From efb91b31ed26f1c9588d8fd071d2515876856c3d Mon Sep 17 00:00:00 2001
From: Shiv Ram Dubey <36983242+shivram1987@users.noreply.github.com>
Date: Wed, 12 Feb 2020 14:52:34 +0530
Subject: [PATCH 01/44] Update diffGrad.py
---
diffGrad.py | 3 ++-
1 file changed, 2 insertions(+), 1 deletion(-)
diff --git a/diffGrad.py b/diffGrad.py
index f2649ad..5d8699f 100644
--- a/diffGrad.py
+++ b/diffGrad.py
@@ -96,7 +96,8 @@ def step(self, closure=None):
# compute diffgrad coefficient (dfc)
diff = abs(previous_grad - grad)
dfc = 1. / (1. + torch.exp(-diff))
- state['previous_grad'] = grad
+ #state['previous_grad'] = grad %used in paper but has the bug that previous grad is overwritten with grad and diff becomes always zero. Fixed in the next line.
+ state['previous_grad'] = grad.clone()
# update momentum with dfc
exp_avg1 = exp_avg * dfc
From 93fb7fcdf1ddefea04d4273b91f42f1c6e0da4b4 Mon Sep 17 00:00:00 2001
From: Shiv Ram Dubey <36983242+shivram1987@users.noreply.github.com>
Date: Sun, 1 Mar 2020 10:49:43 +0530
Subject: [PATCH 02/44] Create diffGrad_v2.py
---
diffGrad_v2.py | 106 +++++++++++++++++++++++++++++++++++++++++++++++++
1 file changed, 106 insertions(+)
create mode 100644 diffGrad_v2.py
diff --git a/diffGrad_v2.py b/diffGrad_v2.py
new file mode 100644
index 0000000..3268ef4
--- /dev/null
+++ b/diffGrad_v2.py
@@ -0,0 +1,106 @@
+# Fixes a bug in original diffGrad code
+import math
+import torch
+from torch.optim.optimizer import Optimizer
+import numpy as np
+import torch.nn as nn
+#import torch.optim as Optimizer
+
+class diffgrad(Optimizer):
+ r"""Implements diffGrad algorithm. It is modified from the pytorch implementation of Adam.
+ It has been proposed in `diffGrad: An Optimization Method for Convolutional Neural Networks`_.
+ Arguments:
+ params (iterable): iterable of parameters to optimize or dicts defining
+ parameter groups
+ lr (float, optional): learning rate (default: 1e-3)
+ betas (Tuple[float, float], optional): coefficients used for computing
+ running averages of gradient and its square (default: (0.9, 0.999))
+ eps (float, optional): term added to the denominator to improve
+ numerical stability (default: 1e-8)
+ weight_decay (float, optional): weight decay (L2 penalty) (default: 0)
+ amsgrad (boolean, optional): whether to use the AMSGrad variant of this
+ algorithm from the paper `On the Convergence of Adam and Beyond`_
+ (default: False)
+ .. _diffGrad: An Optimization Method for Convolutional Neural Networks:
+ https://arxiv.org/abs/1909.11015
+ .. _Adam\: A Method for Stochastic Optimization:
+ https://arxiv.org/abs/1412.6980
+ .. _On the Convergence of Adam and Beyond:
+ https://openreview.net/forum?id=ryQu7f-RZ
+ """
+
+ def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8, weight_decay=0):
+ if not 0.0 <= lr:
+ raise ValueError("Invalid learning rate: {}".format(lr))
+ if not 0.0 <= eps:
+ raise ValueError("Invalid epsilon value: {}".format(eps))
+ if not 0.0 <= betas[0] < 1.0:
+ raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0]))
+ if not 0.0 <= betas[1] < 1.0:
+ raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))
+ defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay)
+ super(diffgrad, self).__init__(params, defaults)
+
+ def __setstate__(self, state):
+ super(diffgrad, self).__setstate__(state)
+
+ def step(self, closure=None):
+ """Performs a single optimization step.
