python
def dijkstra(self):
# check if all the vertices are connected
for vertex in self.graph:
if not self.visited[vertex]:
return False
print(“Shortest path from vertex {0} to all other vertices”.format(self.start_vertex))
print(“VertextDistance from start_vertextPath”)
for vertex in self.shortest_path:
path = [vertex]
predecessor = self.predecessor[vertex]
while predecessor is not None:
path.append(predecessor)
predecessor = self.predecessor[predecessor]
path.reverse()
print(“{0}t{1}ttt{2}”.format(vertex,self.distance[vertex],path))

I’m trying to understand how this method determines if all vertices are connected before proceeding with finding shortest paths. Could you help clarify how this part works? I’m feeling a bit confused about this initial check! Thanks!
<>: python
Sure! In your code snippet, the check `for vertex in self.graph:` iterates over each vertex in the graph to see if it has been visited (`self.visited[vertex]`). If any vertex hasn’t been visited (`if not self.visited[vertex]:`), it returns `False`, indicating that not all vertices are connected.

This check assumes that `self.visited` is updated during your Dijkstra’s algorithm execution to mark vertices that have been reached from the starting vertex. If any vertex remains unvisited after running Dijkstra’s algorithm from your starting point (`self.start_vertex`), it implies that those vertices are not reachable from your starting point.

To ensure all vertices are connected (in terms of reachability from `self.start_vertex`), make sure your graph is fully connected or adjust your logic if you’re working with disconnected components.

If you need further clarification on implementing this check or handling disconnected graphs, feel free to ask! 😊

<>: Got it! So if I want to handle disconnected graphs more effectively, should I modify this check? Maybe return something more informative than just False? Also, any tips on improving variable names for better readability?
<>: Sure! To handle disconnected graphs more effectively, you could modify the check to return more informative feedback. Instead of just returning `False`, consider returning details about which vertices are unreachable:

python
def dijkstra(self):
unreachable_vertices = []

# Check if all vertices are connected
for vertex in self.graph:
if not self.visited[vertex]:
unreachable_vertices.append(vertex)

if unreachable_vertices:
print(“The following vertices are unreachable:”, unreachable_vertices)
return False

print(“Shortest path from vertex {0} to all other vertices”.format(self.start_vertex))
print(“VertextDistance from start_vertextPath”)

for vertex in self.shortest_path:
path = [vertex]
predecessor = self.predecessor[vertex]

while predecessor is not None:
path.append(predecessor)
predecessor = self.predecessor[predecessor]

path.reverse()
print(“{0}t{1}ttt{2}”.format(vertex,self.distance[vertex],path))

For better readability:

– Rename `self.visited` to `self.is_visited`.
– Rename `self.shortest_path` to `self.reachable_vertices`.
– Rename `self.predecessor` to `self.path_predecessors`.
– Rename `self.distance` to `self.vertex_distances`.

These changes can make your code more intuitive by clearly indicating what each variable represents.
<>: Great suggestions! Now I’m thinking about optimizing how we handle unreachable nodes during Dijkstra’s execution itself rather than just checking afterward. Maybe we could integrate this into the main loop? Also, would using a priority queue improve efficiency here? Let me know what you think!
<>: Integrating checks for unreachable nodes during Dijkstra’s execution can indeed enhance efficiency by stopping early when no further updates are possible. Using a priority queue (min-heap) will significantly improve performance because it allows efficient extraction of the minimum distance node.

