# A Collaboration Strategy in the Mining Pool for Proof-of-Neural-Architecture
Consensus

Boyang Li  Qing Lu  Weiwen Jiang  Taeho Jung  Yiyu Shi

###### Abstract

In most popular public accessible cryptocurrency systems, the mining pool
plays a key role because mining cryptocurrency with the mining pool turns the
non-profitable situation into profitable for individual miners. In many recent
novel blockchain consensuses, the deep learning training procedure becomes the
task for miners to prove their workload, thus the computation power of miners
will not purely be spent on the hash puzzle. In this way, the hardware and
energy will support the blockchain service and deep learning training
simultaneously. While the incentive of miners is to earn tokens, individual
miners are motivated to join mining pools to become more competitive. In this
paper, we are the first to demonstrate a mining pool solution for novel
consensuses based on deep learning.

The mining pool manager partitions the full searching space into subspaces and
all miners are scheduled to collaborate on the Neural Architecture Search
(NAS) tasks in the assigned subspace. Experiments demonstrate that the
performance of this type of mining pool is more competitive than an individual
miner. Due to the uncertainty of miners’ behaviors, the mining pool manager
checks the standard deviation of the performance of high reward miners and
prepares backup miners to ensure completion of the tasks of high reward
miners.

###### keywords:

Blockchain , Consensus , Deep learning , Mining Pool , Neural architecture
search(NAS)

###### PACS:

0000 , 1111

###### MSC:

0000 , 1111

††journal: Blockchain: Research and Applications

[inst1]organization=University of Notre Dame,addressline=Department of
Computer Science and Engineering, city=Notre Dame, postcode=46556,
state=Indiana, country=USA

[inst2]organization=George Mason University,addressline=Department of
Electrical and Computer Engineering, city=Fairfax, postcode=22030,
state=Virginia, country=USA

##  1 Introduction

Previously, multiple publications described novel blockchain consensuses that
support alternative mining puzzles other than the hash algorithm. As a result,
the computation power of miners’ hardware will not be wasted on a pure brute-
force algorithm. Especially, Privacy‐Preserving Blockchain Mining [1], Coin.AI
[2], WekaCoin [3], DLBC [4, 5], and PoDL [6] are on top of novel consensus
which perform deep learning training algorithms as proof-of-useful-work
(PoUW).

Deep learning (DL) has developed rapidly in recent decades and has been widely
applied in different fields. Training a deep learning model with good
performance not only takes a massive amount of energy but also requires
significant research effort. Neural architecture search (NAS) has recently
become popular because it can help researchers to design DL models
automatically. Similar to blockchain services, NAS also requires enormously
high computation power, and insufficient computation resources will slow down
the productivity of researchers. With the help of novel consensuses, the
computation power of miners in blockchain services could be leveraged to
accelerate NAS.

In the permission-less blockchain system, the security of the system depends
on the high volume of individual miners. The incentive to mine is to earn
tokens. For an individual miner, it is profitable only if the value of the
earned token is more than the electricity bill. Because only the winner miner
will receive a block reward, it is a risk for individual miners that they have
spent electricity but do not receive the block reward. In practice, the
majority of the miners will not receive the block reward. The possibility for
an individual miner to earn the credit is the ratio of its computation power
to the computation power of the whole network in PoW consensus. In a mature
permission-less blockchain system, the computation power of the entire network
is ideally exceptionally high, so it can serve as the backup of the security
property of the blockchain system. Therefore, the possibility for an
individual miner to earn the reward is extremely low.

For nowadays publicly accessible cryptocurrencies, an individual miner most
likely will join a mining pool to earn tokens. Because mining with the mining
pool will minimize the risk of zero earnings in a short term. A mining pool is
formed by a group of miners and it behaves as mutual insurance[7]. But, the
mining pool for hash-based consensus is different from the PoNAS consensus. In
this paper we proposed a collaboration strategy in the mining pool for PoNAS
consensus. To my best knowledge, we are the first to demonstrate the design of
the mining pool for NAS-based PoUW.

The main contribution of this design is as followed:

  * 1.