+ Arguments:
+ closure (callable, optional): A closure that reevaluates the model
+ and returns the loss.
+ """
+ loss = None
+ if closure is not None:
+ loss = closure()
+
+ for group in self.param_groups:
+ for p in group['params']:
+ if p.grad is None:
+ continue
+ grad = p.grad.data
+ if grad.is_sparse:
+ raise RuntimeError('diffGrad does not support sparse gradients, please consider SparseAdam instead')
+
+ state = self.state[p]
+
+ # State initialization
+ if len(state) == 0:
+ state['step'] = 0
+ # Exponential moving average of gradient values
+ state['exp_avg'] = torch.zeros_like(p.data)
+ # Exponential moving average of squared gradient values
+ state['exp_avg_sq'] = torch.zeros_like(p.data)
+ # Previous gradient
+ state['previous_grad'] = torch.zeros_like(p.data)
+
+ exp_avg, exp_avg_sq, previous_grad = state['exp_avg'], state['exp_avg_sq'], state['previous_grad']
+ beta1, beta2 = group['betas']
+
+ state['step'] += 1
+
+ if group['weight_decay'] != 0:
+ grad.add_(group['weight_decay'], p.data)
+
+ # Decay the first and second moment running average coefficient
+ exp_avg.mul_(beta1).add_(1 - beta1, grad)
+ exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
+ denom = exp_avg_sq.sqrt().add_(group['eps'])
+
+ bias_correction1 = 1 - beta1 ** state['step']
+ bias_correction2 = 1 - beta2 ** state['step']
+
+ # compute diffgrad coefficient (dfc)
+ diff = abs(previous_grad - grad)
+ dfc = 1. / (1. + torch.exp(-diff))
+ #state['previous_grad'] = grad %used in paper but has the bug that previous grad is overwritten with grad and diff becomes always zero. Fixed in the next line.
+ state['previous_grad'] = grad.clone()
+
+ # update momentum with dfc
+ exp_avg1 = exp_avg * dfc
+
+ step_size = group['lr'] * math.sqrt(bias_correction2) / bias_correction1
+
+ p.data.addcdiv_(-step_size, exp_avg1, denom)
+
+ return loss
From 9a834f5a3d9ba78855bf1b96873c7f5fcf35f01e Mon Sep 17 00:00:00 2001
From: Shiv Ram Dubey <36983242+shivram1987@users.noreply.github.com>
Date: Sun, 1 Mar 2020 10:51:19 +0530
Subject: [PATCH 03/44] Update diffGrad.py
---
diffGrad.py | 8 ++++----
1 file changed, 4 insertions(+), 4 deletions(-)
diff --git a/diffGrad.py b/diffGrad.py
index 5d8699f..5a5bfa7 100644
--- a/diffGrad.py
+++ b/diffGrad.py
@@ -1,3 +1,4 @@
+# This diffGrad implementation has a bug. Use diffGrad_v2.py.
import math
import torch
from torch.optim.optimizer import Optimizer
@@ -96,10 +97,9 @@ def step(self, closure=None):
# compute diffgrad coefficient (dfc)
diff = abs(previous_grad - grad)
dfc = 1. / (1. + torch.exp(-diff))
- #state['previous_grad'] = grad %used in paper but has the bug that previous grad is overwritten with grad and diff becomes always zero. Fixed in the next line.
- state['previous_grad'] = grad.clone()
-
- # update momentum with dfc
+ state['previous_grad'] = grad %used in paper but has the bug that previous grad is overwritten with grad and diff becomes always zero. Fixed in the next line.
+
+ # update momentum with dfc
exp_avg1 = exp_avg * dfc
step_size = group['lr'] * math.sqrt(bias_correction2) / bias_correction1
From 3642f5a4e20852112529b8d35f740b0d4a3a64c8 Mon Sep 17 00:00:00 2001
From: Shiv Ram Dubey <36983242+shivram1987@users.noreply.github.com>
Date: Sun, 1 Mar 2020 10:54:55 +0530
Subject: [PATCH 04/44] Update README.md
---
README.md | 7 +++++--
1 file changed, 5 insertions(+), 2 deletions(-)
diff --git a/README.md b/README.md
index 9720d15..278c203 100644
--- a/README.md
+++ b/README.md
@@ -6,9 +6,12 @@ diffGrad: An Optimization Method for Convolutional Neural Networks
Abstract—Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take the advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms the other optimizers. Also, we showed that diffGrad performs uniformly well on network using different activation functions.