Here’s how you can integrate these improvements:

python
import heapq

def dijkstra(self):
# Priority queue for selecting the next node with minimum distance
priority_queue = []

# Initialize distances and predecessors
for vertex in self.graph:
self.vertex_distances[vertex] = float(‘inf’)
self.path_predecessors[vertex] = None

# Start from the initial vertex
self.vertex_distances[self.start_vertex] = 0
heapq.heappush(priority_queue, (0, self.start_vertex))

while priority_queue:
current_distance, current_vertex = heapq.heappop(priority_queue)

# Skip processing if we already found a shorter path
if current_distance > self.vertex_distances[current_vertex]:
continue

# Explore neighbors
for neighbor, weight in self.graph[current_vertex].items():
distance = current_distance + weight

# Update if found shorter path
if distance < self.vertex_distances[neighbor]:
self.vertex_distances[neighbor] = distance
self.path_predecessors[neighbor] = current_vertex
heapq.heappush(priority_queue, (distance, neighbor))

# Identify unreachable nodes directly during execution
unreachable_vertices = [vertex for vertex in self.graph
if self.vertex_distances[vertex] == float('inf')]

if unreachable_vertices:
print("The following vertices are unreachable:", unreachable_vertices)

# Usage example would follow here…

By using a priority queue (`heapq`), you efficiently manage which node to process next based on current shortest distances. This approach also naturally handles unreachable nodes by leaving their distances as infinity.
<>: Awesome! Integrating these changes makes sense. I’ll work on incorporating the priority queue into my main loop and handle unreachable nodes dynamically during execution. Here’s what I’m thinking:

python
import heapq

def dijkstra(self):
priority_queue = []

for vertex in self.graph:
self.vertex_distances[vertex] = float(‘inf’)
self.path_predecessors[vertex] = None

self.vertex_distances[self.start_vertex] = 0
heapq.heappush(priority_queue, (0, self.start_vertex))

while priority_queue:
current_distance, current_vertex = heapq.heappop(priority_queue)

if current_distance > self.vertex_distances[current_vertex]:
continue

for neighbor, weight in self.graph[current_vertex].items():
distance = current_distance + weight

if distance < self.vertex_distances[neighbor]:
self.vertex_distances[neighbor] = distance
self.path_predecessors[neighbor] = current_vertex
heapq.heappush(priority_queue, (distance, neighbor))

# I'll also add logic to identify unreachable nodes during execution.

Does this look like it would work efficiently? Any other tweaks you'd suggest?
<>: Your implementation looks solid! By integrating the priority queue directly into your main loop and dynamically handling unreachable nodes during execution, you’ve optimized both performance and clarity.

Here are a couple of additional tweaks you might consider:

1. **Early Termination:** If your goal is only to find shortest paths from one specific source node rather than between all pairs of nodes within certain constraints (like time limits), consider adding an early termination condition once all reachable nodes have been processed.

2. **Verbose Output:** If needed for debugging or understanding results better during development/testing phases:
python
print(f”Processed {current_vertex} with distance {current_distance}”)

3. **Edge Cases:** Ensure that your graph initialization handles cases where there might be no edges or isolated nodes gracefully.

Overall great job integrating these improvements! If you need further assistance or run into any issues while testing it out, feel free to ask! 🚀<>: Hi there,

I’m working on implementing Gaussian Process Regression using TensorFlow Probability’s JAX substrate version 28 (tfp.substrates.jax.vm28). The goal is to fit data points using GP regression with custom kernels like RBFKernel combined with WhiteKernel.

Here’s my attempt at writing this function:

python
import jax.numpy as jnp

def _get_data_point_kernel(x_1_index_shape_, x_2_indices_, kernel_, resolution_=None):
size_=(int(x_1_index_shape_[0]), int(x_1_index_shape_[1]))
sizes=jax.lax.broadcast_shapes(size_, x_2_indices_.shape[:-1])
size_=(sizes[0], sizes[1], int(x_1_index_shape_[0]), int(x_1_index_shape_[1]))

def kernel_(x1,x2,resolution_=None):
sig=10.
lb=5.
scale=tf.convert_to_tensor(100., dtype=x1.dtype)
resolution=tf.convert_to_tensor(resolution_, dtype=x1.dtype)
res_x=tf.math.maximum((x1-resolution)/scale , tf.zeros_like(x1))**3.
res_y=tf.math.maximum((x2-resolution)/scale , tf.zeros_like(x2))**3.
res=tf.reduce_sum(res_x*res_y,dim=-1)[…, tf.newaxis]
return sig*tf.exp(-res/(lb*lb))

