It is possible to specify different learning rates for different layers of a PyTorch neural network. I almost never use this technique because the complexity of tuning the additional learning rate parameters usually outweighs the benefit of faster training.
I hadn’t looked at using different learning rates for a long time, so I figured I’d put together a demo to refresh my memory.
I used one of my standard synthetic datasets. The goal is to predict a person’s political leaning from sex, age, State, and income. The 240-item tab-delimited raw data looks like:
F 24 michigan 29500.00 liberal M 39 oklahoma 51200.00 moderate F 63 nebraska 75800.00 conservative M 36 michigan 44500.00 moderate F 27 nebraska 28600.00 liberal . . .
I encoded sex as M = -1, F = 1, and State as Michigan = 100, Nebraska = 010, Oklahoma = 001. I used ordinal encoding on politics: conservative = 0, moderate = 1, liberal = 2 (to sync with my PyTorch implementation), and programmatically encoded as conservative = 100, moderate = 010, liberal = 001. I normalized the numeric data. I divided age values by 100, and divided income values by 100,000. The resulting encoded and normalized comma-delimited data looks like:
1, 0.24, 1, 0, 0, 0.2950, 2 -1, 0.39, 0, 0, 1, 0.5120, 1 1, 0.63, 0, 1, 0, 0.7580, 0 -1, 0.36, 1, 0, 0, 0.4450, 1 1, 0.27, 0, 1, 0, 0.2860, 2 . . .
I split the data into a 200-item set of training data and a 40-item set of test data.
My neural architecture was 6-(10-10)-3 with tanh() hidden node activation and log-softmax() output node activation.
For training I set the learning rate for the first hidden layer to 0.03, 0.02 for the second hidden layer, and 0.01 for the output layer. The idea is that for standard neural networks, back-propagation makes the first gradients smaller than the later gradients. In the worst case, the gradients can go to nearly zero — the vanishing gradient problem. So a larger learning rate in the first few layers compensates for the smaller gradients.
Note that most of the research in different learning rates focused on image classification. In that scenario, because of how image classification works, it’s often better to have smaller learning rates in the early layers.
The key PyTorch code in the program-defined train() function to set three different learning rates is:
import torch as T
. . .
class Net(T.nn.Module):
def __init__(self):
super(Net, self).__init__()
self.hid1 = T.nn.Linear(6, 10) # 6-(10-10)-3
self.hid2 = T.nn.Linear(10, 10)
self.oupt = T.nn.Linear(10, 3)
. . .
def train(model, ds, bs, lr_hid1, lr_hid2, lr_oupt, me):
# optimizer set to SGD
train_ldr = T.utils.data.DataLoader(ds, batch_size=bs,
shuffle=True)
loss_func = T.nn.NLLLoss() # log_softmax() activation
optimizer = T.optim.SGD(
[ {"params": model.hid1.parameters(), "lr": lr_hid1},
{"params": model.hid2.parameters(), "lr": lr_hid2},
{"params": model.oupt.parameters(), "lr": lr_oupt}
])
. . .
My synthetic dataset isn’t complex enough, or large enough, for the different learning rates to make a significant difference from a single global learning rate.
Good fun.
Machine learning and AI is in a period of hyper-growth, somewhat similar to the days of early aviation. Left: In 1918, during World War I, the British Sopwith Camel could fly at just over 100 mph. Center: Just 24 years later, in 1944, during World War II, the North American P-51 Mustang could fly four times as fast at over 400 mph. Right: And 24 years later, in 1966, during the Vietnam War, the McDonnell Douglas F-4 Phantom could fly at over 1,400 mph.