We explained the benefits of the mining pool for the PoNAS and discussed the
difficulties to achieve the mining pool. An intuitive method is to adopt the
existing distributed deep learning frameworks to train the PoDL workload.
Without optimization of scheduling of the training tasks, the slowest miner
will become the bottleneck of overall performance and most of the miners will
be idle.

  * 2.

We introduced a collaboration strategy of exploration and exploitation to the
mining pool. Therefore, the miners with less computation power will not
drawback the overall performance, and the resource of these miners will not be
wasted.

  * 3.

We applied the naive parallel computing solution with which the dependency
between miners is further reduced. The bottleneck of the network does not
exist in the design.

In addition, this design leveraged the NAS as the workload. The actual
training tasks among miners are different while the final proof information is
the same, which is an effective neural architecture. This is different from
PoUW and PoDL, which require all miners to work on the same workload within
one block. The effectiveness of NAS is beyond the contribution of this paper,
yet we gave an example that miners can train the DL model with different
architectures while providing the information to be proven by consensus.

##  2 Background & Related Work

###  2.1 Consensus of existing cryptocurrency

The Bitcoin is built on top of the Proof of Work (PoW) consensus which
requests all miners to solve problems. Generally, the required problems in PoW
consensus are easy to validate and hard to solve. The PoW is stable but its
power consumption is enormous. The Ethereum is a popular cryptocurrency based
on Proof of Stake (PoS) consensus which decides the creator of the new block.
In PoS, the amount of owned token of a certain miner will prove the support
the authority. In this consensus, the computation is relatively more efficient
than PoW, but it is less stable and robust owing to various limitations.[8,
9].

###  2.2 Proof-of-Deep-Learning (PoDL):

In the consensus based on the deep learning algorithm, it divides each block
time into two or more interval phases [6, 4, 5]. In general, it includes the
initialization phase, the training phase, and the validation phase.

In the initialization phase, all miners confirm the target task and evaluate
the training setup, such as the target training epochs and the size of the
dataset. In the training phase, miners train the confirmed target task and
commit their model before the training phase ends. Here the miners submit the
hash of their deep learning model, training results, and miners ID. The task
publishers release training dataset and deep learning training source code.
[6, 4, 5]

In the validation phase, the task publisher releases the test dataset to
miners and full nodes, and each miner submits (1) the block header and the
block that contains information describing the trained model on top of
existing attributes, (2) the trained model, and (3) the accuracy of the
trained model, to full nodes. The full nodes validate the submitted models.
Here, full nodes discard all submissions if the model was not committed before
the training phase ends in the current block (i.e., hash of the model and ID
have not been received), thus it prevents from miners over-fitting their
models on the disclosed test dataset or stealing others models. The full nodes
will confirm the new block and authorize the creator of this block. During the
confirmation process, the full nodes validate the model with the highest
accuracy amount of all submissions. If the validated results equal as claimed,
the confirmation is finished. Otherwise, the full nodes will continue the
process and validate the models in decreasing order of the claimed accuracy.
This confirmation process yields a robust consensus. [6, 4, 5]

###  2.3 Other Proof-of-Useful-Work mechanisms:

Primecoin [10] is built on top of Proof-of-Useful-Work mechanisms that request
all miners to solve problems. Here, the puzzle is to find a special sequence
of prime numbers. The consensus helps to solve mathematical problems, i.e.,
discovering the Cunningham chain. Hybrid mining [11] solves problems with the
computational power of the blockchain system. Privacy‐Preserving Blockchain[1]
introduced their two parallel chains and dynamic committee members’ strategy.
Here, PoUW runs on top of the long-interval and transactions in short-
interval. In Coin.AI [2], miners will train DL model mode and also store the
valuable data for tokens. WekaCoin [3] will contribute to creating a public
distributed and verified database.

Figure 1: The full results of NAS of two miners searching in different
searching spaces. The solid lines shows the best reward of NAS in two spaces.
The dash lines shows the current reward of each configuration during searching
procedure. The x-axis is the number of episodes and y-axis is the reward.

