Sensitivity analysis of network of Epileptors

benchmark-autodiff.ipynb

epinet.fut

import "util"

let a = 1.0f32
let b = 3.0f32
let c = 1.0f32
let d = 5.0f32
let r = 0.00015f32
let s = 4.0f32
let Iext = 3.1f32
let slope = 0.0f32
let Iext2 = 0.45f32
let tau = 10.0f32
let aa = 6.0f32
let bb = 2.0f32
let Kvf = 0.0f32
let Kf = 0.00f32
let Ks = 0.00f32
let tt = 1.0f32
let modification = 0.0f32
let x0 = -2f32

type node = (f32,f32,f32, f32,f32,f32)

let coupling (w:[][]f32) (x:[]f32): []f32 =
    let per_node wi xi = map2 (\wij xj -> wij * (xj - xi)) wi x |> reduce (+) 0f32
    in map2 per_node w x

let node (y:node) (c_pop1:f32) (c_pop2:f32): node =
    let (x1,y1,z,x2,y2,g) = y
    let dx1' = if x1 < 0
        then ((-a) * x1*x1) + b * x1
        else (slope - x2) + 0.6f32 * (z - 4f32)*(z - 4f32)
    let dx1 = tt * (y1 - z + Iext + Kvf * c_pop1 + dx1' * x1)
    let dy1 = tt * (c - d * x1*x1 - y1)
    let dz = if z < 0
        then -0.1f32 * z*z*z*z*z*z*z
        else 0f32
    let h = if modification>0
        then x0 + 3f32/(1f32 + f32.exp(-(x1 + 0.5f32)/0.1f32))
        else 4f32 * (x1 - x0) + dz
    let dz = tt * (r * (h - z + Ks * c_pop1))
    let dx2 = tt * (-y2 + x2 - x2*x2*x2 + Iext2 + bb * g - 0.3f32 * (z - 3.5) + Kf * c_pop2)
    let dy2 = if x2 < -0.25f32 then 0f32 else aa * (x2 + 0.25f32)
    let dy2 = tt * ((-y2 + dy2) / tau)
    let dg = tt * (-0.01f32 * (g - 0.1 * x1))
    in (dx1, dy1, dz, dx2, dy2, dg)

entry node_eval (y:[6]f32) (c_pop1:f32) (c_pop2:f32): [6]f32 =
    let y' = (y[0],y[1],y[2],y[3],y[4],y[5])
    let (d1,d2,d3,d4,d5,d6) = node y' c_pop1 c_pop2
    in [d1,d2,d3,d4,d5,d6]

let network (y:[]node) (w:[][]f32): []node =
    let (x1, y1, z, x2, y2, g) = unzip6 y
    let c_pop1 = coupling w x1
    let c_pop2 = coupling w x2
    in map3 node y c_pop1 c_pop2

let heun (dt:f32) (y:[]node) (w:[][]f32): []node =
    let half_dt:f32 = dt / 2
    let dy1 = network y w
    let yi = map2 (\(x1, y1, z, x2, y2, g) (dx1, dy1, dz, dx2, dy2, dg) -> 
        (x1 + dt * dx1, y1 + dt * dy1, z + dt * dz, x2 + dt * dx2, y2 + dt * dy2, g + dt * dg))
        y dy1
    let dy2 = network yi w
    in map3 (\(x1, y1, z, x2, y2, g) (dx1, dy1, dz, dx2, dy2, dg) (ex1, ey1, ez, ex2, ey2, eg) -> 
        (x1 + half_dt * (dx1 + ex1),
        y1 + half_dt * (dy1 + ey1),
        z + half_dt * (dz + ez),
        x2 + half_dt * (dx2 + ex2),
        y2 + half_dt * (dy2 + ey2),
        g + half_dt * (dg + eg)))
        y dy1 dy2

let init = (-1.5f32, -11.3f32, 3.0f32, -0.82f32, 0.04f32, -0.15f32)

let run [n] (nt:i64) (dt:f32) (init:[n]node) (w:[n][n]f32): [][n]node = 
    let y = tabulate nt (\_ -> init)
    in loop (y) for i < (nt - 1) do
        let y[i+1] = heun dt (copy y[i]) w
        in y

let lfp ((x1,_,_,x2,_,_):node): f32 = x2 - x1

-- welford online variance algorithm
type welf = {count: i64, mean: f32, m2: f32}