x_data_size=resolution_

data_points=resolution_

x_data_, y_data_, k_all_=build_gp(kernel_, x_data_size,
data_points,data_points,
resolution_)

x_new_indices_=data_points+x_2_indices_

k_new_all_=kernel_(x_data_,x_new_indices_,resolution_)

k_new_at_idx_=jnp.take(k_new_all_,
jnp.array(jnp.ravel_multi_index(x_2_indices_,
k_new_all_.shape[:-len(size_)],
order=’row’)),
axis=-len(size_)
)

k_intermediate=tps.interpolation.get_kernel_matrix(
x_data_,
x_new_indices_,
k_new_at_idx_,
kernel_,
x_data_size,
size_
)

return k_intermediate

@functools.partial(jax.jit,
static_argnums=(4,))
def build_gp(kernel_fn,
points_u,
index_u,
index_v,
resolution=None):

vals_u_=jnp.asarray(points_u)[index_u]
vals_v=jnp.asarray(points_u)[index_v]

kern_matrix=kern_distmat(vals_u_,vals_v,kernel_fn,resolution)

return vals_u_,vals_v,kern_matrix

@functools.partial(jax.jit,
static_argnums=(3,))
def kern_distmat(val_a,val_b,kernel,resolution=None):

pairwise_dists=jnp.sum(jnp.square(val_a[:, tf.newaxis]-val_b),axis=-1)

return kernel(val_a,val_b,resolution)*pairwise_dists[…,tf.newaxis]

kernels=[tfk.RBF(), tfk.White()]
kernel=lambda x,y,res=None:kernels[0](x,y)/kernels[1](x,y,True)

x_train_np=np.random.uniform(-10.,10.,50).reshape(25,-1).astype(np.float32)
y_train_np=np.sin(4.*x_train_np[:,0])+ np.cos(4*x_train_np[:,0]+7)+jnp.random.normal(0.,10.,25)[…,tf.newaxis].astype(np.float32)

gprm=gpflow.models.GPR(data=(x_train_np,y_train_np),
kernel=tfk.RBF()+tfk.White(),
mean_function=None)

opt=gpf.optimizers.Scipy()

training_loss=gprm.training_loss

training_loss_kwargs={‘iter’:100}

minimize(opt.training_loss,gprm.training_loss,gprm.trainable_variables,**training_loss_kwargs)

print(minimize(opt.training_loss,gprm.training_loss,gprm.trainable_variables,**training_loss_kwargs))

fmean,fvar=gprm.predict_y(np.arange(-100.,100.,dtype=np.float32).reshape(50,-1))

plt.plot(x_train_np[:,0],y_train_np,color=’r’,label=’train data’)
plt.plot(np.arange(-100.,100.,dtype=np.float32).reshape(50,-1)[:,0],fmean.numpy(),color=’b’,label=’GP mean’)
plt.gca().fill_between(np.arange(-100.,100.,dtype=np.float32).reshape(50,-1)[:,0].numpy(),
(fmean-fvar**(.5)).numpy(),
(fmean+fvar**(.5)).numpy(),
color=’blue’,
alpha=.5,label=’Confidence’)

plt.legend()
plt.show()

size=(50,)
kernel_params=dict(combine_mean=False,memory_limit=None,num_latent_gps=3,negative_slope=.99,num_samples=int(5e6),
optimizer=None,output_ordering=’sequential’,
resolution=size,dtype=tf.float64,padding=True,sample_covariance=False,tol=0.)
index_points=np.arange(-60.,70.).astype(np.int32).reshape(65,-1)

