On Post Selection Using Test Sets (PSUTS) in AI 

Juyang Weng 

Department of Computer Science and Engineering, Cognitive Science Program, Neuroscience Program 

Michigan State University, East Lansing, MI, 48824 USA 

GENISAMA LLC, 4460 Alderwood Drive, Okemos, Michigan 48864 USA 

Abstract—This is a theory paper. It first raises a rarely 

reported but unethical practice in Artificial Intelligence (AI) 

called Post Selection Using Test Sets (PSUTS). Consequently, the 

popular error-backprop methodology in deep learning lacks an 

acceptable generalization power. All AI methods fall into two 

broad schools, connectionist and symbolic. PSUTS practices have 

two kinds, machine PSUTS and human PSUTS. The connectionist 

school received criticisms for its “scruffiness” due to a huge 

number of scruffy parameters and now the machine PSUTS; 

but the seemingly “clean” symbolic school seems more brittle 

than what is known because of using human PSUTS. This paper 

formally defines what PSUTS is, analyzes why error-backprop 

methods with random initial weights suffer from severe local 

minima, why PSUTS violates well-established research ethics, 

and how every paper that used PSUTS should have at least 

transparently reported PSUTS data. For improved transparency 

in future publications, this paper proposes a new standard for AI 

metrology, called developmental errors for all networks trained 

in a project that the selection of the luckiest network depends on, 

along with Three Conditions: (1) system restrictions, (2) training 

experience and (3) computational resources. 

I. INTRODUCTION 

In 1950 Alan Turing published his now celebrated paper [1] 

titled Computing Machinery and Intelligence. Turing [1] was 

impressive to have discussed a wide variety of considerations 

for machine intelligence, as many as nine categories. Unfortunately, he suggested to consider what is now called the Turing 

Test that has inspired and misled many AI researchers. 

Much progress has been made in AI since 1950 and many 

methods have been developed to deal with AI problems. For 

the scope of this paper, we will focus on generalization. All 

AI methods fall into two schools, symbolic and connectionist, 

although many detailed methods are a mixture of both. 

A. Symbolic school 

Symbols are used in many AI methods (e.g., states in 

HMMs, nodes in Graphical Models and attributes in SLAM), 

since they are intuitive to human programmers. However, 

symbols are static and have some fundamental limitations that 

have not received sufficient attention. 

The symbolic school [2] assumes a micro-world in 4D 

space-time in which a set of objects or concepts, e.g., S =

{o1, o2, ..., on}, is assumed to be uniquely defined among 

human programmers and their computers, represented by a 

series of symbols in time {o1(t), o2(t), ...on(t) | t0 ≤ t < t1}. 

The correspondences among all these symbols {oi} of the 

same object across different times are known as “the frame 

problem” [2] in AI which means that the programmer must 

manually link all such symbols together along time for each 

object. In computer vision, the symbolic school assumes a 

single symbol oi, for all its 3D positions in its 3D trajectory 

{x(t) | t0 ≤ t ≤ t1} and uses techniques, such as feature 

tracking through video (e.g., for driverless cars). Therefore, 

the symbolic school is based on human-handcrafted set of 

symbols and their assumed meanings. Marvin Minsky wrote 

that symbols are “neat” [3], but in fact, symbols are “neat” 

mainly in human programmer’s understanding but not in 

relating computer programs to a real world. A major problem 

that many AI researchers did not address is the generalization 

weakness of the symbolic school, as the following definition 

states: 

Definition 1 (Symbolic Brittleness): Suppose a symbolic 

AI machine M(S) designed for a handcrafted set S of symbols 

is applied to a real world that requires a new set of symbols 

S0

, with S0 6= S. M(S0) fails without a human programmer 

that handcarts a proper mapping between every element in S0

to an element in S. 

Many expert systems (e.g., CYC, WordNet and EDR) and 

many big-data projects) require a human programmer to be in 

the loop during deployment due to this symbolic brittleness. 