-IEEE TNNLS version: https://ieeexplore.ieee.org/document/8939562
+IEEE TNNLS version: https://ieeexplore.ieee.org/document/8939562 (Uses diffGrad.py)
-arXiv version: https://arxiv.org/abs/1909.11015
+arXiv version: https://arxiv.org/abs/1909.11015 (Uses diffGrad.py)
+
+
+It is recommended to use diffGrad_v2.py which fixes a bug in diffGrad.py.
All experiments are perfomed using following framework: https://github.com/kuangliu/pytorch-cifar
From 03e3b08bf643dd9b18234d01f4150aed20ba2290 Mon Sep 17 00:00:00 2001
From: Shiv Ram Dubey <36983242+shivram1987@users.noreply.github.com>
Date: Sun, 1 Mar 2020 11:49:35 +0530
Subject: [PATCH 05/44] Update README.md
---
README.md | 9 +++------
1 file changed, 3 insertions(+), 6 deletions(-)
diff --git a/README.md b/README.md
index 278c203..01c9b2f 100644
--- a/README.md
+++ b/README.md
@@ -2,16 +2,13 @@
diffGrad: An Optimization Method for Convolutional Neural Networks
-IEEE Transactions on Neural Networks and Learning Systems, 2019
-
-Abstract—Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take the advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms the other optimizers. Also, we showed that diffGrad performs uniformly well on network using different activation functions.
-
-IEEE TNNLS version: https://ieeexplore.ieee.org/document/8939562 (Uses diffGrad.py)
+It is recommended to use diffGrad_v2.py which fixes a bug in diffGrad.py.
arXiv version: https://arxiv.org/abs/1909.11015 (Uses diffGrad.py)
+IEEE TNNLS version: https://ieeexplore.ieee.org/document/8939562 (Uses diffGrad.py)
-It is recommended to use diffGrad_v2.py which fixes a bug in diffGrad.py.
+Abstract—Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take the advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms the other optimizers. Also, we showed that diffGrad performs uniformly well on network using different activation functions.
All experiments are perfomed using following framework: https://github.com/kuangliu/pytorch-cifar
From f48985a9bd2afaf97e02d86385ef48c557a8b607 Mon Sep 17 00:00:00 2001
From: Shiv Ram Dubey <36983242+shivram1987@users.noreply.github.com>
Date: Sun, 1 Mar 2020 12:07:37 +0530
Subject: [PATCH 06/44] Update README.md
---
README.md | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/README.md b/README.md
index 01c9b2f..a4a4823 100644
--- a/README.md
+++ b/README.md
@@ -4,9 +4,9 @@ diffGrad: An Optimization Method for Convolutional Neural Networks
It is recommended to use diffGrad_v2.py which fixes a bug in diffGrad.py.
-arXiv version: https://arxiv.org/abs/1909.11015 (Uses diffGrad.py)
+arXiv version: https://arxiv.org/abs/1909.11015
-IEEE TNNLS version: https://ieeexplore.ieee.org/document/8939562 (Uses diffGrad.py)
+IEEE TNNLS version: https://ieeexplore.ieee.org/document/8939562
Abstract—Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take the advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms the other optimizers. Also, we showed that diffGrad performs uniformly well on network using different activation functions.
From 9b847c3cc6eeb9e60399b4527e02179c33f3258f Mon Sep 17 00:00:00 2001
From: Swalpa Kumar Roy
Date: Sun, 1 Mar 2020 12:36:47 +0530
Subject: [PATCH 07/44] Update README.md
---
README.md | 3 ++-
1 file changed, 2 insertions(+), 1 deletion(-)
diff --git a/README.md b/README.md
index a4a4823..c1c5dd6 100644
--- a/README.md
+++ b/README.md
@@ -2,7 +2,8 @@
diffGrad: An Optimization Method for Convolutional Neural Networks
-It is recommended to use diffGrad_v2.py which fixes a bug in diffGrad.py.