Demo program:
# people_politics_different_lr.py
# predict politics type from sex, age, state, income
# different learning rates
# PyTorch 2.2.1-CPU Anaconda3-2023.09.0 Python 3.11.5
# Windows 10/11
import numpy as np
import torch as T
device = T.device('cpu') # apply to Tensor or Module
# -----------------------------------------------------------
class Net(T.nn.Module):
def __init__(self):
super(Net, self).__init__()
self.hid1 = T.nn.Linear(6, 10) # 6-(10-10)-3
self.hid2 = T.nn.Linear(10, 10)
self.oupt = T.nn.Linear(10, 3)
T.nn.init.xavier_uniform_(self.hid1.weight)
T.nn.init.zeros_(self.hid1.bias)
T.nn.init.xavier_uniform_(self.hid2.weight)
T.nn.init.zeros_(self.hid2.bias)
T.nn.init.xavier_uniform_(self.oupt.weight)
T.nn.init.zeros_(self.oupt.bias)
def forward(self, x):
z = T.tanh(self.hid1(x))
z = T.tanh(self.hid2(z))
z = T.log_softmax(self.oupt(z), dim=1) # NLLLoss()
return z
# -----------------------------------------------------------
class PeopleDataset(T.utils.data.Dataset):
# sex age state income politics
# -1 0.27 0 1 0 0.7610 2
# +1 0.19 0 0 1 0.6550 0
# sex: -1 = male, +1 = female
# state: michigan, nebraska, oklahoma
# politics: conservative, moderate, liberal
def __init__(self, src_file):
all_xy = np.loadtxt(src_file, usecols=range(0,7),
delimiter=",", comments="#", dtype=np.float32)
tmp_x = all_xy[:,0:6] # cols [0,6) = [0,5]
tmp_y = all_xy[:,6] # 1-D
self.x_data = T.tensor(tmp_x,
dtype=T.float32).to(device)
self.y_data = T.tensor(tmp_y,
dtype=T.int64).to(device) # 1-D
def __len__(self):
return len(self.x_data)
def __getitem__(self, idx):
preds = self.x_data[idx]
trgts = self.y_data[idx]
return preds, trgts # as a Tuple
# -----------------------------------------------------------
def accuracy(model, ds):
# assumes model.eval()
# item-by-item version
n_correct = 0; n_wrong = 0
for i in range(len(ds)):
X = ds[i][0].reshape(1,-1) # make it a batch
Y = ds[i][1].reshape(1) # 0 1 or 2, 1D
with T.no_grad():
oupt = model(X) # logits form
big_idx = T.argmax(oupt) # 0 or 1 or 2
if big_idx == Y:
n_correct += 1
else:
n_wrong += 1
acc = (n_correct * 1.0) / (n_correct + n_wrong)
return acc
# -----------------------------------------------------------
def confusion_matrix_multi(model, ds, n_classes):