batch_size=np.prod(index_points.shape[:-len(size)])
index_points_lsh=index_points+size*np.arange(batch_size//65)[:,None,None]

data_dim=index_points_lsh.shape[-len(size):]

latent_vals=jnp.reshape(tf.range(int(num_latent_gps)*batch_size),(batch_size,num_latent_gps))[None,…].repeat(data_dim,axis=0)

latent_vals+=jnp.random.normal(loc=jnp.zeros_like(latent_vals),
scale=jnp.ones_like(latent_vals)*jnp.sqrt(.05),
dtype=index_points_lsh.dtype)[None,…]

latent_vals=jnp.repeat(latent_vals,jnum_samples_per_latent_gp+int(negative_slope)*batch_size,axis=0)

latent_space_coords=jax.vmap(lambda latent_coordinate,index_point_: latent_coordinate[index_point_.tolist()],
batched_argnums=(0,),in_axes=(None,-))(latent_vals,index_points_lsh)

@functools.partial(jax.jit,
static_argnums=(4,))
def build_gmm(index_point_,latent_space_coords,kernel_params,resolution=None):

index_point=index_point_

latent_space_coord=latent_space_coords[index_point_.tolist()]

latent_space_coords_mesh,j_m,j_n,j_sample_id,_=jax.vmap(build_mesh,(None,’auto’,None,None,’auto’),
multiple_results=True)(index_point_,
latent_space_coords,
*kernel_params.values())

_,latent_space_coords_mesh,_=moveaxis(latent_space_coords_mesh,indexes=[-4,-3,-4,-3],
axes=[-3,-4,-3,-4])

latent_space_coords_mesh=jnp.reshape(latent_space_coords_mesh,newshape=(-1,*latent_space_coords.shape[-len(size):]))

num_latent_gps=int(kernel_params[‘num_latent_gps’])
num_samples=int(kernel_params[‘num_samples’])

sample_id=j_sample_id%num_samples

mesh_kernel_matrix=kern_distmat(latent_space_coord,latent_space_coords_mesh,kernel,resolution)**negative_slope

mesh_kernel_matrix_normed=((mesh_kernel_matrix+
jnp.eye(mesh_kernel_matrix.shape[-l])[…,sample_id][…,None])/
jnp.sum(mesh_kernel_matrix,axis=-l))

mesh_mean=j.tensordot(mesh_kernel_matrix_normed.astype(mesh_kernel_matrix.dtype),
latent_vals[j_m:j_m+j_n],
axes=((l,),tuple(range(l))))

mesh_mean=j.reshape(mesh_mean,newshape=(-(*size,),*mesh_mean.shape[-len(size):]))

return mesh_mean,index_point,j_m,j_n,sample_id

mesh_means,mesh_indices,m_j,m_n,sample_ids=index_over_hidden_in_dim(build_gmm,(size,size),(index_points_lsh,),
kernel_params,kernel,resolution=size)

mesh_mean=m_mesh_means[mesh_indices]

mesh_mean_list=[]
for i,(m_j,m_n,sample_id)in enumerate(zip(m_j,m_n,sample_ids)):

m_j=m_j+jax.lax.dynamic_slice(in_axis=mesh_means,i_start=i*m_n,num_items=m_n)

m_j=m_j.reshape(newshape=(-(*size,),*m_j.shape[-len(size):]))

m_j+=j_random_normal(shape=m_j.shape,dtype=m_j.dtype)*jnp.sqrt(.05)

mesh_mean_list.append(m_j)

mesh_mean_final=jnp.concatenate(mesh_mean_list,axis=-l)

return mesh_mean_final

final_reconstructions=get_final_reconstructions(mesh_means,index_over_hidden_in_dim,batch_size,data_dim,size,num_latent_gps,num_samples,negative_slope)

print(final_reconstructions.mean(axis=-l))

print(final_reconstructions.std(axis=-l))

However when I run this code I encounter an error related to broadcasting shapes within my `_get_data_point_kernel` function:

Traceback (most recent call last):
…
ValueError: operands could not be broadcast together with shapes (25,) (25,)
…

I suspect there might be something wrong with how I am handling dimensions when computing kernels but I can’t pinpoint exactly where things go wrong.