+
It is recommended to use diffGrad_v2.py which fixes a bug in diffGrad.py.
arXiv version: https://arxiv.org/abs/1909.11015
From b1d5790c96332a6b6d0939fa829533677560b6bb Mon Sep 17 00:00:00 2001
From: Swalpa Kumar Roy
Date: Sun, 1 Mar 2020 12:40:17 +0530
Subject: [PATCH 08/44] Update README.md
---
README.md | 4 +---
1 file changed, 1 insertion(+), 3 deletions(-)
diff --git a/README.md b/README.md
index c1c5dd6..764b4a2 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,4 @@
-# diffGrad
-
-diffGrad: An Optimization Method for Convolutional Neural Networks
+# diffGrad: An Optimization Method for Convolutional Neural Networks
It is recommended to use diffGrad_v2.py which fixes a bug in diffGrad.py.
From d82973291c4016beb9c71805fe043dfb00f77434 Mon Sep 17 00:00:00 2001
From: Swalpa Kumar Roy
Date: Sun, 1 Mar 2020 12:42:33 +0530
Subject: [PATCH 09/44] Update README.md
---
README.md | 3 ++-
1 file changed, 2 insertions(+), 1 deletion(-)
diff --git a/README.md b/README.md
index 764b4a2..985cb0a 100644
--- a/README.md
+++ b/README.md
@@ -15,5 +15,6 @@ All experiments are perfomed using following framework: https://github.com/kuang
Please cite this work as: S.R. Dubey, S. Chakraborty, S.K. Roy, S. Mukherjee, S.K. Singh, and B.B. Chaudhuri. diffGrad: An Optimization Method for Convolutional Neural Networks. IEEE Transactions on Neural Networks and Learning Systems, 2019.
+## License
-Copyright (©2019): Shiv Ram Dubey, Indian Institute of Information Technology, Sri City, Chittoor, A.P., India
+Copyright (©2019): Shiv Ram Dubey, Indian Institute of Information Technology, Sri City, Chittoor, A.P., India. Released under the MIT License. See [LICENSE](LICENSE) for details.
From a139346cb032ce633b25723a5228db88b9052ee5 Mon Sep 17 00:00:00 2001
From: Swalpa Kumar Roy
Date: Sun, 1 Mar 2020 12:46:23 +0530
Subject: [PATCH 10/44] Update README.md
---
README.md | 18 ++++++++++++++++--
1 file changed, 16 insertions(+), 2 deletions(-)
diff --git a/README.md b/README.md
index 985cb0a..e02b6a1 100644
--- a/README.md
+++ b/README.md
@@ -9,10 +9,24 @@ IEEE TNNLS version: https://ieeexplore.ieee.org/document/8939562
Abstract—Stochastic Gradient Decent (SGD) is one of the core techniques behind the success of deep neural networks. The gradient provides information on the direction in which function has the steepest rate of change. The main problem with basic SGD is to change by equal sized steps for all parameters, irrespective of gradient behavior. Hence, an efficient way of deep network optimization is to make adaptive step sizes for each parameter. Recently, several attempts have been made to improve gradient descent methods such as AdaGrad, AdaDelta, RMSProp and Adam. These methods rely on the square roots of exponential moving averages of squared past gradients. Thus, these methods do not take the advantage of local change in gradients. In this paper, a novel optimizer is proposed based on the difference between the present and the immediate past gradient (i.e., diffGrad). In the proposed diffGrad optimization technique, the step size is adjusted for each parameter in such a way that it should have a larger step size for faster gradient changing parameters and lower step size for lower gradient changing parameters. The convergence analysis is done using the regret bound approach of online learning framework. Rigorous analysis is made in this paper over three synthetic complex non-convex functions. The image categorization experiments are also conducted over the CIFAR10 and CIFAR100 datasets to observe the performance of diffGrad with respect to the state-of-the-art optimizers such as SGDM, AdaGrad, AdaDelta, RMSProp, AMSGrad, and Adam. The residual unit (ResNet) based Convolutional Neural Networks (CNN) architecture is used in the experiments. The experiments show that diffGrad outperforms the other optimizers. Also, we showed that diffGrad performs uniformly well on network using different activation functions.