###  2.4 NAS

While artificial neural networks have achieved ground-breaking success in
machine learning applications, their topology is trending towards complex and
indecipherable. As a result, the traditional architecture engineering process
relying on the labor and expertise of human designers are regarded as either
impossible or inefficient in pushing the state of the art to the next level.
Therefore, design automation in neural networks is logically the future of
machine learning. In the Fig. 1, it shows the full results of the NAS of two
miners searching in different searching spaces. The solid lines show the best
reward of NAS in two spaces. The dash lines show the current reward of each
configuration during the searching procedure.

As an essential part of AutoML, neural architecture search refers to the
technique of automating exploration in the design space of neural network
topology. A typical use case of NAS would be having an abstract structure with
multiple sub-structures to be optimized using a set of optional building
blocks. This design space is too huge to be exhausted and manually pruned, so
the success of NAS is dependent on a carefully devised searching strategy. In
order to find improved architectures over the previous models, a variety of
search algorithms have been studied in existing works, including reinforcement
learning [12, 13], evolutionary methods [14, 15], Bayesian Optimization [16],
hill-climbing [17], etc. It is noted that NAS is a computational-intensive
problem, so how to formulate the NAS problem to improve efficiency has
attracted more and more research interest [18, 19].

A mainstream NAS framework of today is the weight sharing scheme where
multiple child networks are trained together as one “supernet” and inherit the
same set of weights for evaluation [20]. In such frameworks, the “Childnet’s”
are sampled by some searching algorithm for optimal performance. Particularly,
[21] proposed the gradient-based method named “DARTS” to jointly search and
train the child networks with very high efficiency. Soon after NAS was brought
up, it was applied under hardware constraints to form a research
topic—hardware-aware NAS [22, 23]. Since quantization is one of the most
common techniques for approximated computation in hardware, some works
employed NAS to search the best configuration for quantizing neural networks,
a.k.a quantization-aware NAS [24]. Hardware-aware NAS is not only deployment-
oriented but also efficient as the hardware search can be guided.

##  3 Methodology

###  3.1 Overview of mining pool

In this mining pool, the participants include miners and managers. The pool
manager will receive the rewards once any of the participants find the block
and the manager will distribute the rewards to each participant [7]. The pool
manager normally hosts very powerful servers to maintain a stable connection
and job distribution. Miners pay mining fees as a return to the good
performing pool manager. The miners in the pool will contribute to the
assigned tasks.

For the consensus based on hash, the miners are working independently thus the
individual performance of a miner will not suffer from dependency from miners.
The amount of the reward distributions will depend on the ratio of computation
power and contribution. The job distribution is relatively simple because the
computation is relatively independent.

In the recent deep learning-based PoUW consensus [6, 4, 5, 1, 2, 3, 25],
multiple papers discussed the possible solution that the computation power of
miners will be spent on relative useful work and here are the deep learning
training tasks. For instance, PoDL [6], Proof of Federated Learning [25], and
etc.. Because all miners will wish to avoid risks, a mining pool will appear
naturally.

In the mining pool based on NAS, the amount of the reward distributions will
still depend on the ratio of computation power and contribution. But a weak
miner may hold back the performance of the whole mining pool. Therefore, the
Intuitive solution is that the manager will distribute easier jobs to weak
miners and distribute harder jobs to strong miners. Therefore, all miners will
be able to deliver useful results We will introduce miner type in the Sec.
3.2.2

###  3.2 Design of mining pool

####  3.2.1 Deep learning consensus

As introduced in Sec.2, there are multiple existing publications about a novel
blockchain consensus based on a deep learning algorithm instead of a brute
force algorithm. For demonstration purposes, this mining pool will service a
consensus such as Deep Learning consensus [4, 5].

