| """Differentiable conditional logical likelihood through exact DEM elimination.""" |
| import jax |
| import jax.numpy as jnp |
|
|
|
|
| def make_loss_and_grad(width): |
| indices=jnp.arange(1<<width,dtype=jnp.int32) |
| @jax.jit |
| def evaluate(dets,labels,probabilities,masks,measured): |
| |
| f=jnp.zeros((len(dets),1<<width),jnp.float32).at[:,0].set(1) |
| def forward(f,args): |
| p,mask,d=args |
| def error(f): |
| return (1-p[:,None])*f+p[:,None]*f[:,indices^mask],jnp.ones(len(dets)) |
| def project(f): |
| dst=(indices[None,:]&~mask)|(dets[:,d,None].astype(jnp.int32)*mask) |
| g=jnp.take_along_axis(f,dst,axis=1)*((indices&mask)==0) |
| norm=jnp.maximum(g.sum(axis=1),1e-30) |
| return g/norm[:,None],norm |
| out,norm=jax.lax.cond(d<0,error,project,f) |
| return out,(f,norm) |
| f,(history,norms)=jax.lax.scan(forward,f,(probabilities,masks,measured)) |
| indicator=((indices[None,:]&1)==labels[:,None]) |
| correct=jnp.maximum(jnp.sum(f*indicator,axis=1),1e-10) |
| predicted=jnp.sum(f[:,1::2],axis=1) |
| initial=1-indicator/correct[:,None] |
| def backward(b,args): |
| p,mask,d,old,norm=args |
| def error(b): |
| flipped=b[:,indices^mask] |
| grad=jnp.sum(old*(flipped-b),axis=1) |
| return (1-p[:,None])*b+p[:,None]*flipped,grad |
| def project(b): |
| obs=((indices[None,:]&mask)==dets[:,d,None].astype(jnp.int32)*mask) |
| values=b[:,indices&~mask] |
| mean=jnp.sum(old*obs*values,axis=1)/norm |
| prior=(values-mean[:,None])*obs/norm[:,None] |
| return prior,jnp.zeros(len(dets)) |
| return jax.lax.cond(d<0,error,project,b) |
| _,grad=jax.lax.scan(backward,initial,(probabilities,masks,measured,history,norms),reverse=True) |
| return -jnp.log(correct),predicted,grad |
| return evaluate |
|
|