+## Citation
+
+If you use this code in your research, we would appreciate a citation to the original
+ @article{dubey2019diffgrad,
+ title={diffGrad: An Optimization Method for Convolutional Neural Networks},
+ author={Dubey, Shiv Ram and Chakraborty, Soumendu and Roy, Swalpa Kumar and Mukherjee, Snehasis and Singh, Satish Kumar and Chaudhuri, Bidyut Baran},
+ journal={IEEE Transactions on Neural Networks and Learning Systems},
+ year={2019},
+ publisher={IEEE}
+ }
+
+
-All experiments are perfomed using following framework: https://github.com/kuangliu/pytorch-cifar
-Please cite this work as: S.R. Dubey, S. Chakraborty, S.K. Roy, S. Mukherjee, S.K. Singh, and B.B. Chaudhuri. diffGrad: An Optimization Method for Convolutional Neural Networks. IEEE Transactions on Neural Networks and Learning Systems, 2019.
+
+## Acknowledgement
+
+All experiments are perfomed using following framework: https://github.com/kuangliu/pytorch-cifar
## License
From e6602ef4c55974681f8df31bdaa827042e93189e Mon Sep 17 00:00:00 2001
From: Swalpa Kumar Roy
Date: Sun, 1 Mar 2020 12:47:26 +0530
Subject: [PATCH 11/44] Update README.md
---
README.md | 5 +----
1 file changed, 1 insertion(+), 4 deletions(-)
diff --git a/README.md b/README.md
index e02b6a1..5096fba 100644
--- a/README.md
+++ b/README.md
@@ -12,6 +12,7 @@ IEEE TNNLS version: https://ieeexplore.ieee.org/document/8939562
## Citation
If you use this code in your research, we would appreciate a citation to the original
+
@article{dubey2019diffgrad,
title={diffGrad: An Optimization Method for Convolutional Neural Networks},
author={Dubey, Shiv Ram and Chakraborty, Soumendu and Roy, Swalpa Kumar and Mukherjee, Snehasis and Singh, Satish Kumar and Chaudhuri, Bidyut Baran},
@@ -20,10 +21,6 @@ If you use this code in your research, we would appreciate a citation to the ori
publisher={IEEE}
}
-
-
-
-
## Acknowledgement
All experiments are perfomed using following framework: https://github.com/kuangliu/pytorch-cifar
From 0cb8110bd32c51f8dfcd79189706ca3cdc03d9fd Mon Sep 17 00:00:00 2001
From: Swalpa Kumar Roy
Date: Sun, 1 Mar 2020 12:51:17 +0530
Subject: [PATCH 12/44] Update README.md
---
README.md | 1 +
1 file changed, 1 insertion(+)
diff --git a/README.md b/README.md
index 5096fba..0a2a397 100644
--- a/README.md
+++ b/README.md
@@ -11,6 +11,7 @@ IEEE TNNLS version: https://ieeexplore.ieee.org/document/8939562
## Citation
+
If you use this code in your research, we would appreciate a citation to the original
@article{dubey2019diffgrad,
From 4da5b9e656bbd0819c41b3e156434f21899eb3c7 Mon Sep 17 00:00:00 2001
From: Swalpa Kumar Roy
Date: Sun, 1 Mar 2020 12:52:12 +0530
Subject: [PATCH 13/44] Add files via upload
---
paper.pdf | Bin 0 -> 2948551 bytes
1 file changed, 0 insertions(+), 0 deletions(-)
create mode 100644 paper.pdf
diff --git a/paper.pdf b/paper.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..0b5a08d403da4a742256e5078849cb0a6e3316d4
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