let welford_init (y:node): welf = {count=1, mean=lfp y, m2=0f32}

let welford_update ({count,mean,m2}:welf) (y:node): welf =
    let lfp' = lfp y
    let count = count + 1
    let delta = lfp' - mean
    let mean = mean + delta / (f32.i64 count)
    let delta2 = lfp' - mean
    let m2 = m2 + delta * delta2
    in {count, mean, m2}

let welford_finalize ({count,mean,m2}:welf): (f32,f32) =
    (mean, m2 / (f32.i64 count))

let run_online_std [n] (nt:i64) (dt:f32) (init:[n]node) (w:[n][n]f32): [n]f32 =
    let v = map welford_init init
    let (_, v) = loop (y, v) = (init, v)
        for i < (nt - 1) do
            let y = heun dt y w
            let v = map2 welford_update v y
            in (y, v)
    in map (\v -> f32.sqrt (welford_finalize v).1) v

let run_z [n] (nt:i64) (dt:f32) (z:[n]f32) (w:[n][n]f32): [][n]node = 
    let (x1,y1,_,x2,y2,g) = init
    let y0 = map (\z -> (x1,y1,z,x2,y2,g)) z
    in run nt dt y0 w

let run_z_online [n] (nt:i64) (dt:f32) (z:[n]f32) (w:[n][n]f32): []f32 = 
    let (x1,y1,_,x2,y2,g) = init
    let y0 = map (\z -> (x1,y1,z,x2,y2,g)) z
    in run_online_std nt dt y0 w

entry run_z_array [n] (nt:i64) (dt:f32) (z:[n]f32) (w:[n][n]f32): [nt][n][6]f32 =
  let y = run_z nt dt z w
  let to_array (yi:[n]node): [n][6]f32 = map (\(a,b,c,d,e,f) -> [a,b,c,d,e,f]) yi
  in map to_array y

let std [n] (xs:[n]f32): f32 =
    let mu = (reduce (+) 0f32 xs) / (f32.i64 n)
    let n_var = map (\x -> (x - mu)*(x - mu)) xs |> reduce (+) 0f32
    in f32.sqrt (n_var / (f32.i64 n))

let forward [nt] [n] (y:[nt][n]node) = 
    let lfp: [n][nt]f32 = map (map (\(x1,_,_,x2,_,_) -> x2 - x1)) y |> transpose
    in map std lfp

entry forward_array [nt] [n] (y:[nt][n][6]f32): [n]f32 =
    let lfp: [n][nt]f32 = map (map (\x -> x[3] - x[0])) y |> transpose
    in map std lfp

let sse [n] (x:[n]f32) (y:[n]f32): f32 =
    map2 (\x y -> (x - y)*(x - y)) x y |> reduce (+) 0f32

entry loss [n] (nt:i64) (dt:f32) (w:[n][n]f32) (z:[n]f32) (zh:[n]f32): f32 =
    run_z nt dt zh w |> forward |> sse z

entry loss_online [n] (nt:i64) (dt:f32) (w:[n][n]f32) (z:[n]f32) (zh:[n]f32): f32 =
    run_z_online nt dt zh w |> sse z

entry vjp_loss_online [n] (nt:i64) (dt:f32) (w:[n][n]f32) (z:[n]f32) (zh:[n]f32): [n]f32 =
  vjp (loss_online nt dt w z) zh 1f32

entry jvp_loss_online [n] (nt:i64) (dt:f32) (w:[n][n]f32) (z:[n]f32) (zh:[n]f32): [n]f32 =
  let one i = jvp (loss_online nt dt w z) zh (tabulate n (\j -> if i==j then 1f32 else 0f32))
  in map one (iota n)

entry vjp_loss [n] (nt:i64) (dt:f32) (w:[n][n]f32) (z:[n]f32) (zh:[n]f32): [n]f32 =
  vjp (loss nt dt w z) zh 1f32

entry jvp_loss [n] (nt:i64) (dt:f32) (w:[n][n]f32) (z:[n]f32) (zh:[n]f32): [n]f32 =
  let one i = jvp (loss nt dt w z) zh (tabulate n (\j -> if i==j then 1f32 else 0f32))
  in map one (iota n)
-- because of the type of jvp we need to write the overall loss differently to
-- push jvp further down.


