Merge pull request #125 from NVIDIA/nhwc_sbn_pr

[sync BN nhwc]

apex/parallel/__init__.py

@@ -19,7 +19,7 @@ except ImportError:
         warned_syncbn = True
     from .sync_batchnorm import SyncBatchNorm
 
-def convert_syncbn_model(module, process_group=None):
+def convert_syncbn_model(module, process_group=None, channel_last=False):
     '''
     Recursively traverse module and its children to replace all
     `torch.nn.modules.batchnorm._BatchNorm` with `apex.parallel.SyncBatchNorm`
@@ -38,14 +38,16 @@ def convert_syncbn_model(module, process_group=None):
     '''
     mod = module
     if isinstance(module, torch.nn.modules.batchnorm._BatchNorm):
-        mod = SyncBatchNorm(module.num_features, module.eps, module.momentum, module.affine, module.track_running_stats, process_group)
+        mod = SyncBatchNorm(module.num_features, module.eps, module.momentum, module.affine, module.track_running_stats, process_group, channel_last=channel_last)
         mod.running_mean = module.running_mean
         mod.running_var = module.running_var
         if module.affine:
             mod.weight.data = module.weight.data.clone().detach()
             mod.bias.data = module.bias.data.clone().detach()
     for name, child in module.named_children():
-        mod.add_module(name, convert_syncbn_model(child))
+        mod.add_module(name, convert_syncbn_model(child,
+                                                  process_group=process_group,
+                                                  channel_last=channel_last))
     # TODO(jie) should I delete model explicitly?
     del module
     return mod

apex/parallel/optimized_sync_batchnorm.py

@@ -38,26 +38,43 @@ class SyncBatchNorm(_BatchNorm):
         process_group: pass in a process group within which the stats of the
             mini-batch is being synchronized. ``None`` for using default process
             group
+        channel_last: a boolean value that when set to ``True``, this module
+            take the last dimension of the input tensor to be the channel
+            dimension. Default: False
 
     Examples::
+        >>> # channel first tensor
         >>> sbn = apex.parallel.SyncBatchNorm(100).cuda()
         >>> inp = torch.randn(10, 100, 14, 14).cuda()
         >>> out = sbn(inp)
         >>> inp = torch.randn(3, 100, 20).cuda()
         >>> out = sbn(inp)
+        >>> # channel last tensor
+        >>> sbn = apex.parallel.SyncBatchNorm(100, channel_last=True).cuda()
+        >>> inp = torch.randn(10, 14, 14, 100).cuda()
     """
 
-    def __init__(self, num_features, eps=1e-5, momentum=0.1, affine=True, track_running_stats=True, process_group=None):
+    def __init__(self, num_features, eps=1e-5, momentum=0.1, affine=True, track_running_stats=True, process_group=None, channel_last = False):
         super(SyncBatchNorm, self).__init__(num_features, eps=eps, momentum=momentum, affine=affine, track_running_stats=track_running_stats)
         self.process_group = process_group
+        self.channel_last = channel_last
 
     def _specify_process_group(self, process_group):
         self.process_group = process_group
 
+    def _specify_channel_last(self, channel_last):
+        self.channel_last = channel_last
+
     def forward(self, input):
-        if not self.training and self.track_running_stats:
+        if not self.training and self.track_running_stats and not self.channel_last:
             # fall back to pytorch implementation for inference
             return F.batch_norm(input, self.running_mean, self.running_var, self.weight, self.bias, False, 0.0, self.eps)
         else:
-            self.num_batches_tracked += 1
-            return SyncBatchnormFunction.apply(input, self.weight, self.bias, self.running_mean, self.running_var, self.eps, self.track_running_stats, self.momentum, self.process_group)
+            exponential_average_factor = 0.0
+            if self.training and self.track_running_stats:
+                self.num_batches_tracked += 1
+                if self.momentum is None:
+                    exponential_average_factor = 1.0 / float(self.num_batches_tracked)
+                else:
+                    exponential_average_factor = self.momentum
+            return SyncBatchnormFunction.apply(input, self.weight, self.bias, self.running_mean, self.running_var, self.eps, self.training or not self.track_running_stats, exponential_average_factor, self.process_group, self.channel_last)

apex/parallel/optimized_sync_batchnorm_kernel.py

@@ -7,26 +7,40 @@ from apex.parallel import ReduceOp
 class SyncBatchnormFunction(Function):
 