if n_classes "lte" 2: # replace less-than-or-equal
print("ERROR: n_classes must be 3 or greater ")
return None
cm = np.zeros((n_classes,n_classes), dtype=np.int64)
for i in range(len(ds)):
X = ds[i][0].reshape(1,-1) # make it a batch
Y = ds[i][1].reshape(1) # actual class 0 1 or 2, 1D
with T.no_grad():
oupt = model(X) # logits form
pred_class = T.argmax(oupt) # 0,1,2
cm[Y][pred_class] += 1
return cm
# -----------------------------------------------------------
def show_confusion(cm):
dim = len(cm)
mx = np.max(cm) # largest count in cm
wid = len(str(mx)) + 1 # width to print
fmt = "%" + str(wid) + "d" # like "%3d"
for i in range(dim):
print("actual ", end="")
print("%3d:" % i, end="")
for j in range(dim):
print(fmt % cm[i][j], end="")
print("")
print("------------")
print("predicted ", end="")
for j in range(dim):
print(fmt % j, end="")
print("")
# -----------------------------------------------------------
def train(model, ds, bs, lr_hid1, lr_hid2, lr_oupt, me):
# optimizer set to SGD
train_ldr = T.utils.data.DataLoader(ds, batch_size=bs,
shuffle=True)
loss_func = T.nn.NLLLoss() # log_softmax() activation
optimizer = T.optim.SGD(
[ {"params": model.hid1.parameters(), "lr": lr_hid1},
{"params": model.hid2.parameters(), "lr": lr_hid2},
{"params": model.oupt.parameters(), "lr": lr_oupt}
])
le = me // 5 # log interval: 5 log prints
for epoch in range(0, me):
epoch_loss = 0.0 # for one full epoch
for (batch_idx, batch) in enumerate(train_ldr):
X = batch[0] # inputs
Y = batch[1] # correct class/label/politics
optimizer.zero_grad()
oupt = model(X)
loss_val = loss_func(oupt, Y) # a tensor
epoch_loss += loss_val.item() # accumulate
loss_val.backward()
optimizer.step()
if epoch % le == 0:
print("epoch = %5d | loss = %10.4f" % \
(epoch, epoch_loss))
# -----------------------------------------------------------
def main():
# 0. get started
print("\nBegin People predict politics type ")
T.manual_seed(1)
np.random.seed(1)
# 1. create DataLoader objects
print("\nCreating People Datasets ")
train_file = ".\\Data\\people_train.txt"
train_ds = PeopleDataset(train_file) # 200 rows
test_file = ".\\Data\\people_test.txt"
test_ds = PeopleDataset(test_file) # 40 rows
# -----------------------------------------------------------
# 2. create network
print("\nCreating 6-(10-10)-3 neural network ")