-- ==
-- random input { 75i64 [76]f32 [76]f32 [76][76]f32 0i64 }
-- random input { 75i64 [76]f32 [76]f32 [76][76]f32 1i64 }
-- random input { 75i64 [76]f32 [76]f32 [76][76]f32 2i64 }
-- random input { 750i64 [76]f32 [76]f32 [76][76]f32 0i64 }
-- random input { 750i64 [76]f32 [76]f32 [76][76]f32 1i64 }
-- random input { 750i64 [76]f32 [76]f32 [76][76]f32 2i64 }
let main [n] (nt:i64) (z:[n]f32) (zh:[n]f32) (w:[n][n]f32) (mode:i64): [n]f32 =
  let dt: f32 = 0.01 in
  match mode
  case 0i64 -> loss nt dt w z zh |> replicate n
  case 1i64 -> vjp_loss nt dt w z zh
  case 2i64 -> jvp_loss nt dt w z zh
  case _ -> replicate n 0f32

epinet.jl

# using OrdinaryDiffEq
using DelimitedFiles
# using Plots
# using Statistics
# using DiffEqSensitivity
# using ForwardDiff
# using Zygote
# using SliceMap
# using BenchmarkTools

# TVB conn_76
weights = Float32.(readdlm("weights.txt"));
# tract_lengths = Float32.(readdlm("mpr-append/tract_lengths.txt"));

function make_epileptor(weights)
    a = 1.0f0
    b = 3.0f0
    c = 1.0f0
    d = 5.0f0
    r = 0.00015f0
    s = 4.0f0
    Iext = 3.1f0
    slope = 0.0f0
    Iext2 = 0.45f0
    tau = 10.0f0
    aa = 6.0f0
    bb = 2.0f0
    Kvf = 0.0f0
    Kf = 0.01f0
    Ks = 0.01f0
    tt = 1.0f0
    modification = 0.0f0
    x0 = -2f0
    weights = Float32.(weights)

    @inline function node(i,y,p,t,c_pop1,c_pop2)
        if y[1] < 0.0
            ydot1 = - a * y[1] ^ 2 + b * y[1]
        else
            ydot1 = slope - y[3] + 0.6 * (y[3] - 4.0) ^ 2
        end
        ydot1 = tt * (y[2] - y[3] + Iext + Kvf * c_pop1 + ydot1 * y[1])
        ydot2 = tt * (c - d * y[1] ^ 2 - y[2])

        # energy
        if y[3] < 0.0
            ydot3 = - 0.1 * y[3] ^ 7
        else
            ydot3 = 0.0
        end
        if modification>0
            h =  x0 + 3/(1 + exp(-(y[1]+0.5)/0.1))
        else
            h = 4 * (y[1] - x0) + ydot3
        end
        ydot3 = tt * (r * (h - y[3]  + Ks * c_pop1))

        # population 2
        ydot4 = tt * (-y[5] + y[4] - y[4] ^ 3 + Iext2 + bb * y[6] - 0.3 * (y[3] - 3.5) + Kf * c_pop2)
        if y[4] < -0.25
            ydot5 = 0.0
        else
            ydot5 = aa * (y[4] + 0.25)
        end
        ydot5 = tt * ((-y[5] + ydot5) / tau)

        # filter
        ydot6 = tt * (-0.01 * (y[6] - 0.1 * y[1]))
        return [ydot1, ydot2, ydot3, ydot4, ydot5, ydot6]
    end

    function network(ydot,y,p,t)
        c_pop1 = dropdims(sum(weights .* (y[:,1] .- y[:,1]'); dims=2); dims=2)
        c_pop2 = dropdims(sum(weights .* (y[:,4] .- y[:,4]'); dims=2); dims=2)
        for i=1:size(weights,1)
            node(i,ydot,(y[:,i]),p,t,c_pop1[i],c_pop2[i])
        end
    end

    return network
end

network = make_epileptor(weights)

function make_predict(nwin=33,sensealg=ForwardSensitivity())
    function predict(z)
        u0 = [[-1.5, -11.3, 3.0, -0.82, 0.04, -0.15] for i=1:size(weights,1)]
        u0 = Float32.(reduce(hcat, u0)')
        u0 = reduce(hcat, [u0[:,1], u0[:,2], z, u0[:,4], u0[:,5], u0[:,6]])
        win = 15f0
        prob = ODEProblem(network,u0,(0f0,nwin * win))
        @show nwin*win/0.1f0
        sol = solve(prob, Heun(), dt=0.1f0, saveat=win,sensealg=sensealg)
        zt = reduce(hcat,[u[:,4]-u[:,1] for u in sol.u])
        zs = [std(zt[i,:]) for i=1:76]
        zs, zt
    end
    predict
end

function make_loss(sz, nwin=33, sensealg=ForwardSensitivity())
    predict = make_predict(nwin, sensealg)
    function loss(zh)
        szh, _ = predict(zh)
        sum((szh .- sz).^2)
    end
    loss
end

function runstuff()
    z = Float32.(randn(76)) .+ 3f0;
    sz, zt = make_predict(5)(z);
    # p1=heatmap(zt)
    # p2=plot(z, sz, seriestype = :scatter)
    # plot(p1,p2)

    loss = make_loss(sz, 5, ForwardSensitivity())
    @time loss(z)
    @time loss(z)
    @time loss(z)
    ForwardDiff.gradient(loss, z) 
    @time ForwardDiff.gradient(loss, z)  # ~200s?
    @time ForwardDiff.gradient(loss, z)