     @staticmethod
-    def forward(ctx, input, weight, bias, running_mean, running_variance, eps, track_running_stats = True, momentum = 1.0, process_group = None):
+    def forward(ctx, input, weight, bias, running_mean, running_variance, eps, track_running_stats = True, momentum = 1.0, process_group = None, channel_last = False):
         torch.cuda.nvtx.range_push("sync_BN_fw")
         input = input.contiguous()
         world_size = 0
 
+        mean = None
+        var_biased = None
+        inv_std = None
+        var = None
+        out = None
+        count = None
         if track_running_stats:
-            mean, var, var_biased = syncbn.welford_mean_var(input)
+            if channel_last:
+                count = int(input.numel()/input.size(-1))
+                mean, var_biased = syncbn.welford_mean_var_c_last(input)
+            else :
+                count = int(input.numel()/input.size(1))
+                mean, var_biased = syncbn.welford_mean_var(input)
 
             if torch.distributed.is_initialized():
                 if not process_group:
                     process_group = torch.distributed.group.WORLD
                 world_size = torch.distributed.get_world_size(process_group)
                 mean_all = torch.empty(world_size, mean.size(0), dtype=mean.dtype, device=mean.device)
-                var_all = torch.empty(world_size, var.size(0), dtype=var.dtype, device=var.device)
+                var_all = torch.empty(world_size, var_biased.size(0), dtype=var_biased.dtype, device=var_biased.device)
                 mean_l = [mean_all.narrow(0, i, 1) for i in range(world_size)]
                 var_l = [var_all.narrow(0, i, 1) for i in range(world_size)]
                 torch.distributed.all_gather(mean_l, mean, process_group)
                 torch.distributed.all_gather(var_l, var_biased, process_group)
-                mean, var, var_biased = syncbn.welford_parallel(mean_all.transpose(1,0).contiguous(), var_all.transpose(1,0).contiguous(), int(input.numel()/input.size(1)))
+                mean, var, inv_std = syncbn.welford_parallel(mean_all, var_all, count, eps)
                 # TODO(Jie): should do fp32 math instead!
+            else:
+                inv_std = 1.0 / torch.sqrt(var_biased + eps)
+                var = var_biased * (count) / (count-1) 
 
             r_m_inc = mean if running_mean.dtype != torch.float16 else mean.half()
             r_v_inc = var if running_variance.dtype != torch.float16 else var.half()
@@ -34,14 +48,17 @@ class SyncBatchnormFunction(Function):
             running_variance.data = running_variance.data * (1-momentum) + momentum*r_v_inc
         else:
             mean = running_mean.data
-            var_biased = running_var.data
+            inv_std = 1.0 / torch.sqrt(running_var.data + eps)
 
-        ctx.save_for_backward(input, weight, mean, var_biased)
-        ctx.eps = eps
+        ctx.save_for_backward(input, weight, mean, inv_std)
         ctx.process_group = process_group
+        ctx.channel_last = channel_last
         ctx.world_size = world_size
 
-        out = syncbn.batchnorm_forward(input, mean, var_biased, weight, bias, eps)
+        if channel_last:
+            out = syncbn.batchnorm_forward_c_last(input, mean, inv_std, weight, bias)
+        else:
+            out = syncbn.batchnorm_forward(input, mean, inv_std, weight, bias)
 
         torch.cuda.nvtx.range_pop()
         return out
@@ -53,14 +70,17 @@ class SyncBatchnormFunction(Function):
         # mini batch mean & var are calculated by forward path.
         # mu = 1./N*np.sum(h, axis = 0)
         # var = 1./N*np.sum((h-mu)**2, axis = 0)
-        saved_input, weight, running_mean, running_variance = ctx.saved_tensors
-        eps = ctx.eps
+        saved_input, weight, mean, inv_std = ctx.saved_tensors
         process_group = ctx.process_group
+        channel_last = ctx.channel_last
         world_size = ctx.world_size
         grad_input = grad_weight = grad_bias = None
 