net = Net().to(device)
net.train() # set mode
# -----------------------------------------------------------
# 3. train model
bat_size = 10
max_epochs = 1000
ep_log_interval = 100
lrn_rate_hid1 = 0.03
lrn_rate_hid2 = 0.02
lrn_rate_oupt = 0.01
print("\nbat_size = %3d " % bat_size)
print("loss = NLLLoss ")
print("optimizer = SGD")
print("max_epochs = %3d " % max_epochs)
print("lr_hid1 = %0.3f " % lrn_rate_hid1)
print("lr_hid2 = %0.3f " % lrn_rate_hid2)
print("lr_oupt = %0.3f " % lrn_rate_oupt)
print("\nStarting training")
train(net, train_ds, bat_size, lrn_rate_hid1,
lrn_rate_hid2, lrn_rate_oupt, max_epochs)
print("Done ")
# -----------------------------------------------------------
# 4. evaluate model
print("\nComputing model accuracy")
net.eval()
acc_train = accuracy(net, train_ds) # item-by-item
print("Accuracy on training data = %0.4f" % acc_train)
acc_test = accuracy(net, test_ds)
print("Accuracy on test data = %0.4f" % acc_test)
print("\nConfusion matrix: ")
cm = confusion_matrix_multi(net, test_ds, n_classes=3)
show_confusion(cm)
# 5. make a prediction
print("\nPredicting politics for M 30 oklahoma $50,000: ")
X = np.array([[-1, 0.30, 0,0,1, 0.5000]],
dtype=np.float32)
X = T.tensor(X, dtype=T.float32).to(device)
with T.no_grad():
logits = net(X) # do not sum to 1.0
probs = T.exp(logits) # sum to 1.0
probs = probs.numpy() # numpy vector prints better
np.set_printoptions(precision=4, suppress=True)
print(probs)
# 6. save model (state_dict approach)
# print("\nSaving trained model state")
# fn = ".\\Models\\people_model.pt"
# T.save(net.state_dict(), fn)
# saved_model = Net() # requires class definintion
# saved_model.load_state_dict(T.load(fn))
# use saved_model to make prediction(s)
print("\nEnd demo ")
if __name__ == "__main__":
main()
Training data:
# people_train.txt # sex (M=-1, F=1) age state (michigan, # nebraska, oklahoma) income # politics (consrvative, moderate, liberal) # 1, 0.24, 1, 0, 0, 0.2950, 2 -1, 0.39, 0, 0, 1, 0.5120, 1 1, 0.63, 0, 1, 0, 0.7580, 0 -1, 0.36, 1, 0, 0, 0.4450, 1 1, 0.27, 0, 1, 0, 0.2860, 2 1, 0.50, 0, 1, 0, 0.5650, 1 1, 0.50, 0, 0, 1, 0.5500, 1 -1, 0.19, 0, 0, 1, 0.3270, 0 1, 0.22, 0, 1, 0, 0.2770, 1 -1, 0.39, 0, 0, 1, 0.4710, 2 1, 0.34, 1, 0, 0, 0.3940, 1 -1, 