2d:null 2e:["$","title",null,{"children":"Polynomial Filter Network Equations | Ameya Daigavane | Observable"}] 33:T74a,cheb_figure = html`

Start with the original features.

${tex.block`\quad {${main_col} h^{(0)}} = x`}

Then iterate, for ${tex`k = 1, 2, \ldots `} upto ${tex` K`}:

${tex.block` \begin{aligned} \quad {p^{(k)}} &= p_{${param_col} w^{(k)}}(L) \\ \\ \quad {g^{(k)}} &= p^{(k)} \times {${main_col} h^{(k - 1)}} \\ \\ \quad {${main_col} h^{(k)}} &= \sigma \left({g^{(k)}} \right) \end{aligned} `}

Compute the matrix ${tex`p^{(k)}`} as the polynomial defined by the filter weights ${tex`${param_col} w^{(k)}`} evaluated at ${tex`L`}.

Multiply ${tex`p^{(k)}`} with ${tex`${main_col} h^{(k - 1)}`}: a standard matrix-vector multiply operation.

Apply a non-linearity ${tex`\sigma`} to ${tex`{g}^{(k)}`} to get ${tex`${main_col} {h}^{(k)}`}.

Color Codes:

Computed node embeddings.
Learnable parameters.

`34:[] 31:{"id":"44c527928fa32294","slug":"updated-chebnet-equations","title":"Polynomial Filter Network Equations","thumbnail":"302e6de9f57b9397e1e8a87d426f904eac4a0eee0d41ec3834e278520818602c","access_level":"public","create_time":"$D2021-06-24T13:41:56.870Z","update_time":"$D2021-07-01T15:53:22.408Z","view_time":null,"first_public_time":"$D2021-06-24T13:47:51.034Z","has_unpublished_edits":null,"fork":true,"stars":1,"starred":false,"owner":{"type":"team","id":"29561bb86c3368e7","login":"ameyasd","name":"Ameya Daigavane","avatar_url":"https://avatars-next.observableusercontent.com/a49e3c1e1711d4b1515f7df765b7a0faaac424a417af48a5fad9be5b3e748720","tier":"starter_2024"},"version":414,"publish_version":414,"role":null,"authored":false,"authors":[{"type":"individual","id":"aa35c1e295926184","login":"ameyasd","name":"Ameya Daigavane","avatar_url":"https://avatars-next.observableusercontent.com/a49e3c1e1711d4b1515f7df765b7a0faaac424a417af48a5fad9be5b3e748720","tier":null}],"members":[{"type":"individual","id":"aa35c1e295926184","login":"ameyasd","name":"Ameya Daigavane","avatar_url":"https://avatars-next.observableusercontent.com/a49e3c1e1711d4b1515f7df765b7a0faaac424a417af48a5fad9be5b3e748720","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":2,"collection":null,"type":"notebook","body":{"title":"Polynomial Filter Network Equations","cells":[{"id":0,"value":"md`# Polynomial Filter Network Equations`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":332,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"style = html`\n \n`","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":353,"value":"import {param_col_rgb, param_col, main_col_rgb, main_col, spectral_col, natural_col} from \"@ameyasd/gnn-styles\";","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"1","titling":"auto"}} 32:"$31:body"