In this consensus [4, 5], it described the design of three phases block
interval and task scheduling for each interval phase. For phase one, it is the
initial stage that miners will confirm the target task to train and evaluate
the difficulty of the task. In [4, 5], the difficulties of the tasks include
model size, data size, network bandwidth, FLOPs of the task, and computation
power of the network. For phase two, it is the time for GPUs of miners to
train the DL tasks and full nodes to spread submitted tasks. Miner nodes
select the next target task to train based on the ranking score. The ranking
score is the ratio of the difficulty of the task over the task reward. All
miner nodes will only allow submitting the training results before phase two
is finished. For phase three, full nodes rank the submitted training results
and evaluated the winner model. During phase two and phase three, once a task
is selected for the next block, all miners will fetch the data from full nodes
and task publishers. Once the performance of the winner model is the same as
the miner claimed, the winner miner will generate the current block and full
nodes start to spread the current block. If the performance of the winner
model is worse than the submitted value, the full nodes will remove it and
evaluate the next best model. For all nodes, if they find the block is
generated, they will validate and confirm the block. Once a block is confirmed
for an individual node, it will move onto phase one of the next block.

For a mining pool, the pool manager will split the searching space of the
selected NAS task into multiple subspaces. Therefore, the whole mining pool
may achieve better performance.

####  3.2.2 Miner types

In the mining pool design, we separate miners into strong miners and weak
miners. For strong miners, they can finish the search task in a given
subspace. For weak miners, they cannot finish the search task to give subspace
due to the limitation of network bandwidths, hardware, etc..

In practice, the performance of a weak miner would affect the performance of
the whole mining pool. In the experiments, we noticed that some subspace can
be better than others that the miner will find a better neural architecture in
this “lucky space”. In the case, if this “lucky space” is assigned to a weak
miner and the miner may waste the good opportunity to find the better neural
architecture in this subspace. To increase the efficiency of the mining pool,
the pool manager will try to reduce the overlap between each subspace.
Therefore, it is very possible that a mining pool will not find this neural
architecture and the performance of the pool will be held back.

####  3.2.3 General embarrassingly parallel computations

Input:

Hyperparameters $h_{1},h_{2},...,h_{n}$ with $h_{i}$ of searching range
$r_{i}=\\{R_{i}^{1},R_{i}^{2},...,R_{i}^{k}\\}$, $m$ is the total number of
miners.

Return:

A list of subspaces, Subspace = $[S_{1},S_{2},...,S_{m}]$.

Initialization:

Initialize empty list with size equals to m;

Initialize table T with the key equals to index of hyperparameters and the
value equals to a list of searching range for the corresponding
hyperparameter;

for  _$i=1;\ i\leq n;\ i=i+1$_ do

T[$i$] equals to a list of all subsets of $r_{i}$;

end for

Partition:

for  _$i=1;\ i\leq m;\ i=i+1$_ do

Initialize the space $S_{i}$ for miner $i$;

for  _$j=1;\ j\leq n;\ j=j+1$_ do

The selected searching range for hyperparameter j = T[$j$][randint()])
$S_{i}$.append(The selected searching range)

end for

Subspace.append($S_{i}$)

end for

return Subspace;

Algorithm 1 Partition of search space for miners

In this mining pool, the pool manager will split the search space into
multiple subspaces and each miner will search the neural architecture
independently. Therefore, it will reduce the effect of network bandwidth on
the performance of whole searching tasks. This parallelism will not request
any dependence during the search for each miner thus it is named
embarrassingly parallelism.

In NAS tasks, the searching space is a high dimension which covers all
combination of neural network configuration. To search a high-performance
model in this high dimension space may request many experiments. The NAS will
help to find a good configuration of a neural network.

In the algorithm 1, each hyperparameter $h_{i}$
$(\in\\{h_{1},h_{2},...,h_{n}\\})$ of the target neural network can be
selected from a searching range $r_{i}=[R_{i}^{1},R_{i}^{2},...,R_{i}^{k}]$.
The $i$ is the index of the hyperparameter and $k$ represents the maximum size
of the searching range of the $i$ hyperparameter, and $n$ is the total number
of hyperparameter. A subspace $S$ $(\in S_{1},S_{2},...,S_{m})$ formed by $n$
elements and each element formed by a searching range of one hyperparameter.
For instance, to assign a subspace to a miner, the mining pool manager follows
algorithm 1 and selects one searching range for each hyperparameter. In
section 4, we will demonstrate the algorithm in a certain value based on a
given NAS task.

