0.2",
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        "notebooks/butterfly_mechanics/04_fast_inverse_gs/lecture.ipynb",
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