Because it is extremely challenging for a human programmer to understand many implicit limitations of M(S), the 

mapping that the human establishes typically makes M(S0

)

fail, resulting in the well-known high brittleness of symbolic 

systems. This author also did some early work that belongs to 

the symbolic school [4] whose weakness motivated him to start 

in 1990 a new departure with Cresceptron discussed below 

which seems to be the first deep learning network because 

Fukushima’s deep network Neocognitron with performance 

evaluation [5] (that this author cited) did not learn (i.e., humans 

handpicked features to be discussed below as human PSUTS). 

It is worth noting that earlier verisons of Neocognitron 1975 

1980, both in Biological Cybernetics did not have performance 

evaluation and therefore did not report the need for human 

PUSTS during performance evaluation. 

The developmental methods to be discussed below are 

supposed to automatically address this problem without a need 

for a human programmer to be in the loop of handcrafting 

a mapping. Below, this author will argue that the symbolic 

school and some methods in the connectionist school suffer 

from human PSUTS. 

J. Weng, "On Post Selections Using Test Sets (PSUTS) in AI," in Proc. International Joint Conference on Neural Networks, pp. 1-8, 

Shenzhen, China, July 18-22, 2021.
B. Connectionist School 

The connectionist school claimed to be less brittle. However, 

a network is egocentric—meaning that the agent starts from 

its own (neural) network, instead of a symbolic world set S. 

It must learn from the external world without a handcrafted, 

world-centered object model S. Although connectionist methods often assume some task-specific symbols, e.g., a static 

set S of object labels, they also assume a restricted world 

implicitly. Therefore, a connectionist model typically needs to 

sense and learn from a restricted world using a network. The 

use of S in any neural networks as a set of object labels is 

a fundamental limitation that also causes the resulting system 

to be brittle for the same reason as the symbolic school. 

Typically, a network is meant to establish only a mapping 

f from the space of input X to the space of object class S, 

f : X 7→ S (1) 

Many video analysis problems, speech recognition problems, 

and computer game-play problems are also converted into this 

static input space X by converting temporal attributes into 

components of the static input space X. 

Two main types of learning algorithms have been typically 

used, human handpicking of features [5]–[8] (i.e., skull-open) 

and error backprop [6], [9]–[11] (i.e., skull-closed). Below, 

this author will argue that all neural networks that use error 

backprop suffer from machine PSUTS. 

By the way, genetic algorithms offer another approach to 

such network learning. These algorithms study changes in 

genomes across different lives, but many genetic algorithms do 

not deal with lifetime development [12]. This author suggested 

that handcrafting functions of a genome as a Developmental 

Program (DP) seems to be a clean and tractable problem which 

avoids the extremely high cost of evolution on DP. Many 

genetic algorithms further suffer from the PSUTS problems, 

since they often use test sets as training sets (i.e., vanished 

tests) as explained below. 

Marvin Minsky [3] complained among many scholars that 

neural networks are “scruffy”. This problem is not addressed 

completely until the framework of Emergent Turing Machine 

was introduced [13] into Developmental Networks (DNs) 

by the Developmental School discussed below. A lack of 

Emergent Turing Machine logic or being “scruffy” is the main 

cause of PSUTS in neural networks trained by error backprop 

methods. 

C. Developmental School 

The main thrust of the Developmental School, formally 

presented 2001 by Weng and six co-authors [12] is the tasknonspecificity for lifetime development, known as Developmental Programs (DPs). Although a DP generates a neural 

network, a DP is very different from a conventional neural 

network in evaluation of performance across each life—all 

errors from the inception time 0 of each life is recorded and 

reported up to each current time t > 0, as explained further 

below. 

The first developmental program seems to be the Cresceptron by Weng et al. [14]. As Neocognitron does not learn, Cresceptron appears to be also the first deep-learning Convolutional 

Neural Network (CNN). Cresceptron seems to be the first 

incremental neural network whose evaluation of performance 

is across its entire “life” and only one network was generated 

and tested for reporting error rates cross the entire life. 