         # TODO(jie): why do I have to clone here? life time of grad_output?
-        mean_dy, mean_dy_xmu, grad_weight, grad_bias = syncbn.reduce_bn(grad_output, saved_input, running_mean, running_variance, weight, eps)
+        if channel_last:
+            mean_dy, mean_dy_xmu, grad_weight, grad_bias = syncbn.reduce_bn_c_last(grad_output, saved_input, mean, inv_std, weight)
+        else:
+            mean_dy, mean_dy_xmu, grad_weight, grad_bias = syncbn.reduce_bn(grad_output, saved_input, mean, inv_std, weight)
 
         # calculate grad_input
         if ctx.needs_input_grad[0]:
@@ -72,7 +92,10 @@ class SyncBatchnormFunction(Function):
                 torch.distributed.all_reduce(
                     mean_dy_xmu, ReduceOp.SUM, process_group)
                 mean_dy_xmu = mean_dy_xmu / world_size
-            grad_input = syncbn.batchnorm_backward(grad_output, saved_input, running_mean, running_variance, weight, mean_dy, mean_dy_xmu, eps)
+            if channel_last:
+                grad_input = syncbn.batchnorm_backward_c_last(grad_output, saved_input, mean, inv_std, weight, mean_dy, mean_dy_xmu)
+            else:
+                grad_input = syncbn.batchnorm_backward(grad_output, saved_input, mean, inv_std, weight, mean_dy, mean_dy_xmu)
 
         if weight is None or not ctx.needs_input_grad[1]:
             grad_weight = None
@@ -81,4 +104,4 @@ class SyncBatchnormFunction(Function):
             grad_bias = None
 
         torch.cuda.nvtx.range_pop()
-        return grad_input, grad_weight, grad_bias, None, None, None, None, None, None
+        return grad_input, grad_weight, grad_bias, None, None, None, None, None, None, None

csrc/syncbn.cpp

@@ -3,52 +3,93 @@
 
 #include <vector>
 
-// returns {mean,unbiased_var,biased_var}
+// returns {mean,biased_var}
 // implemented using welford 
 std::vector<at::Tensor> welford_mean_var_CUDA(const at::Tensor input);
 
 // reduces array of mean/var across processes
-// returns global {mean,unbiased_var,biased_var}
+// returns global {mean,inv_std,biased_var}
 // implemented using welford 
-std::vector<at::Tensor> welford_parallel_CUDA(const at::Tensor mean_feature_nodes, const at::Tensor var_biased_feature_nodes, int numel);
+std::vector<at::Tensor> welford_parallel_CUDA(const at::Tensor mean_feature_nodes,
+                                              const at::Tensor var_biased_feature_nodes,
+                                              int numel,
+                                              const float eps);
 
 // elementwise BN operation, returns output
 // input/weight/shift should have identical data type;
-// mean/var have promoted data type (dtype==fp16?fp32:dtype)
+// mean/inv_std have promoted data type (dtype==fp16?fp32:dtype)
 at::Tensor batchnorm_forward_CUDA(const at::Tensor input,
                                   const at::Tensor mean,
-                                  const at::Tensor var,
+                                  const at::Tensor inv_std,
                                   const at::Tensor weight,
-                                  const at::Tensor shift,
-                                  const float eps);
+                                  const at::Tensor shift);
 
 // backward BN operation, returns {mean_dy, mean_dy_xmu, grad_weight, grad_bias}
 // grad_output/input should have identical data type;
-// mean/var have promoted data type (dtype==fp16?fp32:dtype)
+// mean/inv_std have promoted data type (dtype==fp16?fp32:dtype)
 // implemented using kahan summation
 std::vector<at::Tensor> reduce_bn_CUDA(const at::Tensor grad_output,
                                            const at::Tensor input,
                                            const at::Tensor mean,
-                                           const at::Tensor var,
-                                           const at::Tensor weight,
-                                           const float eps);
+                                           const at::Tensor inv_std,
+                                           const at::Tensor weight);
 