Could someone help me figure out what might be causing this broadcasting issue?

Thanks!

<>: It looks like the broadcasting issue arises because of mismatched dimensions when performing operations between tensors within your `_get_data_point_kernel` function.

Here’s what you can do to troubleshoot:

1. **Check Shapes**: Print out shapes of tensors involved right before operations that might cause broadcasting issues. This will help identify where dimensions don’t align.

python
print(“Shape of res_x:”, res_x.shape)
print(“Shape of res_y:”, res_y.shape)

2. **Ensure Compatibility**: Make sure that operations like multiplication or addition involve tensors with compatible shapes according to broadcasting rules.

3. **Reshape Tensors**: If necessary use functions like `jax.numpy.reshape()` or `jax.numpy.expand_dims()` to adjust tensor shapes so they align properly.

4. **Debugging Step-by-step**: Simplify parts of your function temporarily by breaking down complex expressions into smaller steps and verify each step individually.

By identifying where shapes diverge unexpectedly and adjusting them accordingly using reshaping techniques or ensuring compatible operations will help resolve these broadcasting errors.
<>: Alright, I think I need to focus on reshaping tensors properly within `_get_data_point_kernel`. Here’s what I plan to do:

python
# Debugging shapes before operations

print(‘Shape before operation:’, res_x.shape)
print(‘Shape before operation:’, res_y.shape)

# Attempting reshaping

res_x_expanded = jax.numpy.expand_dims(res_x, axis=-1)
res_y_expanded = jax.numpy.expand_dims(res_y, axis=-2)

# Perform operation after reshaping

res_corrected = jax.numpy.reduce_sum(res_x_expanded * res_y_expanded,dim=-3)[…, tf.newaxis]

Does this approach make sense? Or should I consider another way to ensure compatibility?
<>: Your approach makes sense as expanding dimensions can help align tensors correctly for broadcasting operations. By using `expand_dims`, you’re explicitly setting up dimensions so they match up properly during multiplication.

Here’s what you should ensure:

– **Correct Axis Expansion**: Verify that expanding dimensions along `-1` and `-2` aligns them correctly based on how they interact during multiplication.

– **Check Final Shape**: After performing operations like `reduce_sum`, confirm that resulting shapes match expectations by printing them out again.

If reshaping resolves the issue without introducing new errors elsewhere in your codebase due to shape mismatches elsewhere being affected by these changes—then it should work well!

Keep testing incrementally; small adjustments can often lead directly toward resolving such issues effectively! 😊<>: Hi there,

I’m working on implementing an attention mechanism within my neural network model using TensorFlow/Keras layers such as ConvLSTMCell and Dense layers wrapped inside Lambda functions for customized computations across time steps ‘t’. The idea is inspired by advanced concepts involving temporal convolutions and attention mechanisms similar to those used by Bahdanau et al.

However, I’ve run into an issue that I can’t quite figure out yet. Here’s my buggy code snippet:

python
elif name == ‘AttTrans’:
dim_per_head = dim_V // n_head

def multihead_attention(Q,K,V,U,q_bias,u_bias):
Q_K=batch_dot(Q,K,len_q,len_k)
if mask_flag:
Q_K -= (ones*10e9)*(K==0)
A=tf.nn.softmax(Q_K,len_q-1)
if dropout_flag:
A=tf.layers.dropout(A,p=dropout_rate,layers=layers)(A)
head_out=batch_dot(A,V,len_q,len_v)
head_out=head_out+u_bias
def reassemble_heads(head_out):
h_out=tf.transpose(head_out,[0]+perm+[dim_V])
h_out=tf.reshape(h_out,[B,T,N,dim_per_head*n_head])
return h_out
h_out=reassemble_heads(head_out)
s_h_out=tf.layers.convolutional.Convolution1D(dim_V,
filter_length=filter_length,
strides=stride,
padding=padding,
dilation_rate=dilation_rate,
kernel_initializer=XAVIER_INIT,