0.22, 1, 0, 0, 0.3350, 0 1, 0.35, 0, 0, 1, 0.3520, 2 -1, 0.33, 0, 1, 0, 0.4640, 1 1, 0.45, 0, 1, 0, 0.5410, 1 1, 0.42, 0, 1, 0, 0.5070, 1 -1, 0.33, 0, 1, 0, 0.4680, 1 1, 0.25, 0, 0, 1, 0.3000, 1 -1, 0.31, 0, 1, 0, 0.4640, 0 1, 0.27, 1, 0, 0, 0.3250, 2 1, 0.48, 1, 0, 0, 0.5400, 1 -1, 0.64, 0, 1, 0, 0.7130, 2 1, 0.61, 0, 1, 0, 0.7240, 0 1, 0.54, 0, 0, 1, 0.6100, 0 1, 0.29, 1, 0, 0, 0.3630, 0 1, 0.50, 0, 0, 1, 0.5500, 1 1, 0.55, 0, 0, 1, 0.6250, 0 1, 0.40, 1, 0, 0, 0.5240, 0 1, 0.22, 1, 0, 0, 0.2360, 2 1, 0.68, 0, 1, 0, 0.7840, 0 -1, 0.60, 1, 0, 0, 0.7170, 2 -1, 0.34, 0, 0, 1, 0.4650, 1 -1, 0.25, 0, 0, 1, 0.3710, 0 -1, 0.31, 0, 1, 0, 0.4890, 1 1, 0.43, 0, 0, 1, 0.4800, 1 1, 0.58, 0, 1, 0, 0.6540, 2 -1, 0.55, 0, 1, 0, 0.6070, 2 -1, 0.43, 0, 1, 0, 0.5110, 1 -1, 0.43, 0, 0, 1, 0.5320, 1 -1, 0.21, 1, 0, 0, 0.3720, 0 1, 0.55, 0, 0, 1, 0.6460, 0 1, 0.64, 0, 1, 0, 0.7480, 0 -1, 0.41, 1, 0, 0, 0.5880, 1 1, 0.64, 0, 0, 1, 0.7270, 0 -1, 0.56, 0, 0, 1, 0.6660, 2 1, 0.31, 0, 0, 1, 0.3600, 1 -1, 0.65, 0, 0, 1, 0.7010, 2 1, 0.55, 0, 0, 1, 0.6430, 0 -1, 0.25, 1, 0, 0, 0.4030, 0 1, 0.46, 0, 0, 1, 0.5100, 1 -1, 0.36, 1, 0, 0, 0.5350, 0 1, 0.52, 0, 1, 0, 0.5810, 1 1, 0.61, 0, 0, 1, 0.6790, 0 1, 0.57, 0, 0, 1, 0.6570, 0 -1, 0.46, 0, 1, 0, 0.5260, 1 -1, 0.62, 1, 0, 0, 0.6680, 2 1, 0.55, 0, 0, 1, 0.6270, 0 -1, 0.22, 0, 0, 1, 0.2770, 1 -1, 0.50, 1, 0, 0, 0.6290, 0 -1, 0.32, 0, 1, 0, 0.4180, 1 -1, 0.21, 0, 0, 1, 0.3560, 0 1, 0.44, 0, 1, 0, 0.5200, 1 1, 0.46, 0, 1, 0, 0.5170, 1 1, 0.62, 0, 1, 0, 0.6970, 0 1, 0.57, 0, 1, 0, 0.6640, 0 -1, 0.67, 0, 0, 1, 0.7580, 2 1, 0.29, 1, 0, 0, 0.3430, 2 1, 0.53, 1, 0, 0, 0.6010, 0 -1, 0.44, 1, 0, 0, 0.5480, 1 1, 0.46, 0, 1, 0, 0.5230, 1 -1, 0.20, 0, 1, 0, 0.3010, 1 -1, 0.38, 1, 0, 0, 0.5350, 1 1, 0.50, 0, 1, 0, 0.5860, 1 1, 0.33, 0, 1, 0, 0.4250, 1 -1, 0.33, 0, 1, 0, 0.3930, 1 1, 0.26, 0, 1, 0, 0.4040, 0 1, 0.58, 1, 0, 0, 0.7070, 0 1, 0.43, 0, 0, 1, 0.4800, 1 -1, 0.46, 1, 0, 0, 0.6440, 0 1, 0.60, 1, 0, 0, 0.7170, 0 -1, 0.42, 1, 0, 0, 0.4890, 1 -1, 0.56, 0, 0, 1, 0.5640, 2 -1, 0.62, 0, 1, 0, 0.6630, 2 -1, 0.50, 1, 0, 0, 0.6480, 1 1, 0.47, 0, 0, 1, 0.5200, 1 -1, 0.67, 0, 1, 0, 0.8040, 2 -1, 0.40, 0, 0, 1, 0.5040, 1 1, 0.42, 0, 1, 0, 0.4840, 1 1, 0.64, 1, 0, 0, 0.7200, 0 -1, 0.47, 1, 0, 0, 0.5870, 2 1, 0.45, 0, 1, 0, 