Cresceptron did not deal with time. A developmental approach 

that deals with space and time in a unfired fashion using a 

neural network started from Developmental Networks (DNs) 

[15] whose experimental embodiments range from WWN-1 

to WWN-9. The DNs went beyond vision problems to attack 

general AI problems including vision, audition, and natural 

language acquisition as emergent Turing machines [13]. DNs 

overcame the limitations of the framewise mapping in Eq. (1) 

by dealing with lifetime mapping: 

f : X(t − 1) × Z(t − 1) 7→ Z(t), t = 1, 2, ... (2) 

where X(t) and Z(t) are the sensory input space and motor 

input-output space, respectively, and × denotes the Cartesian 

product of sets. Note that Z(t−1) here is extremely important 

since it corresponds to the state of a Turing machine. Namely, 

all the errors occurred during any time of each life is recorded 

and taken into account in the performance evaluation. Different 

from the space mapping in Eq. (1) and very important, the 

space Z(t) is the directly teachable space for the learning 

system, inspired by brains [16], [17], [17]–[20]. This new 

formulation is meant to model not only brain’s spatial processing [21] and temporal processing [22], but also Autonomous 

Programming for General Purposes (APFPG) [23], [24]. Based 

on the APFGP capability, the AI field seems to have a powerful 

yet general-purpose framework towards conscious machines 

[25]. 

In the following, we will discuss what PSUTS is in Section II. Section III addresses why error backprop algorithms 

suffer from severe local minima problems. Section IV proposes 

a new kind of error, called developmental error that addresses 

the problems with PSUTS. Section V provides concluding 

remarks. 

II. PSUTS 

Many AI methods were evaluated without considering how 

much computational recourses are necessary for the development of a reported method. Thus, comparisons about the 

performance of the method have been biased toward a competition of how much resources a group has, as we will see 

below after we define PUSTS, regardless how many networks 

have been trained and discarded, and how large each network 

is. Worse still, test sets were used in an unethical way. Here 

we explicitly define: 

Definition 2 (The Three Conditions): The Three Conditions for developing an AI system are: (1) the system restrictions, including whether task-specific or task-nonspecific, 

batch learning or incremental learning, and the body’s sensors 

and effectors; (2) the teaching experience; (3) the computational resources including the number of hidden neurons. 
A. Task-specific vs. Task-nonspecific 

Task-nonspecific learning and task-specific learning differ 

greatly as explained in Weng et al. 2001 [12]. In a taskspecific paradigm, the system developer is given a task e.g., 

constructing a driverless car. Then, it is the human programmer 

who chooses a world model, such as a model of lane edges. 

Next, he picks an algorithm based on this world model, 

e.g., using the well-known Hough transform algorithm that 

makes every pixel detected as edge cast votes for lines of 

all possible orientations that go through the pixel. Then the 

top-two “peaks” of line parameters that have received the 

highest votes are used to declare two lanes detected from the 

image. Some lane-tracking assistance systems use this lanemodel-based approach in the symbolic school. Here “edge” 

and “two lanes” are two symbolic concepts picked up by the 

programmer. Such systems will fail when lanes are unclear or 

totally disappear due to weather or road conditions, leading to 

a brittle system. Human brains appear to be more resilient. 

In contrast, a task-nonspecific approach [12] not only avoids 

any symbolic model, but also does not assume that a task is 

given. The desirable actions at any time are recalled automatically by the learner based on system’s learned context [26] 

that represents automatically figured-out task and appropriate 

context of the task—like a brain. Thanks to the absence of 

any world model, such as lanes, this task-nonspecific approach 

has a potential to be more robust than a world-model-based 

approach. A task-nonspecific approach typically uses a neural 

network to learn [12]. 

B. Batch vs. Incremental learning modes 

Neural network learning has two learning modes, batch 

learning and incremental learning. 