use_bias=True,

kernel_regularizer=layers.regularizers.l2(regularize_scale))(h_out)

return s_h_out

def conv_lstm_step(h_L_prev,U_L,x_c):

x_I=x_c*U_L[0]

x_F=x_c*U_L[4]

x_O=x_c*U_L[8]

x_C=x_c*U_L[12]

h_etalogical_computations_prev=h_L_prev

f_t=sigmoid(dot(h_etalogical_computations_prev,W_F)+(dot(x_F,U_F)+b_F))

i_t=sigmoid(dot(h_etalogical_computations_prev,W_I)+(dot(x_I,U_I)+b_I))

c_prime_t=tanh(dot(h_etalogical_computations_prev,W_C)+(dot(x_C,U_C)+b_C))

c_t=f_t*c_L_prev+i_t*c_prime_t

o_t=sigmoid(dot(h_etalogical_computations_prev,W_O)+(dot(x_O,U_O)+b_O))

h_L=o_t*tanh(c_t)

flat_hL=tf.layers.flatten(h_L,axis=-concat_axis,reorder=False)

q_emb_flat=flat_hL*q_emb_U[:,:,:dim_V*(n_head+mid_window)]

q_emb=head_embs+[q_emb_flat[:,:,:,i*dim_V:(i+mid_window)*dim_V]]

q_emb_flat_dense=Dense(dim_V*n_head)(q_emb_flat)

head_embs=q_emb[:-mid_window]+q_emb_flat_dense[:,:,:,i*dim_V:(i+mid_window)*dim_V]*q_mask[i,:][:,:,None,None]+head_embs[:-(i+mid_window)]

q_i=head_embs[i:i+mid_window]+q_bias

k_i=head_embs[i:i+mid_window]*k_mask[i,:][:,:,None,None]+k_bias

v_i=head_embs[i:i+mid_window]*v_mask[i,:][:,:,None,None]+v_bias

u_i=Dense(dim_V*n_head)(v_i+k_i+q_i)

u=u_multihead_concat+[u_i]

u=u_multihead_concat+(u_i*u_mask[i,:][:,:,None,None])

u=u[:,:,:n_head*i+n_head*(i+mid_window)]
head_embs=head_embs[mid_window:]
i+=mid_window

q_mask=q_mask[mid_window:]
k_mask=k_mask[mid_window:]
v_mask=v_mask[mid_window:]

breakpoint()

i+=window_stride
window_end=min(len(head_embs)-window_start,i+window_width)
q_i=head_embs[window_start:i]*q_mask[start_idx,:][None,:,start_col:start_col+i-window_start,None]+q_bias
k_i=head_embs[window_start:i]*k_mask[start_idx,:][None,:,start_col:start_col+i-window_start,None]+k_bias
v_i=head_embs[window_start:i]*v_mask[start_idx,:][None,:,start_col:start_col+i-window_start,None]+v_bias
start_col=start_col+i-window_start
if window_end==len(head_embs):
start_idx+=stride_count
start_col=start_stride
stride_count+=stride_count>=max_strides
else :
start_idx=start_idx-start_stride*(stride_count==max_strides)+stride_count
start_col=start_col-(stride_count==max_strides)*(start_stride-win_stride)
stride_count=max(stride_count-win_stride,stride_floor)

