Tutorial on particle filters should emphasize that model that calls Unfold needs to be static

[ztangent]

After going through the tutorial on particle filters, @kach ran into issues trying to get incremental computation working, and it turned out this was because of not annotating the model that calls the Unfold combinator with static. Ideally, this would be emphasized in the tutorial (and the docs) so that others don't run into the same issue!

[bgroenks96]

Why is this necessary, actually?

[ztangent]

In the current implementation, if the static annotation isn't added, then the model which calls Unfold ends up passing a conservative change hint / "argdiff" in the Gen.update call to the Unfold combinator, causing Unfold to conservatively assume that the model needs to be rerun from the very beginning, instead of just simulating the next time step. This results in a $O(T^2)$ run time instead of an $O(T)$ runtime, where $T$ is the number of steps.

I think there are slight changes we could make to the current implementation of Unfold so that (static) isn't necessary, but it will require more runtime checking of whether the arguments have changed.

[bgroenks96]

Ok, so at least it's a performance concern rather than a correctness concern.

[bgroenks96]

I actually can't reproduce this in a standalone example...?

@gen (static) function kernel(i::Int, zₜ, σ)
    zₜ₊₁ ~ normal(zₜ, σ)
    return zₜ₊₁
end

@gen (static) function static_unfold(z₀, n::Int)
    σ ~ exponential(0.1)
    return @trace(Unfold(kernel)(n, z₀, σ), :unfold)
end

@gen function dynamic_unfold(z₀, n::Int)
    σ ~ exponential(0.1)
    return @trace(Unfold(kernel)(n, z₀, σ), :unfold)
end

@benchmark simulate(static_unfold, (0.0,1000))
@benchmark simulate(dynamic_unfold, (0.0,1000))

BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  305.523 μs …   8.214 ms  ┊ GC (min … max):  0.00% … 85.66%
 Time  (median):     371.969 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   489.648 μs ± 732.991 μs  ┊ GC (mean ± σ):  15.00% ±  9.41%

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  306 μs           Histogram: frequency by time         6.77 ms <

 Memory estimate: 1.68 MiB, allocs estimate: 4139.

BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  299.787 μs …   7.530 ms  ┊ GC (min … max):  0.00% … 85.84%
 Time  (median):     348.430 μs               ┊ GC (median):     0.00%
 Time  (mean ± σ):   453.382 μs ± 694.182 μs  ┊ GC (mean ± σ):  15.33% ±  9.40%

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  ████▇▅▃▃▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▃▁▄▅▆ █
  300 μs        Histogram: log(frequency) by time       6.43 ms <

 Memory estimate: 1.68 MiB, allocs estimate: 4169.

Does it depend on the type of arguments?