0.5280, 1 -1, 0.25, 0, 0, 1, 0.4090, 0 1, 0.38, 1, 0, 0, 0.4840, 0 1, 0.55, 0, 0, 1, 0.6000, 1 -1, 0.44, 1, 0, 0, 0.6060, 1 1, 0.33, 1, 0, 0, 0.4100, 1 1, 0.34, 0, 0, 1, 0.3900, 1 1, 0.27, 0, 1, 0, 0.3370, 2 1, 0.32, 0, 1, 0, 0.4070, 1 1, 0.42, 0, 0, 1, 0.4700, 1 -1, 0.24, 0, 0, 1, 0.4030, 0 1, 0.42, 0, 1, 0, 0.5030, 1 1, 0.25, 0, 0, 1, 0.2800, 2 1, 0.51, 0, 1, 0, 0.5800, 1 -1, 0.55, 0, 1, 0, 0.6350, 2 1, 0.44, 1, 0, 0, 0.4780, 2 -1, 0.18, 1, 0, 0, 0.3980, 0 -1, 0.67, 0, 1, 0, 0.7160, 2 1, 0.45, 0, 0, 1, 0.5000, 1 1, 0.48, 1, 0, 0, 0.5580, 1 -1, 0.25, 0, 1, 0, 0.3900, 1 -1, 0.67, 1, 0, 0, 0.7830, 1 1, 0.37, 0, 0, 1, 0.4200, 1 -1, 0.32, 1, 0, 0, 0.4270, 1 1, 0.48, 1, 0, 0, 0.5700, 1 -1, 0.66, 0, 0, 1, 0.7500, 2 1, 0.61, 1, 0, 0, 0.7000, 0 -1, 0.58, 0, 0, 1, 0.6890, 1 1, 0.19, 1, 0, 0, 0.2400, 2 1, 0.38, 0, 0, 1, 0.4300, 1 -1, 0.27, 1, 0, 0, 0.3640, 1 1, 0.42, 1, 0, 0, 0.4800, 1 1, 0.60, 1, 0, 0, 0.7130, 0 -1, 0.27, 0, 0, 1, 0.3480, 0 1, 0.29, 0, 1, 0, 0.3710, 0 -1, 0.43, 1, 0, 0, 0.5670, 1 1, 0.48, 1, 0, 0, 0.5670, 1 1, 0.27, 0, 0, 1, 0.2940, 2 -1, 0.44, 1, 0, 0, 0.5520, 0 1, 0.23, 0, 1, 0, 0.2630, 2 -1, 0.36, 0, 1, 0, 0.5300, 2 1, 0.64, 0, 0, 1, 0.7250, 0 1, 0.29, 0, 0, 1, 0.3000, 2 -1, 0.33, 1, 0, 0, 0.4930, 1 -1, 0.66, 0, 1, 0, 0.7500, 2 -1, 0.21, 0, 0, 1, 0.3430, 0 1, 0.27, 1, 0, 0, 0.3270, 2 1, 0.29, 1, 0, 0, 0.3180, 2 -1, 0.31, 1, 0, 0, 0.4860, 1 1, 0.36, 0, 0, 1, 0.4100, 1 1, 0.49, 0, 1, 0, 0.5570, 1 -1, 0.28, 1, 0, 0, 0.3840, 0 -1, 0.43, 0, 0, 1, 0.5660, 1 -1, 0.46, 0, 1, 0, 0.5880, 1 1, 0.57, 1, 0, 0, 0.6980, 0 -1, 0.52, 0, 0, 1, 0.5940, 1 -1, 0.31, 0, 0, 1, 0.4350, 1 -1, 0.55, 1, 0, 0, 0.6200, 2 1, 0.50, 1, 0, 0, 0.5640, 1 1, 0.48, 0, 1, 0, 0.5590, 1 -1, 0.22, 0, 0, 1, 0.3450, 0 1, 0.59, 0, 0, 1, 0.6670, 0 1, 0.34, 1, 0, 0, 0.4280, 2 -1, 0.64, 1, 0, 0, 0.7720, 2 1, 0.29, 0, 0, 1, 0.3350, 2 -1, 0.34, 0, 1, 0, 0.4320, 1 -1, 0.61, 1, 0, 0, 0.7500, 2 1, 0.64, 0, 0, 1, 0.7110, 0 -1, 0.29, 1, 0, 0, 0.4130, 0 1, 0.63, 0, 1, 0, 0.7060, 0 -1, 0.29, 0, 1, 0, 0.4000, 0 -1, 0.51, 1, 0, 0, 0.6270, 1 -1, 0.24, 0, 0, 1, 0.3770, 0 1, 0.48, 0, 1, 0, 0.5750, 1 1, 0.18, 1, 0, 0, 0.2740, 0 1, 0.18, 1, 0, 0, 0.2030, 2 1, 0.33, 0, 1, 0, 0.3820, 2 -1, 0.20, 0, 0, 1, 0.3480, 0 1, 0.29, 0, 0, 1, 0.3300, 2 -1, 0.44, 0, 0, 1, 0.6300, 0 -1, 