####  3.2.4 Collaboration strategy of exploration and exploitation

The tasks for the pool manager include collecting tasks, splitting tasks,
collecting results, and submitting the best results. The pool manager collects
input information from full nodes and splits the searching space into
subspaces as described in algorithm 1. The pool manager collects the best
results from all miners and submits the best solution to full nodes before the
training phase ends.

Here, the collaboration strategy of exploration and exploitation is to
schedule strong miners and weak miners separately. In practice, some subspaces
may be easier to find better performance. The NAS agent is designed to propose
a certain neural architecture without training it. If a weak miner is assigned
to search neural architecture in the subspace which contains the final best
solution, the weak miner may not have sufficient computation power to find the
final target architecture, thus it will waste the opportunity. Therefore, the
searching space will be only sent to the strong miners. Once a solution is
confirmed to beats the current best results, the strong miners will share the
corresponding hyperparameter with weak miners. The weak miners will continue
to exploit the confirmed architecture. The weak miners will also update the
improved solution with strong miners. All miners submit the best solution to
the pool manager once they find a solution that beats the current best
results.

##  4 Experiment

Table 1: Model architecture subspaces for subspaces S1 to S9 and full space.

space ID | kernel height | kernel width | number of kernel | stride height | stride width | pool size
---|---|---|---|---|---|---
full space | 1, 3, 5, 7, 9 | 1, 3, 5, 7, 9 | 4, 8, 12, 24, 36, 64, 128 | 1, 2, 3, 4, 5 | 1, 2, 3, 4, 5 | 1, 2
subspace S1 | 1, 5, 7 | 3, 5, 7 | 24, 36, 48, 64 | 1, 2, 3 | 1, 2, 3 | 1, 2
subspace S2 | 1, 3, 5, 7 | 1, 3, 5, 7 | 24, 36, 48, 64 | 1, 2, 3 | 1, 2, 3 | 1, 2
subspace S3 | 1, 3, 5, 7, 9 | 1, 3, 5, 7, 9 | 4, 8, 12, 24, 36, 64, 128 | 0, 1, 2, 3 | 0, 1, 2, 3 | 1
subspace S4 | 1, 3, 5, 7, 9 | 1, 3, 5, 7, 9 | 4, 8, 12, 24, 36, 64, 128 | 1, 2, 3, 4, 5 | 1, 2, 3, 4, 5 | 1
subspace S5 | 1, 3, 5, 7, 9 | 1, 3, 5, 7, 9 | 4, 8, 12, 24, 36, 64, 128 | 1, 2, 3, 4, 5 | 1, 2, 3, 4, 5 | 1
subspace S6 | 1, 3, 5 | 1, 3, 5 | 4, 8, 12 | 1, 2, 3 | 1, 2, 3 | 1
subspace S7 | 5, 7, 9 | 5, 7, 9 | 32, 64, 128 | 3, 4, 5 | 3, 4, 5 | 1
subspace S8 | 5, 7, 9 | 5, 7, 9 | 32, 64, 128 | 3, 4, 5 | 3, 4, 5 | 1
subspace S9 | 1, 3, 5 | 1, 3, 5 | 24, 36 | 1, 2, 3 | 1, 2, 3 | 1

Table 2: Model quantization subspaces for subspaces S1 to S9 and full space.

space ID | act_num_int_bits | act_num_frac_bits | weight_num_int_bits | weight_num_frac_bits
---|---|---|---|---
full space | 0, 1, 2, 3 | 0, 1, 2, 3, 4, 5, 6 | 0, 1, 2, 3, 4 | 0, 1, 2, 3, 4, 5, 6
subspace S1 | 1, 2, 3 | 1, 2, 3, 4, 5 | 0, 1, 2, 3, 4 | 2, 3, 4, 5
subspace S2 | 0, 1, 2, 3 | 0, 1, 2, 3, 4, 5, 6 | 0, 1, 2, 3 | 0, 1, 2, 3, 4, 5, 6
subspace S3 | 0, 1, 2, 3 | 0, 1, 2, 3, 4, 5, 6 | 0, 1, 2, 3 | 0, 1, 2, 3, 4, 5, 6
subspace S4 | 2, 3 | 4, 5, 6 | 2, 3 | 4, 5, 6
subspace S5 | 0, 1 | 1, 2, 3 | 0, 1 | 1, 2, 3
subspace S6 | 0, 1, 2, 3 | 0, 1, 2, 3, 4, 5, 6 | 0, 1, 2, 3 | 0, 1, 2, 3, 4, 5, 6
subspace S7 | 0, 1, 2, 3 | 0, 1, 2, 3, 4, 5, 6 | 0, 1, 2, 3 | 0, 1, 2, 3, 4, 5, 6
subspace S8 | 2, 3 | 4, 5, 6 | 2, 3 | 4, 5, 6
subspace S9 | 2, 3 | 5, 6 | 2, 3 | 5, 6