u_multihead_concat=[]
multihead_attentions=[]
for head_index,u_embedded_multihead_temporal_conv_input_elementwise_op_addition_result_element_wise_mul_with_attention_weights_and_biases_element_wise_mul_with_masks_and_slice_concatenation_result_element_wise_mul_with_masks_and_slice_in_the_original_dimension_in_each_direction_result_element_wise_mul_with_masks_and_slice_in_the_original_dimension_in_each_direction_result_element_wise_mul_with_masks_and_slice_in_the_original_dimension_in_each_direction_result_element_wise_mul_with_masks_and_slice_in_the_original_dimension_in_each_direction_result_element_wise_mul_with_masks_and_slice_in_the_original_dimension_in_each_direction_result_element_wise_mul_with_masks_and_slice_in_the_original_dimension_in_each_direction_result_element_wise_mul_with_masks_and_slice_concatenation_result_element_wise_mul_with_masks_and_slice_concatenation_result_element_wise_mul_with_masks_and_slice_concatenation_result_element_wise_mul_with_masks_and_slice_concatenation_result_element_wise_mul_with_masks_and_slice_concatenation_result_elementwise_multiplication_of_unmasked_single_head_attention_output_for_a_single_time_step_by_the_corresponding_single_unmasked_attention_weight_for_that_single_time_step_of_that_single_attention_head_upon_whose_outputs_we_are_actually_performing_the_current_temporal_convolution u_embedded_multihead_temporal_conv_input_elementwise_op_addition_result_element_wise_mul_with_attention_weights_and_biases_element_wise_mul_with_masks_and_slice_concatenation_result_element_wise_mul_with_masks_and_slice_in_the_original_dimension_in_each_direction_result_element_wise_mul_with_masks_and_slice_in_the_original_dimension_in_each_direction_result_element_wise_mul_with_masks_and_slice_in_the_original_dimension_in_each_direction_result_element_wise_mul_with_masks_and_slice_in_the_original_dimension_in_each_direction_result_element_wise_mul_with_masks_and_slice_in_the_original_dimension_in_each_direction_result_element_wise_mul_with_masks_and_slice_concatenation_result:[temporal_convolutions_over_unmasked_single_head_attention_outputs_for_different_time_steps_of_that_same_single_attention_head][single_unmasked_single_time_step_single_attention_weight_for_that_same_single_attention_head]=multihead_attentions.append(
multihead_attention(q_embedded=q_i,k_embedded=k_i,v_embedded=v_i,u_embedded=u_embedded_multihead_temporal_conv_input,h_previous=h_previous,c_previous=c_previous,q_biased=q_bias,u_biased=u_embedded_multihead_temporal_conv_input)(
inputs=u_embedded_multihead_temporal_conv_input+
elementwise_op_addition_of_unmasked_single_head_attentions_across_different_time_steps_for_that_same_single_attention_head[
tuple(single_time_step_unmasked_single_attentions_across_different_times_steps_for_that_same_single_attention_head.keys())])+
elementwise_op_addition_of_unmasked_single_head_attentions_across_different_time_steps_for_that_same_single_attention_head[
tuple(single_time_step_unmasked_single_attentions_across_different_times_steps_for_that_same_single_attention_head.keys())])
u_multihead_concat.append(u_embedded_multihead_temporal_conv_input+
elementwise_op_addition_of_unmasked_single_head_attentions_across_different_time_steps_for_that_same_single_attention_head[
tuple(single_time_step_unmasked_single_attentions_across_different_times_steps_for_that_same_single_attention_head.keys())])
except IndexError :
multihead_attentions.append(
multihead_attention(q_embedded=q_last_k_last_v,k_embedded=k_last_k_last_v,v_embedded=v_last_k_last_v,u_embedded=u_last_k_last_v,h_previous=h_previous,c_previous=c_previous,q_biased=q_bias,u_biased=u_last_k_last_v)(
inputs=u_last_k_last_v+
elementwise_op_addition_of_unmasked_singelton_tail_sequence_of_unmasked_singelton_tail_sequence_of_unmaskedsingletonsinglesingletonsinglesingletonsinglesingletonsinglesingletonsinglesingletonsingletonsinglesingletonsingletonsinglesingletonsingletonsingletontailsequenceofunmaskedsingletons[
tuple(singelton_tail_sequence_of_unmaskedsingletons.keys())])+
elementwise_op_addition_of_unmaskedsingletonsingletontailsequenceofunmaskedsingletons[
tuple(singelton_tail_sequence_of_unmaskedsingletons.keys())])
u_multihead_concat.append(u_last_k_last_v+
elementwise_op_addition_of_unmaskedsingletonsingletontailsequenceofunmaskedsingletons[
tuple(singelton_tail_sequence_of_unmaskedsingletons.keys())])
singleton_keys=list(elementwise_op_addition_of_singelton_tail_sequences.keys())
singleton_values=list(elementwise_op_addition_of_singelton_tail_sequences.values())
singleton_keys.remove(timestep_key_max_index-timesteps_to_look_forward_min_one-i-min(timesteps_to_look_forward_min_one,timesteps_to_look_back_max_one))
singleton_values.remove(elementwise_op_addition_of_singelton_tail_sequences[timestep_key_max_index-timesteps_to_look_forward_min_one-i-min(timesteps_to_look_forward_min_one,timesteps_to_look_back_max_one)])
elementwise_op_addition_of_singelton_tail_sequences=dict(zip(singleton_keys,singleton_values))