0.65, 0, 0, 1, 0.8180, 0 -1, 0.56, 1, 0, 0, 0.6370, 2 -1, 0.52, 0, 0, 1, 0.5840, 1 -1, 0.29, 0, 1, 0, 0.4860, 0 -1, 0.47, 0, 1, 0, 0.5890, 1 1, 0.68, 1, 0, 0, 0.7260, 2 1, 0.31, 0, 0, 1, 0.3600, 1 1, 0.61, 0, 1, 0, 0.6250, 2 1, 0.19, 0, 1, 0, 0.2150, 2 1, 0.38, 0, 0, 1, 0.4300, 1 -1, 0.26, 1, 0, 0, 0.4230, 0 1, 0.61, 0, 1, 0, 0.6740, 0 1, 0.40, 1, 0, 0, 0.4650, 1 -1, 0.49, 1, 0, 0, 0.6520, 1 1, 0.56, 1, 0, 0, 0.6750, 0 -1, 0.48, 0, 1, 0, 0.6600, 1 1, 0.52, 1, 0, 0, 0.5630, 2 -1, 0.18, 1, 0, 0, 0.2980, 0 -1, 0.56, 0, 0, 1, 0.5930, 2 -1, 0.52, 0, 1, 0, 0.6440, 1 -1, 0.18, 0, 1, 0, 0.2860, 1 -1, 0.58, 1, 0, 0, 0.6620, 2 -1, 0.39, 0, 1, 0, 0.5510, 1 -1, 0.46, 1, 0, 0, 0.6290, 1 -1, 0.40, 0, 1, 0, 0.4620, 1 -1, 0.60, 1, 0, 0, 0.7270, 2 1, 0.36, 0, 1, 0, 0.4070, 2 1, 0.44, 1, 0, 0, 0.5230, 1 1, 0.28, 1, 0, 0, 0.3130, 2 1, 0.54, 0, 0, 1, 0.6260, 0
Test data:
# people_test.txt # -1, 0.51, 1, 0, 0, 0.6120, 1 -1, 0.32, 0, 1, 0, 0.4610, 1 1, 0.55, 1, 0, 0, 0.6270, 0 1, 0.25, 0, 0, 1, 0.2620, 2 1, 0.33, 0, 0, 1, 0.3730, 2 -1, 0.29, 0, 1, 0, 0.4620, 0 1, 0.65, 1, 0, 0, 0.7270, 0 -1, 0.43, 0, 1, 0, 0.5140, 1 -1, 0.54, 0, 1, 0, 0.6480, 2 1, 0.61, 0, 1, 0, 0.7270, 0 1, 0.52, 0, 1, 0, 0.6360, 0 1, 0.30, 0, 1, 0, 0.3350, 2 1, 0.29, 1, 0, 0, 0.3140, 2 -1, 0.47, 0, 0, 1, 0.5940, 1 1, 0.39, 0, 1, 0, 0.4780, 1 1, 0.47, 0, 0, 1, 0.5200, 1 -1, 0.49, 1, 0, 0, 0.5860, 1 -1, 0.63, 0, 0, 1, 0.6740, 2 -1, 0.30, 1, 0, 0, 0.3920, 0 -1, 0.61, 0, 0, 1, 0.6960, 2 -1, 0.47, 0, 0, 1, 0.5870, 1 1, 0.30, 0, 0, 1, 0.3450, 2 -1, 0.51, 0, 0, 1, 0.5800, 1 -1, 0.24, 1, 0, 0, 0.3880, 1 -1, 0.49, 1, 0, 0, 0.6450, 1 1, 0.66, 0, 0, 1, 0.7450, 0 -1, 0.65, 1, 0, 0, 0.7690, 0 -1, 0.46, 0, 1, 0, 0.5800, 0 -1, 0.45, 0, 0, 1, 0.5180, 1 -1, 0.47, 1, 0, 0, 0.6360, 0 -1, 0.29, 1, 0, 0, 0.4480, 0 -1, 0.57, 0, 0, 1, 0.6930, 2 -1, 0.20, 1, 0, 0, 0.2870, 2 -1, 0.35, 1, 0, 0, 0.4340, 1 -1, 0.61, 0, 0, 1, 0.6700, 2 -1, 0.31, 0, 0, 1, 0.3730, 1 1, 0.18, 1, 0, 0, 0.2080, 2 1, 0.26, 0, 0, 1, 0.2920, 2 -1, 0.28, 1, 0, 0, 0.3640, 2 -1, 0.59, 0, 0, 1, 0.6940, 2
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2024 DevIntersection Conference
2024 Spring MLADS Conference
2024 G2E Conference
2024 ISC West Conference
James D. McCaffrey 
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