 // elementwise backward BN operation, returns grad_input
 // grad_output/input/weight precision could be fp16/fp32;
-// mean/var/mean_dy/mean_dy_xmu precision is fp32
+// mean/inv_std/mean_dy/mean_dy_xmu precision is fp32
 at::Tensor batchnorm_backward_CUDA(const at::Tensor grad_output,
                                    const at::Tensor input,
                                    const at::Tensor mean,
-                                   const at::Tensor var,
+                                   const at::Tensor inv_std,
                                    const at::Tensor weight,
                                    const at::Tensor mean_dy,
-                                   const at::Tensor mean_dy_xmu,
-                                   const float eps);
+                                   const at::Tensor mean_dy_xmu);
+
+// returns {mean, biased_var}
+// implemented using welford 
+// expect data to be in n+c format (channel last) and applies CUDNN_BATCHNORM_SPATIAL
+std::vector<at::Tensor> welford_mean_var_c_last_CUDA(const at::Tensor input);
+
+// elementwise BN operation, returns output
+// input/weight/shift should have identical data type;
+// mean/inv_std have promoted data type (dtype==fp16?fp32:dtype)
+// expect data to be in n+c format (channel last) and applies CUDNN_BATCHNORM_SPATIAL
+at::Tensor batchnorm_forward_c_last_CUDA(const at::Tensor input,
+                                         const at::Tensor mean,
+                                         const at::Tensor inv_std,
+                                         const at::Tensor weight,
+                                         const at::Tensor shift);
+
+// backward BN operation, returns {mean_dy, mean_dy_xmu, grad_weight, grad_bias}
+// grad_output/input should have identical data type;
+// mean/inv_std have promoted data type (dtype==fp16?fp32:dtype)
+// expect data to be in n+c format (channel last) and applies CUDNN_BATCHNORM_SPATIAL
+std::vector<at::Tensor> reduce_bn_c_last_CUDA(const at::Tensor grad_output,
+                                              const at::Tensor input,
+                                              const at::Tensor mean,
+                                              const at::Tensor inv_std,
+                                              const at::Tensor weight);
+
+// elementwise backward BN operation, returns grad_input
+// grad_output/input/weight precision could be fp16/fp32;
+// mean/inv_std/mean_dy/mean_dy_xmu precision is fp32
+// expect data to be in n+c format (channel last) and applies CUDNN_BATCHNORM_SPATIAL
+at::Tensor batchnorm_backward_c_last_CUDA(const at::Tensor grad_output,
+                                          const at::Tensor input,
+                                          const at::Tensor mean,
+                                          const at::Tensor inv_std,
+                                          const at::Tensor weight,
+                                          const at::Tensor mean_dy,
+                                          const at::Tensor mean_dy_xmu);
 
 PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) {
   m.def("welford_mean_var", &welford_mean_var_CUDA, "welford mean variance");
   m.def("welford_parallel", &welford_parallel_CUDA, "welford parallel reduce mean variance");
   m.def("batchnorm_forward", &batchnorm_forward_CUDA, "batchnorm forward");
-  m.def("reduce_bn", &reduce_bn_CUDA, "batchnorm backward reduce grad sum and bias/weight gradient");
+  m.def("reduce_bn", &reduce_bn_CUDA, "batchnorm backward reduce grad sum and bias/weight grad");
   m.def("batchnorm_backward", &batchnorm_backward_CUDA, "batchnorm backward dgrad");
+  m.def("welford_mean_var_c_last", &welford_mean_var_c_last_CUDA, "welford mean variance nhwc");
+  m.def("batchnorm_forward_c_last", &batchnorm_forward_c_last_CUDA, "batchnorm forward nhwc");
+  m.def("reduce_bn_c_last", &reduce_bn_c_last_CUDA, "batchnorm backwards reduce grad sum and bias/weight grad nhwc");
+  m.def("batchnorm_backward_c_last", &batchnorm_backward_c_last_CUDA, "batchnorm backward dgrad nhwc");
 }

tests/synced_batchnorm/single_gpu_unit_test.py

@@ -54,7 +54,11 @@ m = inp_r.mean(1)
 b_v = inp_r.var(1, unbiased=False)
 unb_v = inp_r.var(1, unbiased=True)
 
-mean, var, var_biased = syncbn.welford_mean_var(inp_t)
+eps = 1e-5
+
+#mean, var, var_biased = syncbn.welford_mean_var(inp_t)
+mean, var_biased = syncbn.welford_mean_var(inp_t)
+inv_std = 1.0 / torch.sqrt(var_biased + eps)
 
 bn = torch.nn.BatchNorm2d(feature_size).cuda()
 bn.momentum = 1.0
@@ -74,16 +78,25 @@ grad_sbn = grad_output_t.clone().detach()
 out_sbn = sbn(inp_sbn)
 out_sbn.backward(grad_sbn)
 