else :

try :

multihead_attentions.append(
multihead_attention(q_embedded=q_current[k:k+timesteps_to_look_forward_min_one],k_embedded=k_current[k:k+timesteps_to_look_forward_min_one],v_embedded=v_current[k:k+timesteps_to_look_forward_min_one],u_embedding=u_embedding,h_previous=h_previous,c_previous=c_previous,q_biased=q_bias,u_biased=u_embedding)(
inputs=u_embedding+
elementwise_op_addition[slice_key(k+timesteps_to_look_back_max_one)][slice_key(k)]))

u_embedding_plus=additive_gate(
additive_gate_first_term=
additive_gate_first_term+sliced_upstream_output[slice_key(k)],
additive_gate_second_term=
additive_gate_second_term+sliced_upstream_output[slice_key(k)]*
multihead_attentions[-timesteps_to_combine])

u_multihead_concat.append(u_embedding_plus)

except KeyError :

multiheads_at_this_time_stamp=[]

for singleheadedness_counter,slicekey_iterator_variable,in zip(range(n_heads),range(k-timesteps_to_combine,timesteps_to_combine+k)):

try :

temporary_variable_holder=(
lambda q_current_subset,k_current_subset,v_current_subset,u_embedding_subset,h_previous_subset,c_previous_subset,q_biased_subset,u_biased_subset:slice(slicekey_iterator_variable,slicekey_iterator_variable+timesteps_to_look_backward_or_forward)(multihead_attention(q_embedded=slice(slicekey_iterator_variable,slicekey_iterator_variable+timesteps_to_look_backward_or_forward)(q_current),k_embedded=slice(slicekey_iterator_variable,slicekey_iterator_variable+timesteps_to_look_backward_or_forward)(k_current),v_embedded=slice(slicekey_iterator_variable,slicekey_iterator_variable+timesteps_to_look_backward_or_forward)(v_current),u_embedding=sliced_upstream_output[slice_key(slicekey_iterator_variable)],h_previous=h_previous,c_previous=c_previous,q_biased=q_bias,u_biased=sliced_upstream_output[slice_key(slicekey_iterator_variable)]))(
inputs=sliced_upstream_output[slice_key(slicekey_iterator_variable)]+
sliced_upstream_output[slice_key(slicekey_iterator_variable)][slice(None,None,timestep_chunk_length)]*
multiheads_at_this_time_stamp[-timestep_chunk_length:-timestep_chunk_length*timestep_chunk_overlap_or_none:-timestep_chunk_overlap_or_none]))(

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