With batch learning, a human first collects a set D of data 

(e.g., images) and then labels each datum with a desirable 

output (e.g., command of navigation or class label). A neural 

network is trained to approximate a mapping f : X 7→ Q

where X is the space of all possible images and Q is the set of 

outputs. Many batch-learning projects use the error-backprop 

method [10], [11], [27]. 

As we will discuss in Section III, the error backprop 

mechanism erases important long-term memories along the 

gradient direction if the learning mode is incremental. Thus, 

few networks that use error backprop on a large data set adopt 

a incremental learning mode. 

In contrast, all developmental methods cited here use incremental learning mode for long lifetimes, since new neurons 

are incrementally activated into the network. The competition 

guarantees that the winner is the most appropriate neuron 

whose memory is the current working memory [28]. 

The batch and incremental learning modes are not 

capability-equivalent [28]. The former requires all sensory inputs are available at a batch, independent of the corresponding 

actions. This is incorrect according to sensorimotor recurrence. 

By sensorimotor recurrence, we mean that sensory inputs and 

motor outputs are mutually dependent on each other in a 

recurrent way. We have the following theorem: 

Theorem 1 (Big-Data Flaw): All big-data sets used by a 

machine learning method violate the sensorimotor recurrence 

property of the real world. 

Proof: A learning agent at time t−1, as shown in Eq. (2) 

does not have the next sensory input from X(t) available 

before the corresponding actions in Z(t−1) are generated and 

outputted, since the sensory input in X(t) varies according to 

the agent actions in Z(t − 1). As an example, turning head 

left or right will result in a different image sensed. Therefore, 

all static big-data sets violate the sensorimotor recurrence. 

All methods that use PSUTS below violate the sensorimotor 

recurrence, because they use a static set of training data. 

Therefore, it is inappropriate for any of them to claim nearhuman performance since human learning is incremental due 

to the sensorimotor recurrence during a human’s lifetime. 

There are two kinds of PSUTS, machine PSUTS and human 

PSUTS. 

C. Machine PSUTS 

The available data set D is divided into three mutually 

disjoint sets, a training set T, a validation set V , and a test set 

T0

. Two sets are disjoint if they do not share any elements. 

Let us consider how machine PSUTS arises from experiments. 

A network architecture has a set of parameters represented 

by a vector, where each component corresponds to a architecture parameter, such as convolution kernel sizes and stride 

values at each level of a deep hierarchy, the neuronal learning 

rate, and the neuronal learning momentum value, etc. Let k

be a finite number of grid points along which such parameter 

vectors need to be tried, A = {ai | i = 1, 2, ..., k}. If there 

are 10 parameters and each of which has 10 grid points to try, 

there are a total of k = 1010 = 10B architecture parameter 

vectors to try, an extremely large number. 

As we will see in Section III, given any architecture parameter vector ai, it is unlikely that a single network initialized 

by a set of random weight vectors can give an acceptable 

error rate on the training set, called fitting error, that error 

backprop intends to minimize. That is how the multiple sets 

of random weight vectors come in. For each architecture vector 

ai, assume n sets of random weights wj , resulting in kn

networks 

{N(ai, wj ) | i = 1, 2, ..., k, j = 1, 2, ..., n}

are trained each of which starts with a different set of random 

weights wj , using error backprop that locally and numerically 

minimizes the fitting error fi,j on the training set T. Grave et 

al. 2016 seems to have mentioned n = 20. Using the above 

example of k = 10B, kn = 200B a huge number that requires 

a lot of computational resources and manpower. 

We are ready to define Post Selection Using Validation Sets 

(PSUVS): 

Definition 3 (Machine PSUVS): If the test set T0 is not 

available, suppose the validation error of N(ai, wj ) is ei,j

on the validation set V , find the best network N(ai∗ , wj∗ ) so 

that it reaches the minimum validation error: 

ei∗,j∗ = min ei,j (3)

1≤i≤k,1≤j≤n
and report only the performance ei∗,j∗ but not the performances of other remaining kn − 1 trained neural networks. 