    # for sa in [ForwardSensitivity(), ForwardDiffSensitivity(), BacksolveAdjoint(), InterpolatingAdjoint(), QuadratureAdjoint(), ReverseDiffAdjoint(), ReverseDiffVJP(true), SensitivityADPassThrough()]
    #     @show sa
    #     loss = make_loss(sz, 5, ForwardSensitivity())
    #     loss(z)
    #     @time loss(z)
    #     ForwardDiff.gradient(loss, z) 
    #     @time ForwardDiff.gradient(loss, z)
    # end

    # using ReverseDiff

    # loss = make_loss(sz, 5, ReverseDiffVJP(false))
    # @time ReverseDiff.gradient(loss, z);
    # @time ReverseDiff.gradient(loss, z);
    # @time ReverseDiff.gradient(loss, z);
end

epinettest.py

aimport os
import numpy as np
import pylab as pl
if 1:
    #os.system('futhark c --library epinet.fut')
    os.system('build_futhark_ffi epinet')
from futhark_ffi import Futhark
import _epinet
epinet = Futhark(_epinet)
w = np.loadtxt('weights.txt').astype('f')
z = (np.random.randn(76)+ 3.0).astype('f')
nt = 750
zt = epinet.from_futhark(epinet.run_z_array(nt, z, w))
lfp = zt[:,:,3] - zt[:,:,0]
pl.subplot(121); pl.imshow(lfp,aspect='auto',vmin=-5,vmax=5)
pl.subplot(122);
pl.plot(z, epinet.from_futhark(epinet.forward_array(zt)), 'bo')
pl.plot(z, lfp.std(axis=0) + 0.1, 'ko', alpha=0.3)
pl.show()

l1 = epinet.from_futhark(epinet.vjp_loss(nt,w,z,z+1e-2))
l2 = epinet.from_futhark(epinet.jvp_loss(nt,w,z,z+1e-2))
print(np.c_[l1, l2])
# they're the same!
#
import tqdm
for i in tqdm.trange(10):
    l2 = epinet.jvp_loss(nt,w,z,z+1e-2)
for i in tqdm.trange(10):
    l2 = epinet.from_futhark(epinet.jvp_loss(nt,w,z,z+1e-2))
for i in tqdm.trange(10):
    l2 = epinet.from_futhark(epinet.vjp_loss(nt,w,z,z+1e-2))

spatepi.fut

type node = (f32,f32,f32, f32,f32,f32)
type lc = (f32,f32,f32)

let spatepi_dfun
            (gamma11:f32) (gamma22:f32)
            (gamma12:f32) (gamma_glob:f32)
            (Iext:f32) (Iext2:f32) (tt:f32)
            (py0:f32) (tau0:f32) (tau2:f32)
            (y:node) (c:f32) (lc:lc) (x0:f32)
        : node =

    let loc11 = gamma11 * lc.0
    let loc22 = gamma22 * lc.1
    let loc12 = gamma12 * lc.2
    let c_pop = gamma_glob * c
    let (y0,y1,y2,y3,y4,y5) = y

    -- -- pop 1
    let y02 = y0 * y0
    let dy0 = if y0 < 0 
        then (y0 * y02 - 3.0f32 * y02)
        else (y3 - 0.6f32 * (y2 - 4.0f32) * (y2 - 4.0f32)) * y0
    
    let dy0 = tt * (y1 - dy0 - y2 + Iext + loc11 + c_pop)
    let dy1 = tt * (py0 - 5 * y02 - y1)

    -- -- energy
    let y22 = y2 * y2
    let y23 = y22 * y2
    let dy2 = if y2 < 0 then (-0.1f32 * y22 * y22 * y23) else 0f32
    let dy2 = tt * (1.0f32 / tau0 * (4.0f32 * (y0 - x0) - y2 + dy2))

    -- pop 2
    let y33 = y3 * y3 * y3
    let dy3 = tt * (-y4 + y3 - y33 + Iext2 + 2.0f32 * y5 - 0.3f32 * (y2 - 3.5f32) + loc22)
    let dy4 = if (y3 < (-0.25f32)) then 0f32 else 6.0f32 * (y3 + 0.25f32)
    let dy4 = tt * ((-y4 + dy4) / tau2)

