text: 239,60,1308357094136053760,1288452767376445440,Patrick Kidger,"New paper, with @RickyTQChen! ""Hey, that's not an ODE"": Faster ODE Adjoints with 12 Lines of Code <LINK> <LINK> We roughly double the training speed of neural ODEs. 1/ <LINK> We show how to make the backward (adjoint) pass much cheaper. We see a median of 40% fewer function evaluations (NFEs) across experiments on multiple domains: time series problems, generative modelling, and physical control. On some problems we see as much as 62% fewer NFEs. 2/ The best bit is, we do this with just one easy change - the ""12 lines of code"" from the title. (A number that includes visual whitespace, incidentally :D ) This makes it an easy thing to add to any existing project. 3/ The idea is that when solving the adjoint equations, typical adaptive-step differential equation solvers will be overzealous about rejecting steps. By exploiting the particular structure of the adjoint equations, things get much things cheaper/faster. 4/ Questions? Comments? Let me or @RickyTQChen know! 5/5 @MichaelPoli6 @RickyTQChen Haha :D Yup, it's available in torchdiffeq. We even include a short code example in the paper you can just copy-paste.",https://arxiv.org/abs/2009.09457,"Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential equation solver. A proposed step is accepted if its error, \emph{relative to some norm}, is sufficiently small; else it is rejected, the step is shrunk, and the process is repeated. Here, we demonstrate that the particular structure of the adjoint equations makes the usual choices of norm (such as $L^2$) unnecessarily stringent. By replacing it with a more appropriate (semi)norm, fewer steps are unnecessarily rejected and the backpropagation is made faster. This requires only minor code modifications. Experiments on a wide range of tasks -- including time series, generative modeling, and physical control -- demonstrate a median improvement of 40% fewer function evaluations. On some problems we see as much as 62% fewer function evaluations, so that the overall training time is roughly halved. ","""Hey, that's not an ODE"": Faster ODE Adjoints via Seminorms",6,"['New paper, with @RickyTQChen!\n\n""Hey, that\'s not an ODE"": Faster ODE Adjoints with 12 Lines of Code\n<LINK>\n<LINK>\n\nWe roughly double the training speed of neural ODEs.\n\n1/ <LINK>', 'We show how to make the backward (adjoint) pass much cheaper.\n\nWe see a median of 40% fewer function evaluations (NFEs) across experiments on multiple domains: time series problems, generative modelling, and physical control. On some problems we see as much as 62% fewer NFEs.\n\n2/', 'The best bit is, we do this with just one easy change - the ""12 lines of code"" from the title.\n(A number that includes visual whitespace, incidentally :D )\n\nThis makes it an easy thing to add to any existing project.\n\n3/', 'The idea is that when solving the adjoint equations, typical adaptive-step differential equation solvers will be overzealous about rejecting steps. By exploiting the particular structure of the adjoint equations, things get much things cheaper/faster.\n\n4/', 'Questions? Comments? Let me or @RickyTQChen know!\n\n5/5', ""@MichaelPoli6 @RickyTQChen Haha :D Yup, it's available in torchdiffeq. We even include a short code example in the paper you can just copy-paste.""]",20,09,1127