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ins-amu / vbjax

A nascent Jax-based package for virtual brain modeling.
Apache License 2.0
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vbjax

DOI

vbjax is a Jax-based package for working with virtual brain style models.

Installation

Installs with pip install "vbjax", but for the latest features, you can use the source,

git clone https://github.com/ins-amu/vbjax
cd vbjax
pip install -e ".[dev]"

You're encouraged to have the source handy to consult and change, but you can also just

pip install git+https://github.com/ins-amu/vbjax

The primary additional dependency of vbjax is JAX, which itself depends only on NumPy, SciPy & opt-einsum, so it should be safe to add to your existing projects.

gee pee you

CUDA

If you have a CUDA-enabled GPU, you install the requisite dependencies like so

pip install --upgrade "jax[cuda11_pip]" -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html

M1/M2 🍎

On newer Apple machines w/ M1, M2 or M3 GPUs, JAX supports using the GPU experimentally by installing just two extra packages:

pip install ml-dtypes==0.2.0 jax-metal

About a third of vbjax tests fail due to absence of certain operations like n-dim scatter/gather & FFTs, and it may not be faster because these CPUs already have excellent memory bandwidth & latency hiding.

CUDA 🐳

BUT because GPU software stack versions make aligning stars look like child's play, container images are available and auto-built w/ GitHub Actions, so you can use w/ Docker

docker run --rm -it ghcr.io/ins-amu/vbjax:main python3 -c 'import vbjax; print(vbjax.__version__)'

The images are built on Nvidia runtime images, so --gpus all is enough for Jax to discover the GPU(s).

Examples

Here are some examples of simulations which show what you can do with the library. Because they are implemented atop Jax, it is easy to take gradients for optimization or MCMC, or do efficient GPU parallel batching. Or both ಠ_ರೃ

Simple network

Here's the smallest simulation you might want to do: an all-to-all connected network with Montbrio-Pazo-Roxin mass model dynamics,

import vbjax as vb
import jax.numpy as np

def network(x, p):
    c = 0.03*x.sum(axis=1)
    return vb.mpr_dfun(x, c, p)

_, loop = vb.make_sde(dt=0.01, dfun=network, gfun=0.1)
zs = vb.randn(500, 2, 32)
xs = loop(zs[0], zs[1:], vb.mpr_default_theta)
vb.plot_states(xs, 'rV', jpg='example1', show=True)

While integrators and mass models tend to be the same across publications, but the network model itself varies (regions vs surface, stimulus etc), vbjax allows user to focus on defining the network and then getting time series.

Jacobians

Jax makes it easy to compute Jacobians,

y0 = jp.r_[0.1, -2.0]

def eig1_tau(tau):
    theta = vb.mpr_default_theta._replace(tau=tau)
    J = jax.jacobian(vb.mpr_dfun)(y0, (0.4, 0.), theta)
    return jp.linalg.eigvals(J)[0]

jax.vmap(eig1_tau)( jp.r_[1.0:2.0:32j] ).real

Parallel parameter space exploration

One of the key tools in use of these models is to run parameter sweeps, which can be done easily with vbjax and parallelized with builtin Jax tools. 

import jax, jax.numpy as np
import vbjax as vb

Let's look at the effect of coupling, noise and excitability in a small network model, where the p parameter is a tuple of coupling scaling, noise scaling and the base MPR parameters:

def net(x, p):
    r, v = x
    k, _, mpr_p = p
    c = k*r.sum(), k*v.sum()
    return vb.mpr_dfun(x, c, mpr_p)

to ensure noise is a parameter we can tune later, we'll define the SDE with a dynamic noise scaled by the second element of the parameter tuple p,

def noise(_, p):
    _, sigma, _ = p
    return sigma

turn that into an SDE, choose network size (8 nodes here), with random initial conditions and realize an appropriate sample of noise for SDE integration:

_, loop = vb.make_sde(0.01, net, noise)
n_nodes = 8
rv0 = vb.randn(2, n_nodes)
zs = vb.randn(1000, *rv0.shape)

to run map parameters of interest to some metric of interest, we write a function, where we've chosen the standard deviation after a certain time as a index on the steady state of the network dynamics,

def run(pars, mpr_p=vb.mpr_default_theta):
    k, sig, eta = pars                      # explored pars
    p = k, sig, mpr_p._replace(eta=eta)     # set mpr
    xs = loop(rv0, zs, p)                   # run sim
    std = xs[400:, 0].std()                 # eval metric
    return std                              # done

all that is plain virtual brain equations, but to enable efficient & parallel sweeps, we can pull in jax primitives jax.pmap to parallelize over compute devices (by default, cores of the CPU) and jax.vmap to vectorize the function run, or just a jax.vmap if using a GPU,

if vb.is_cpu:
    run_batches = jax.pmap(jax.vmap(run, in_axes=1), in_axes=0)
else:
    run_batches = jax.vmap(run, in_axes=1)

now we run this over a parameter space (adapting for number of cores)

# sweep sigma but just a few values are enough
sigmas = [0.0, 0.2, 0.3, 0.4]
results = []
ng = vb.cores*4 if using_cpu else 32
for i, sig_i in enumerate(sigmas):
    # create grid of k (on logarithmic scale) and eta
    log_ks, etas = np.mgrid[-9.0:-2.0:1j*ng, -4.0:-6.0:1j*ng]
    # reshape grid to big batch of values
    pars = np.c_[
        np.exp(log_ks.ravel()),
        np.ones(log_ks.size)*sig_i,
        etas.ravel()].T.copy()
    # cpu w/ pmap expects a chunk for each core
    if using_cpu:
        pars = pars.reshape((3, vb.cores, -1)).transpose((1, 0, 2))
    # now run
    result = run_batches(pars).block_until_ready()
    results.append(result)

and plot the results,

import pylab as pl
pl.figure(figsize=(8,2))
for i, (sig_i, result) in enumerate(zip(sigmas, results)):
    pl.subplot(1, 4, i + 1)
    pl.imshow(result.reshape(log_ks.shape), vmin=0.2, vmax=0.7)
    pl.ylabel('k') if i==0 else (), pl.xlabel('eta')
    pl.title(f'sig = {sig_i:0.1f}')
pl.show()
pl.savefig('example3.jpg')

A full runnable script is in examples/parsweep.py.

Performance notes

Is (vb)jax fast? Single threaded C/C++ code typically reaches 50 to 200 thousand iterations per second on a single CPU core, for network sizes of e.g. 164 (e.g. Destrieux atlas from FreeSurfer). Let's check efficiency of the Jax code for some hardware on my desk:

You can tweak this script to see what you might expect on your hardware.

Distributed

If you are using a system like Dask or Slurm, you can then invoke that run_batches function in a distributed setting as required, without needing to manage a per core or per node for loop.

Simplest neural field

Here's a neural field,

import jax.numpy as np
import vbjax as vb

# setup local connectivity
lmax, nlat, nlon = 16, 32, 64
lc = vb.make_shtdiff(lmax=lmax, nlat=nlat, nlon=nlon)

# network dynamics
def net(x, p):
    c = lc(x[0]), 0.0
    return vb.mpr_dfun(x, c, p)

# solution + plot
x0 = vb.randn(2, nlat, nlon)*0.5 + np.r_[0.2,-2.0][:,None,None]
_, loop = vb.make_sde(0.1, net, 0.2)
zs = vb.randn(500, 2, nlat, nlon)
xt = loop(x0, zs, vb.mpr_default_theta._replace(eta=-3.9, cr=5.0))
vb.make_field_gif(xt[::10], 'example2.gif')

This example shows how the field forms patterns gradually despite the noise in the simulation, due to the effect of local connectivity

MCMC estimation of neural field activity

For MCMC estimates with NumPyro we define a function to compute posterior log probability p(theta | x), 

  def logp(xt=None):
      x0h = numpyro.sample('x0h', dist.Normal(jnp.zeros((nlat, nlon)), 1))
      xth_mu = loop(x0h, ts, k)
      numpyro.sample('xth', dist.Normal(xth_mu, 1), obs=xt)

run MCMC w/ NUTS,

  mcmc = MCMC(NUTS(logp), num_warmup=500, num_samples=500)
  mcmc.run(jax.random.PRNGKey(0), xt=xt)
  x0h = mcmc.get_samples()['x0h']

check diagnostics like estimated sample size, shrinkage and z-score,

  ess = numpyro.diagnostics.effective_sample_size(x0h.reshape((1, 500, -1)))
  assert ess.min() > 100
  shrinkage, zscore = vbjax.shrinkage_zscore(x0, x0h, 1)
  assert shrinkage.min() > 0.7
  assert zscore.max() < 1.5

Full code is in the test suite, can be run pytest -m slow, since it takes about 5 minutes to run on a GPU, 7 min on m1 CPU core and 12 minutes on an x86_64 CPU core.