    -- filter
    let dy5 = tt * (-0.01f32 * y5 + 0.003f32 * y0 + 0.01f32 * loc12)

    in (dy0, dy1, dy2, dy3, dy4, dy5)

let npsign (x:f32): f32 =
    if x < 0f32 then -1f32 else if x > 0f32 then 1f32 else 0f32

let spatepi_lcfun (theta11:f32) (theta22:f32) (theta12:f32)
                  (y:node): lc =
    let (y0,y1,y2,y3,y4,y5) = y
    in (
        0.5f32 * ((npsign (y0 - theta11)) + 1f32),
        0.5f32 * ((npsign (y3 - theta11)) + 1f32),
        0.5f32 * ((npsign (y0 - theta12)) + 1f32)
    )

-- let full_dfun nodes = 
--     let lcs = map2 (spatepi_lcfun 0f32 0f32 0f32) node |> sht3x2
--     in map4 dfun nodes cs lcs x0s
let unzip6 [n] 'a 'b 'c 'd 'e 'f (xs: [n](a,b,c,d,e,f)): ([n]a, [n]b, [n]c, [n]d, [n]e, [n]f) =
  let (as, bs, cs, ds, efs) = unzip5 (map (\(a,b,c,d,e,f) -> (a,b,c,d,(e,f))) xs)
  let (es, fs) = unzip efs
  in (as, bs, cs, ds, es, fs)

-- ==
-- input { 1024i64 0 }
-- input { 8192i64 0 }
-- input { 16384i64 0 }
-- input { 32768i64 0 }
-- input { 66000i64 0 }
-- input { 400000i64 0 }
entry main (n:i64) (grad:i32): [n]f32 = 
    let t = 1i64
    let nodes = tabulate n (\i -> (-1.4624261f32+((f32.i64 i)*1e-3), -9.6934490f32+((f32.i64 i)*1e-3),  2.9502959f32+((f32.i64 i)*1e-3), -1.1118182f32+((f32.i64 i)*1e-3),
 -9.5610595e-20+((f32.i64 i)*1e-3), -4.3872780e-01+((f32.i64 i)*1e-3)))
    let lcs = tabulate n (\i -> (0.1f32+((f32.i64 i)*1e-3), 0.1f32+((f32.i64 i)*1e-3), 0.1f32+((f32.i64 i)*1e-3)))
    let cs = tabulate n (\i -> 0.1f32+((f32.i64 i) * 1e-3))
    let x0s = tabulate n (\i -> -1.8f32+((f32.i64 i) * 1e-3))
    --     (gamma11:f32) (gamma22:f32)
    -- (gamma12:f32) (gamma_glob:f32)
    -- (Iext:f32) (Iext2:f32) (tt:f32)
    -- (py0:f32) (tau0:f32) (tau2:f32)
    let dfun = spatepi_dfun 0.169 0.318 0.0318 1.0 3.1 0.45 0.17 1.0 2857.0 1.0
    let h = 0.1f32
    let eu (a,b,c,d,e,f) (da,db,dc,dd,de,df) = (a+h*da,b+h*db,c+h*dc,d+h*dd,e+h*de,f+h*df)
    let f (n, c, l, x) = loop (n) for i < t do (eu n (dfun n c l x))
    let g_vjp = f (nodes[0],cs[0],lcs[0],x0s[0])
    let g_jvp =   (nodes[0],cs[0],lcs[0],x0s[0])
    in
    -- if grad==0
    --     then 
        map4 (\n c l x ->     f (n,c,l,x)  ) nodes cs lcs x0s |> unzip6 |> (.0)
    -- else if grad==1
    --     then map4 (\n c l x -> vjp f (n,c,l,x) g_vjp) nodes cs lcs x0s |> unzip4 |> (.0) |> unzip6 |> (.0)
    --     else map4 (\n c l x -> jvp f (n,c,l,x) g_jvp) nodes cs lcs x0s |> unzip6 |> (.0)

util.fut

let unzip6 [n] 'a 'b 'c 'd 'e 'f (xs: [n](a,b,c,d,e,f)): ([n]a, [n]b, [n]c, [n]d, [n]e, [n]f) =
  let (as, bs, cs, ds, efs) = unzip5 (map (\(a,b,c,d,e,f) -> (a,b,c,d,(e,f))) xs)
  let (es, fs) = unzip efs
  in (as, bs, cs, ds, es, fs)

weights.txt

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