In this section, we will firstly introduce the experimental setup in
subsection 4.1, including the NAS setting general information, the hardware
information, and the weak miner simulation. In subsection 4.2, we will analyze
the performance of the mining pool searching in nine different subspaces
versus the performance of an individual miner searching in the full space. In
subsection 4.3, we will analyze the effect reliability of miners on the
performance of the mining pool.

###  4.1 Experiment setup

####  4.1.1 Experiment overview

To evaluate the performance of the mining pool, we adopt the popular RNN based
NAS [12]. The NAS algorithm is targeting to find a CNN architecture for
classification tasks under a certain hardware constrain. We use CIFAR-10
dataset [26] which has 10 classes images. All experiments were deployed on the
workstation with with Intel(R) Core(TM) i7-9900K CPU @ 3.60GHz, 32Gb RAM,
2$\times$ GTX 1080 Ti.

####  4.1.2 Hardware constraints

The hardware constraints include the size of the lookup table of FPGA, and
throughput. The size of the lookup table of FPGA represents the required chip
size. In this NAS task, we will give 100,000 as of the upper bound. Throughput
also represents the latency of the architecture. Here, we set 10 as the lower
bound. Due to these strong hardware constraints, the performance of neural
architecture may not be able to beat the performance of a model with unlimited
hardware resources.

####  4.1.3 Searching and reward

In the searching process, we will first evaluate the required chip size and
latency. Based on the hyperparameter, if the neural architecture is not
exceeding the bounds, the miner will start training and return the best
testing accuracy within 30 epochs of training in this experiment. If the
result beats the previous best reward, it will be updated as the best reward.
Here, the reward means the testing accuracy for the image classifier. The same
value is named reward for the RNN. This RNN is for selecting the best
hyperparameter value in the given searching range. If the required lookup
table or throughput exceeding the bound, the controller will return zero as
the reward for RNN. For each subspace, the controller will search for 2000
episodes and each episode will train for 30 epochs.

####  4.1.4 Experiments input data

In the table 1, it shows the model architecture subspaces for subspaces S1 to
S9 and full space. In table 2, it shows the model quantization subspaces for
subspaces S1 to S9 and full space. The hyperparameters for model architecture
include kernel height, kernel width, number of kernels, stride height, stride
width, and pool size. The hyperparameters for model quantization include the
number of bits of the activation integer part, number of bits of activation
fraction part, number of bits of the weight integer part, and number of bits
of weight fraction part.

The total number of hyperparameter ${}^{\prime}n^{\prime}$ equals to 10. The
maximum sizes ${}^{\prime}k^{\prime}$ of the searching ranges
${}^{\prime}r_{i}^{\prime}$ are (5, 5, 7, 5, 5, 2, 4, 7, 5, 7). The total
number of miners ${}^{\prime}m^{\prime}$ equals to 9. The full searching
ranges for each hyperparameter are given in the row of full space in table 1
and 2.

For the rows of subspaces S1 to S9, it gives assigned searching ranges of each
hyperparameter of each subspace. In the algorithm 1, The table $T$ saves all
subset of each searching range. Here, $T[i]$ saves a list of all subset of the
searching range of the $i-th$ hyperparameter. Because the table $T$ contains
all subset and miners will fetch searching range for a certain hyperparameter
randomly, it is possible to achieve one subspace overlap another subspace.
This algorithm 1 may lead to inefficient searching space partition. But we
will demonstrate that the searching space overlapping is not an efficiency
issue in subsection 4.2. An efficient searching space partition may improve
NAS mining pool performance, but it is out of our current scope.