Fitting an autoregressive process

Here's a 1-lag MVAR

import jax
import jax.numpy as np
import vbjax as vb

nn = 8
true_A = vb.randn(nn,nn)
_, loop = vb.make_sde(1, lambda x,A: -x+(A*x).mean(axis=1), 1)
x0 = vb.randn(nn)
zs = vb.randn(1000, nn)
xt = loop(x0, zs, true_A)

xt and true_A are the simulated time series and ground truth interaction matrices.

To fit anything we need a loss function & gradient descent,


def loss(est_A):
    return np.sum(np.square(xt - loop(x0, zs, est_A)))

grad_loss = jax.grad(loss)
est_A = np.ones((nn, nn))*0.3  # wrong
for i in range(51):
    est_A = est_A - 0.01*grad_loss(est_A)
    if i % 10 == 0:
        print('step', i, 'log loss', np.log(loss(est_A)))

print('mean sq err', np.square(est_A - true_A).mean())

which prints

step 0 log loss 5.8016257
step 10 log loss 3.687574
step 20 log loss 1.7174681
step 30 log loss -0.15798996
step 40 log loss -1.9851608
step 50 log loss -3.7805486
mean sq err 8.422789e-05

This is a pretty simple example but it's meant to show that any model you build with vbjax like this is usable with optimization or NumPyro's MCMC algorithms.

ƪ(ړײ)‎ƪ​​ moar examples‽

More complex examples are in the examples folder:

HPC usage

We use this on HPC systems, most easily with container images. Open an issue if it doesn't work.

CSCS Piz Daint Useful modules ```bash module load daint-gpu module load cudatoolkit/11.2.0_3.39-2.1__gf93aa1c module load TensorFlow ``` then install in some Python environment; the default works fine ```bash pip3 install "jax[cuda]==0.3.8" -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html pip3 install "jaxlib==0.3.8+cuda11.cudnn805" -U -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html ``` This provides an older version of JAX unfortunately. The Sarus runtime can be used to make use of latest versions of vbjax and jax: ```bash $ module load daint-gpu $ module load sarus $ sarus pull ghcr.io/ins-amu/vbjax:main ... $ srun -p debug -A ich042 -C gpu --pty sarus run ghcr.io/ins-amu/vbjax:main python3 -c 'import jax; print(jax.numpy.zeros(32).device())' ... gpu:0 ```
JSC JUSUF A nice module is available to get CUDA libs ```bash module load cuDNN/8.6.0.163-CUDA-11.7 ``` then you might set up a conda env, ```bash wget https://repo.anaconda.com/miniconda/Miniconda3-latest-Linux-x86_64.sh bash Miniconda3-latest-Linux-x86_64.sh -b -p ~/conda . ~/conda/bin/activate conda create -n jax python=3.9 numpy scipy source activate jax ``` once you have an env, install the CUDA-enabled JAX ```bash pip3 install --upgrade "jax[cuda]" -f https://storage.googleapis.com/jax-releases/jax_cuda_releases.html ``` and check it works ```bash (jax) [woodman1@jsfl02 ~]$ srun -A icei-hbp-2021-0002 -p develgpus --pty python3 -c 'import jax.numpy as np ; print(np.zeros(32).device())' gpu:0 ``` JSC also makes Singularity available, so the prebuilt image can be used ``` TODO ```
CEA The prebuilt image is the best route: ``` TODO ```

Development

New ideas or even documenting tricks (like how Jax works) should go into the test suite, and there are some ideas floating there before making it into the library itself.

git clone https://github.com/ins-amu/vbjax
cd vbjax
pip install '.[dev]'
pytest

Installing SHTns

This library is used for some testing. It is impossible to install on Windows natively, so WSLx is required.

On macOS,

brew install fftw
git clone https://bitbucket.org/nschaeff/shtns
./configure --enable-python --disable-simd --prefix=/opt/homebrew
make -j && make install && python setup.py install

Releases

a release of version v1.2.3 requires following steps