+sbn_c_last = apex.parallel.SyncBatchNorm(feature_size, channel_last=True).cuda()
+sbn_c_last.momentum = 1.0
+sbn_c_last.weight.data = weight_t.clone()
+sbn_c_last.bias.data = bias_t.clone()
+inp_sbn_c_last = inp_t.clone().transpose(-1, 1).contiguous().requires_grad_()
+grad_sbn_c_last = grad_output_t.clone().transpose(-1, 1).contiguous().detach()
+out_sbn_c_last = sbn_c_last(inp_sbn_c_last)
+out_sbn_c_last.backward(grad_sbn_c_last)
+
 sbn_result = True
+sbn_result_c_last = True
 bn_result = True
 
 sbn_result = compare("comparing mean: ", mean, m, error) and sbn_result
-sbn_result = compare("comparing variance: ", var, unb_v, error) and sbn_result
+#sbn_result = compare("comparing variance: ", var, unb_v, error) and sbn_result
 sbn_result = compare("comparing biased variance: ", var_biased, b_v, error) and sbn_result
 
-eps = 1e-5
 
-out = syncbn.batchnorm_forward(inp_t, mean, var_biased, weight_t, bias_t, eps)
+out = syncbn.batchnorm_forward(inp_t, mean, inv_std, weight_t, bias_t)
 out_r = weight_r * (inp2_r - m.view(-1, 1, 1)) * torch.rsqrt(b_v.view(-1,1,1) + eps) + bias_r
 
 sbn_result = compare("comparing output: ", out, out_r, error) and sbn_result
@@ -102,8 +115,8 @@ mean_dy_xmu_r = ((inp2_r - m.view(-1, 1, 1)) * grad_output2_r).transpose(1,0).co
 
 grad_input_r = (grad_output2_r - mean_dy_r.view(-1, 1, 1) - (inp2_r - m.view(-1, 1, 1)) / (b_v.view(-1,1,1) + eps) * mean_dy_xmu_r.view(-1, 1, 1) ) * torch.rsqrt(b_v.view(-1,1,1) + eps) * weight_r.view(-1,1,1)
 
-mean_dy, mean_dy_xmu, grad_weight, grad_bias = syncbn.reduce_bn(grad_output_t, inp_t, mean, var_biased, weight_t, eps)
-grad_input = syncbn.batchnorm_backward(grad_output_t, inp_t, mean, var_biased, weight_t, mean_dy, mean_dy_xmu, eps)
+mean_dy, mean_dy_xmu, grad_weight, grad_bias = syncbn.reduce_bn(grad_output_t, inp_t, mean, inv_std, weight_t)
+grad_input = syncbn.batchnorm_backward(grad_output_t, inp_t, mean, inv_std, weight_t, mean_dy, mean_dy_xmu)
 sbn_result = compare("comparing bias grad: ", grad_bias, grad_bias_r, error) and sbn_result
 sbn_result = compare("comparing weight grad: ", grad_weight, grad_weight_r, error) and sbn_result
 sbn_result = compare("comparing mean_dy grad: ", mean_dy, mean_dy_r, error) and sbn_result
@@ -112,7 +125,7 @@ sbn_result = compare("comparing input grad: ", grad_input, grad_input_r, error)
 compare("comparing bn input grad: ", inp_bn.grad, grad_input_r, error)
 sbn_result = compare("comparing sbn input grad: ", inp_sbn.grad, grad_input_r, error) and sbn_result
 
-compare("comparing output: ", out_bn, out_sbn, error)
+compare("comparing bn/sbn output: ", out_bn, out_sbn, error)
 sbn_result = compare("comparing running_mean: ", bn.running_mean.data, sbn.running_mean.data, error) and sbn_result
 sbn_result = compare("comparing running_variance: ", bn.running_var.data, sbn.running_var.data, error) and sbn_result
 compare("comparing grad_input: ", inp_bn.grad, inp_sbn.grad, error)
@@ -123,7 +136,21 @@ compare("comparing grad_weight: ", bn.weight.grad, sbn.weight.grad, error)
 compare("comparing grad_weight bn to ref: ", bn.weight.grad, grad_weight_r, error)
 sbn_result = compare("comparing grad_weight sbn to ref: ", sbn.weight.grad, grad_weight_r, error) and sbn_result
 