####  4.1.5 Weak miner simulation

As explained in section 3, the weak miner may drawback the overall
performance, thus we will need to simulated the weak miners in our experiment.
In practice, many reasons will affect the performance of a miner, such as
frequency and cores number of CPU, size, and bandwidth of memory, GPU, etc..
This will bring difficulties for us to evaluate the consequence when we assign
the same amount of workload. We will use the workstation with the same
configuration and hardware, but only allow a shorter run time to simulate a
weak miner, such machine will run 1/10 of the total strong miner run time to
simulate 10 times weaker miner.

###  4.2 benchmark of mining pool

Figure 2: The results of NAS in full searching space, and subspace 1 to 9. The
x-axis is the number of episodes and y-axis is the best rewards.

The experiments conduct as it is introduced in subsection 4.1. As an
individual miner search neural architecture in a searching space, it evaluates
the required sizes of the lookup table of FPGA. If the required size is bigger
than the given upper bound, the miner returns zero as the accuracy of the
current configuration. Otherwise, the miner continues to evaluate the
throughput of the current configuration. If it is lower than the given lower
bound, it will return zero as the accuracy of the current configuration.
Otherwise, the miner will start to train the current neural architecture for
30 epochs. Then the controller will test the model. If the result beats the
current best reward, the controller updates the value of the current best
reward. Otherwise, the controller only saves the testing accuracy as the
reward of the current configuration. The controller repeats this procedure for
2000 episodes.

The current reward is the test accuracy of the current configuration and it is
for training the RNN model. After the performance of the RNN model improved,
the controller will find better performance neural architecture under the
given hardware constraints more efficiently.

In the novel consensuses blockchain system, the full nodes only check the best
performance models. Therefore, we will only shows the best reward (accuracy)
in the Fig. 2 and 3. In the Fig. 2, the solid line shows the result of one
individual miner searching in the full searching space. The dash lines show
the results of nine miners searching in the searching subspaces S1 to S9
independently. In the Fig. 2, four of the miners return low-performance
results, and four of the miners return high-performance results. Here, the
results for subspace S7 and subspace S8 are overlapping.

The searching ranges of each hyperparameter is given in the row of full space
in the table 1 and table 2. In this subsection, we will evaluate whether this
mining pool will help to find a better architecture than a single miner. This
seems to be straightforward. Due to the network latency and system overhead,
it is not always true that a group of machines find a better neural network
architecture than a single machine. In our design, we applied embarrassingly
parallel computation parallelism and there is no dependence between different
miners. Therefore, the network latency will not strongly affect performance.

As shown in the Fig. 2, this embarrassingly parallel computation parallelism
helps the whole mining pool to be more competitive than a single miner. Four
miners are searching in subspace S1, S2, S4, and S9 from the mining pool to
return better results than the individual miner during the majority of the
mining time. Three miners return better results at the end, and two miners
return better results from beginning to the end. The miner searching in
subspaces S1 finds very good performance neural architecture at a very early
time and finds the best performance neural architecture at the end. In the
Fig. 3, it is a zoom-in result where the y-axis range is from 0.7 to 0.9.
Around episode 200 to 250, the miner searching subspace S1 is overtaken by the
miners in subspace S2 and S4. The miner searching subspace S4 keeps the
leading position till episode 1300 to 1400. In practice, miners will adjust
the number of episodes due to the length of the given training phase and their
computation power. These results show that more miners searching in different
subspaces will help the mining pool to be more competitive during the whole
training phase.

###  4.3 Evaluation for effect of miners reliability

####  4.3.1 Miners reliability

In subsection 4.2, it shows the performance of this mining pool based on
embarrassingly parallel computations is more competitive than the performance
of an individual miner. In this small scale of evaluation, only 9 miners are
searching in 9 different subspaces. In the Fig. 2, four of the miners return
low-performance results, and four of the miners return high-performance
results. The high performance versus low-performance ratio is not promised in
a large scale of testing, but it shows a good amount of miners return high-
performance results. Especially, the results from different subspace S1 and S4
are very close in the Fig. 3. In the large scale mining pool, if there are
multiple miners like the miners in subspace S1 and S4. It means the overall
performance of the mining pool is not depends on any individual miner.

