{
  "purpose": "Inference architecture, sparsity and numerical evaluation protocol for parameterized single-qubit dynamics.",
  "models": {
    "with_data": {
      "input_dimension": 4,
      "hidden_neurons": 32,
      "output_dimension": 4,
      "projection_features": 10,
      "total_parameters": 1284,
      "active_parameters_including_biases": 305,
      "mask_stats": {
        "mask1": {
          "shape": [
            32,
            3
          ],
          "total": 96,
          "active": 32,
          "removed": 64,
          "removed_fraction": 0.6666666666666666,
          "nonzero_weights_outside_mask": 0,
          "active_per_row": [
            1.0
          ]
        },
        "mask_W": {
          "shape": [
            96,
            10
          ],
          "total": 960,
          "active": 96,
          "removed": 864,
          "removed_fraction": 0.9,
          "nonzero_weights_outside_mask": 0
        },
        "mask_W_out": {
          "shape": [
            4,
            32
          ],
          "total": 128,
          "active": 77,
          "removed": 51,
          "removed_fraction": 0.3984375,
          "nonzero_weights_outside_mask": 0
        }
      },
      "architecture_flags": {
        "second_order_input": true,
        "second_order_function": false,
        "normalization_function": false,
        "normalization_neuron": false,
        "dropout": false,
        "output_second_order": false
      }
    },
    "without_data": {
      "input_dimension": 4,
      "hidden_neurons": 32,
      "output_dimension": 4,
      "projection_features": 10,
      "total_parameters": 1284,
      "active_parameters_including_biases": 366,
      "mask_stats": {
        "mask1": {
          "shape": [
            32,
            3
          ],
          "total": 96,
          "active": 32,
          "removed": 64,
          "removed_fraction": 0.6666666666666666,
          "nonzero_weights_outside_mask": 0,
          "active_per_row": [
            1.0
          ]
        },
        "mask_W": {
          "shape": [
            96,
            10
          ],
          "total": 960,
          "active": 144,
          "removed": 816,
          "removed_fraction": 0.85,
          "nonzero_weights_outside_mask": 0
        },
        "mask_W_out": {
          "shape": [
            4,
            32
          ],
          "total": 128,
          "active": 90,
          "removed": 38,
          "removed_fraction": 0.296875,
          "nonzero_weights_outside_mask": 0
        }
      },
      "architecture_flags": {
        "second_order_input": true,
        "second_order_function": false,
        "normalization_function": false,
        "normalization_neuron": false,
        "dropout": false,
        "output_second_order": false
      }
    }
  },
  "inference": {
    "input_order": [
      "hx",
      "hy",
      "hz",
      "t"
    ],
    "output_order": [
      "Re(psi0)",
      "Re(psi1)",
      "Im(psi0)",
      "Im(psi1)"
    ],
    "hamiltonian": "hx*sigma_x + hy*sigma_y + hz*sigma_z; no factor 1/2",
    "hbar": 1,
    "initial_state": {
      "label": "|+>",
      "amplitudes": [
        0.7071067811865476,
        0.7071067811865476
      ]
    },
    "activation_functions": [
      "sin",
      "cos",
      "identity"
    ],
    "projection_feature_order": [
      "hx",
      "hy",
      "hz",
      "t",
      "hx*hy",
      "hx*hz",
      "hx*t",
      "hy*hz",
      "hy*t",
      "hz*t"
    ],
    "forward_order": "torch.stack(functions, dim=1).reshape(batch, 32, 3)"
  },
  "evaluation": {
    "field_component_range": [
      -1,
      1
    ],
    "time_range": [
      0,
      50
    ],
    "preset_time_intervals": [
      [
        0,
        2
      ],
      [
        0,
        5
      ],
      [
        0,
        10
      ]
    ],
    "temporal_reference_interval": [
      0,
      2
    ],
    "reference_interval_interpretation": "Nominal reference domain; does not certify the complete temporal coverage of all fine-tuning stages.",
    "nominal_fields_per_axis": [
      -1,
      -0.75,
      -0.5,
      -0.25,
      0.01,
      0.25,
      0.5,
      0.75,
      1
    ],
    "metric_samples_per_interval": 801,
    "exact_reference": "exp(-i H t) |+>, evaluated analytically and independently verified against QuTiP sesolve.",
    "state_normalization": "Probabilities, Pauli expectations and fidelity use normalized states; raw squared norm is reported separately."
  },
  "references": [
    {
      "title": "MixFunn: A Neural Network for Differential Equations with Improved Generalization and Interpretability",
      "year": 2025,
      "url": "https://arxiv.org/pdf/2503.22528",
      "doi": "10.48550/arXiv.2503.22528"
    }
  ]
}