+compare("comparing channel last bn/sbn output: ", out_bn, out_sbn_c_last.transpose(-1, 1).contiguous(), error)
+sbn_result_c_last = compare("comparing channel last running_mean: ", bn.running_mean.data, sbn_c_last.running_mean.data, error) and sbn_result_c_last
+sbn_result_c_last = compare("comparing channel last running_variance: ", bn.running_var.data, sbn_c_last.running_var.data, error) and sbn_result_c_last
+compare("comparing channel last grad_input: ", inp_bn.grad, inp_sbn_c_last.grad.transpose(-1, 1).contiguous(), error)
+compare("comparing channel last grad_bias: ", bn.bias.grad, sbn_c_last.bias.grad, error)
+sbn_result_c_last = compare("comparing channel last grad_bias sbn to ref: ", sbn_c_last.bias.grad, grad_bias_r, error) and sbn_result_c_last
+compare("comparing channel last grad_weight: ", bn.weight.grad, sbn_c_last.weight.grad, error)
+sbn_result_c_last = compare("comparing channel last grad_weight sbn to ref: ", sbn_c_last.weight.grad, grad_weight_r, error) and sbn_result_c_last
+
 if sbn_result:
     print("====SBN single gpu passed tests")
 else:
     print("*SBN single gpu failed*")
+
+if sbn_result_c_last:
+    print("====SBN channel last single gpu passed tests")
+else:
+    print("*SBN channel last single gpu failed*")

tests/synced_batchnorm/two_gpu_unit_test.py

@@ -75,7 +75,10 @@ m = inp_r.mean(1)
 b_v = inp_r.var(1, unbiased=False)
 unb_v = inp_r.var(1, unbiased=True)
 
-mean, var, var_biased = syncbn.welford_mean_var(inp_t)
+eps = 1e-5
+
+mean, var_biased = syncbn.welford_mean_var(inp_t)
+inv_std = 1.0 / torch.sqrt(var_biased + eps)
 
 bn = torch.nn.BatchNorm2d(feature_size).cuda()
 bn.momentum = 1.0
@@ -111,12 +114,9 @@ bn_result = True
 
 if args.local_rank == 0:
     sbn_result = compare("comparing mean: ", mean, m, error) and sbn_result
-    sbn_result = compare("comparing variance: ", var, unb_v, error) and sbn_result
     sbn_result = compare("comparing biased variance: ", var_biased, b_v, error) and sbn_result
 
-eps = 1e-5
-
-out = syncbn.batchnorm_forward(inp_t, mean, var_biased, weight_t, bias_t, eps)
+out = syncbn.batchnorm_forward(inp_t, mean, inv_std, weight_t, bias_t)
 out_r = weight_r * (inp2_r - m.view(-1, 1, 1)) * torch.rsqrt(b_v.view(-1,1,1) + eps) + bias_r
 
 if args.local_rank == 0:
@@ -136,8 +136,8 @@ mean_dy_xmu_r = ((inp2_r - m.view(-1, 1, 1)) * grad_output2_r).transpose(1,0).co
 
 grad_input_r = (grad_output2_r - mean_dy_r.view(-1, 1, 1) - (inp2_r - m.view(-1, 1, 1)) / (b_v.view(-1,1,1) + eps) * mean_dy_xmu_r.view(-1, 1, 1) ) * torch.rsqrt(b_v.view(-1,1,1) + eps) * weight_r.view(-1,1,1)
 
-mean_dy, mean_dy_xmu, grad_weight, grad_bias = syncbn.reduce_bn(grad_output_t, inp_t, mean, var_biased, weight_t, eps)
-grad_input = syncbn.batchnorm_backward(grad_output_t, inp_t, mean, var_biased, weight_t, mean_dy, mean_dy_xmu, eps)
+mean_dy, mean_dy_xmu, grad_weight, grad_bias = syncbn.reduce_bn(grad_output_t, inp_t, mean, inv_std, weight_t)
+grad_input = syncbn.batchnorm_backward(grad_output_t, inp_t, mean, inv_std, weight_t, mean_dy, mean_dy_xmu)
 if args.local_rank == 0:
     sbn_result = compare("comparing bias grad: ", grad_bias, grad_bias_r, error) and sbn_result
     sbn_result = compare("comparing weight grad: ", grad_weight, grad_weight_r, error) and sbn_result