Project: 002_TopoLM_brain-like_spatio-functional_organization_i | Function: local_spatial_loss (iclr)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Computes spatial correlation loss for a specific neighborhood using Pearson correlation between activation correlations and spatial distances

**KEY TERMS:** {
  "D": "inverse distance matrix dk",
  "r": "activation correlation vector rk",
  "torch.corrcoef": "Pearson correlation corr()",
  "0.5 * (1 - ...)": "SLk formula implementation"
}

**CONTEXT CODE:** @dataclass
class NetworkPositions:

    # dictionary of all layer positions
    layer_positions: Dict[str, LayerPositions]
    version: int

    # load ALL positions from disk
    @classmethod
    def load_from_dir(cls, load_dir: Path):

        load_dir = Path(load_dir)

        assert load_dir.is_dir(), load_dir
        layer_files = list(load_dir.glob('*.pkl'))

        d = {}

        for layer_file in layer_files:

            layer_name = layer_file.stem
            d[layer_name] = LayerPositions.load(layer_file)

        version_path = load_dir / 'version.txt'
        version = 1.0

        if version_path.is_file():
            with version_path.open('r') as f:
                version = int(f.readline())

        return cls(version = version, layer_positions = d)

### SPATIAL LOSS ###

# norm implementation for lp-norm
# for some reason this makes things 20x faster than torch.norm????
def p_norm(positions, p='inf'):

    diff = positions[:, None, :] - positions[None, :, :]

    if p == 1:
        return torch.sum(torch.abs(diff), dim=-1)
    if p == 2:
        return torch.sqrt(torch.sum(diff ** 2, dim=-1))
    if p == 'inf':
        return torch.max(torch.abs(diff), dim=-1)[0]

    raise ValueError(f'norm type {p} not supported')

# compute spatial loss for a specific neighborhood (tensors should already be masked)
def local_spatial_loss(activations, positions):

    raise NotImplementedError("Function implementation has been masked for testing")
# compute spatial loss for an entire batch
def spatial_loss_fn(activations, positions, accum='mean'):

    raise NotImplementedError("Function implementation has been masked for testing")
### PRE OPTIMIZATION ###

# helper function to swap two neurons
def swap_units(positions, swap_ind):
    positions[swap_ind] = positions[torch.flip(swap_ind, [0])]

# run swap optimization on a neighborhood (tensors should already be masked)
def swap_local(activations, positions, neighborhood, steps = 500, p = 'inf', rng=None):
    
    n_swapped = 0
    old_loss = np.inf
    coordinates = positions.coordinates[neighborhood]

    for i in range(steps):

        swap_ind = torch.randperm(coordinates.shape[0], generator = rng)[:2]
        swap_units(coordinates, swap_ind)

        loss = local_spatial_loss(activations[:, neighborhood], coordinates)

        # if the swapping doesn't decrease loss, unswap and move on
        if loss > old_loss:
            swap_units(coordinates, swap_ind)
        else:
            swap_units(neighborhood, swap_ind)
            old_loss = loss
            n_swapped += 1

    return coordinates, n_swapped, neighborhood

# binary mask of points within 'radius' of center
def get_neighborhood(center, positions, radius = 5, p = 'inf'):
    distances = p_norm(positions, p)
    return distances[center] < radius

# randomly select a center point for a neighborhood (avoiding the edges of the layer)
def get_center(positions, radius, rng=None):

    N = int(np.sqrt(positions.shape[0]))

    mask = (positions[:, 0] >= radius - 1) & (positions[:, 0] <= N - radius) & \
           (positions[:, 1] >= radius - 1) & (positions[:, 1] <= N - radius)

    indices = torch.nonzero(torch.Tensor(mask)).flatten()

    return indices[torch.randint(0, len(indices), (1,), generator = rng).item()]

# identify neighborhoods and run local optimization on each
def swap_optimize(activations, positions, num_neighborhoods, local_steps = 500, radius = 5, p = 'inf', rng=None):

    tot_n_swapped = 0

    for i in tqdm(range(num_neighborhoods)):

        # do pre-optimization on predetermined neighborhood
        neighborhood = positions.neighborhood_indices[i].to(bool)
        positions.coordinates[neighborhood], n_swapped, neighborhood = swap_local(activations, positions, neighborhood, local_steps, p, rng=rng)

        # replace the neighborhood with the swapped version
        positions.neighborhood_indices[i] = neighborhood.to(int)

        tot_n_swapped += n_swapped

    return positions, tot_n_swapped

### NUMPY SPATIAL LOSS FUNCTIONS ###
# these are NOT used anywhere, they are just a guide

def p_norm_numpy(positions, p = 'inf'):

    diff = positions[:, np.newaxis, :] - positions[np.newaxis, :, :]

    if p == 1:
        return np.sum(np.abs(diff), axis = -1)
    if p == 2:
        return np.sqrt(np.sum(diff ** 2, axis = -1))
    if p == 'inf':
        return np.max(np.abs(diff), axis = -1)

    raise ValueError(f'norm type {p} not supported')

def local_spatial_loss_numpy(activations, positions):

    num_units = activations.shape[1]
    idx = np.tril_indices(num_units, k = -1)

    D = 1 / (1 + p_norm_numpy(positions, 2))
    r = np.corrcoef(activations.T)

    return 1 - np.corrcoef(r[idx], D[idx])[0][1]

def spatial_loss_numpy(activations, positions):



Complete the function implementation replacing "raise NotImplementedError".