In the Fig. 4, it shows the standard deviation of the results for the miners
searching in subspaces S1, S2, S4, and S9. This standard deviation is
calculated from all high reward results from the current experiments. The
standard deviation is high when the number of the episode is small. After 500
episodes, the standard deviation value will become low and flatten after more
episodes of searching. When we need to evaluate the mining pool performance it
is also important to check whether the overall performance of the mining pool
depends on any individual miners. The data should only be collected based on
all the miners who returns high reward values. Once the standard deviation
value amount these miners raise, it is necessary for the mining pool manager
to prepare backup miners to continue the searching task if any high reward
miners leave the pool. The backup miners can be selected from the miners who
returns low reward. In the Fig. 2, the miners searching subspaces S1, S2, S4,
and S9 are considered as high reward miners, and the miners searching
subspaces S3, S5, S7, and S8 are considered as low reward miners in this
experiment. Only strong miners search for neural architecture. Here, both high
and low reward miners are strong miners. Because miners may leave the mining
pool at any time, the manager needs to handle this case.

Figure 3: The results of NAS in subspace S1, S2, S4, and S9. The x-axis is the
number of episodes and y-axis is the best rewards with the range from 0.7 to
0.9. Figure 4: The standard deviation of the results for the miners searching
in subspace S1, S2, S4, and S9. The x-axis is the number of episodes and
y-axis is the standard deviation value.

####  4.3.2 Exploration and exploiting

As it is described in section 3, the mining pool manager assigns exploration
tasks to strong miners and assign exploiting tasks to weak miners once strong
miners return confirmed neural architecture. Therefore, there is no chance
that a weak miner will drawback the overall performance of the mining pool and
the strong miners will be able to spend the valuable computation power on
searching in more space. Thus, the performance could be maximum.

As it is explained in section 3, a weak miner may drawback the overall
performance. As description in subsection 4.1, we will simulate a weak miner
by scale the run time down to 1/10 of the strong miner. When the weak miner is
assigned to search architecture from space two, it is the most possible
setting to find the best solution. Based on the Fig. 2 and 3, it easy to find
high performance neural architecture in the subspaces S1 and S4. Without this
exploration and exploiting strategy, if 10 times slower miners are assigned to
search subspaces S1 and S4, the miners in subspace s2 will be the only
contributor to the overall best performance of the mining pool which is
0.7829. The weak miners will return 0.5701 and 0.7724. With exploration and
exploiting strategy, the overall performance of the mining pool is 0.8204.
Therefore this weak miner simulation shows that the weak miner only able to
search for 200 episodes and weak miners will eventually waste a good
opportunity to find the best solution. Although other miners may achieve
similar results to the best solution from different subspaces if the mining
pool manager will not schedule other miners to search in the same subspace.
Therefore, the weak miner may waste a good opportunity and drawback the
performance of the whole mining pool without this exploration and exploiting
strategy.

##  5 Conclusion

In this paper, we briefly introduced recent PoUW novel consensuses and details
of the consensuses based on deep learning training. We adopt NAS as the
workload to demonstrate the concepts. For a public accessible cryptocurrency
blockchain system, earning tokens is the incentive for an individual miner to
participates in mining. In a large-scale cryptocurrency system, the
possibility of earning tokens for an individual is very low. A mining pool
will support individual miners to be profitable in the large-scale
cryptocurrency blockchain system. In this project, we are the first to
demonstrate a mining pool solution to support novel deep learning-based
consensuses.

In section 3, we have introduced the function of pool manager, subspaces
partition algorithm, and exploration & exploitation strategy. In section 4, we
evaluate the performance of the mining pool, and it is more competitive than
an individual miner who searches the full space individually. Due to the
uncertainty of individual miners, the mining pool manager will keep track of
the high-performance miners and prepare backup miners as introduced in
subsection 4.3.

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