On the Role of Trainable Parameters in Differentiable Feedback Delay NetworksAdditional Results |
The following results are provided as supplementary material for the article On the Role of Trainable Parameters in Differentiable Feedback Delay Networks, authored by R. Giampiccolo, A. I. Mezza, S. Koyama, M. Pezzoli, A. Bernardini, F. Antonacci, and A. Sarti, and presented at the 2026 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Barcelona, Spain, 4-8 Sept. 2026.
We performed the following tests to unveil the dependence of the FDN optimization on its parameters:
- Freeze \(\mathbf{d}, \bm{m}\): in this test, we learn \(\mathbf{W}\), \(\bm{\Gamma}\), \(\mathbf{b}\), and \(\mathbf{C}\) but we fix the vector of direct path gains \(\mathbf{d}\) (as in [1]) and the delay line lengths \(\bm{m}\) (540 trainable parameters);
- Freeze \(\mathbf{d}, \bm{m}, \mathbf{b}\): in this test, we learn \(\mathbf{W}\), \(\bm{\Gamma}\), and \(\mathbf{C}\) but we fix the vector of direct path gains \(\mathbf{d}\) (as in [1]), the delay line lengths \(\bm{m}\), and the input gains \(\mathbf{b}\) (516 trainable parameters);
- Freeze \(\mathbf{d}, \bm{m}, \mathbf{C}\): in this test, we learn \(\mathbf{W}\), \(\bm{\Gamma}\), and \(\mathbf{b}\) but we fix the vector of direct path gains \(\mathbf{d}\) (as in [1]), the delay line lengths \(\bm{m}\), and the matrix of the output gains \(\mathbf{C}\) (348 trainable parameters);
- Freeze \(\mathbf{d}, \bm{m}, \mathbf{b}, \mathbf{C}\): in this test, we learn \(\mathbf{W}\) and \(\bm{\Gamma}\) but we fix the vector of direct path gains \(\mathbf{d}\) (as in [1]), the delay line lengths \(\bm{m}\), the input gains \(\mathbf{b}\), and the matrix of the output gains \(\mathbf{C}\) (324 trainable parameters);
- Freeze All: in this test, we freeze all parameters to their respective initialization values (no trainable parameters).
Test 1: shoebox room of 5.46 × 14.52 × 3.38 m (W x L x H), source placed in the origin, receiver placed at (−0.37, −0.92, 0) m.
Test 2: shoebox room of 5.46 × 14.52 × 3.38 m (W x L x H), source placed in the origin, receiver placed at (-0.51, −2.98, 0) m.
Test 3: shoebox room of 5.46 × 14.52 × 3.38 m (W x L x H), source placed in the origin, receiver placed at (1.12, −4.56, 0) m.
Test 4: shoebox room of 10 × 12 × 2.7 m (W x L x H), source placed in the origin, receiver placed at (1.19, -1.25, 0) m.