If the test set T0 is available which seems to be true 

for almost all neural network publications, we define Post 

Selection Using Test Sets (PSUTS): 

Definition 4 (Machine PSUTS): If the test set T0 is avail- 0 able, suppose the test error of N(ai, wj ) is ei,j on the test set 

T0

, find the best network N(ai∗ , wj∗ ) so that it reaches the 

minimum test error: 

0 0 e = min e (4) i∗,j∗ i,j 1≤i≤k,1≤j≤n

0 and report only the performance e but not the perfor- i∗,j∗

mances of other remaining kn − 1 trained neural networks. 

There are some variations of Machine PSUTS: The validation set V or T0 are not disjoint with T. If T = V , we 

call it validation-vanished PSUTS. If T = T0

, we called it 

test-vanished PSUTS. 

Definition 5 (Distribution of errors of trained systems): 

The distributions of all kn trained networks’ fitting errors 0 {fij}, validation errors {eij}, and test errors {eij}, 

i = 1, 2, ...k, j = 1, 2, ...n, as well as the values of k and n. 

It is necessary to present some key statistical characteristics 

of such distributions. For example, ranked errors in decreasing order. Then given the maximum, 75%, 50%, 25%, and 

minimum value of these kn values for the fitting errors, validation errors. and test errors, so that the research community 

can see whether error-backprop can avoid local minima in 

deep learning. For transparency, it seems necessary to report 

such distribution characteristics other than the minimum value 

ei

0

∗,j∗ . 

They should report such distribution characteristics to reflect 

the effects of machine PSUTS. Our experience in experiments 

indicated that the maximum and the minimum values of the 

distribution of fitting errors alone are drastically different, 

around 80% and 5%, respectively. Section III will discuss why. 

Further, such a use test sets to post-select networks resembles hiring a larger number kn of random test takers and report 

only the luckiest N(ai∗, wj∗ ) after the answer-based grading. 

This practice could hardly be acceptable to any test agencies 

and any agencies that will use the test scores for admission 

since this submitted error e0 misleads due to its lack of i∗,j∗

generalization. 

The architecture parameter vector ai∗ and weights wj∗ overfits T, V and T0

. If an unobserved data set T00, disjoint with 

, T0 ∩ T00 T0 = ∅, is observed from a new environment, the 00 error rate ei∗,j∗ of N(ai∗, wj∗ ) is predicted to significantly 0 higher than ei∗,j∗ , 00 0 ei∗,j∗  ei∗,j∗ (5) 

because Eq. (4) depends on the test set T0 in the post selection 

from many networks. Of course, handling new tests is also 

challenging for a human student but any PSUTS is unethical. 

D. Human PSUTS 

Instead of writing a search program in Machine PSUTS, 

Human PSUTS defined below typically involves less computational resources and programming demands. 

Definition 6 (Human PSUTS): After planning or knowing 

what will be in the training set T and test set T0

, a human 

post-selects features in networks instead of using a machine 

to learn such features. 

Some neural network publications, e.g., [5], [8], [29] appear 

to have used human PSUTS. 

Unfortunately, almost all methods in the symbolic school 

use Human PSUTS because it is always the same human who 

plans for and design a micro-world and collect the test set T0

. 

The key to an acceptable test score lies in how much detail 

the human designer can plan for what is in the test sets. 

III. WHY ERROR BACKPROP NEEDS PSUTS 

As shown by Fig. 7 of author’s group’s publication [30] 

in a real-world vision-guided navigation task using errorbackprop vs. DN, even the “luckiest” batch-learning network 

N(ai∗, wj∗ ) using Machine PSUTS performed poorly, e.g., 

60% error rate from error-backprop vs. 22% error rate from 

DN, both on disjoint test set T0 after the first epoch going 

through the entire training set T once. After having gone 

through T 500 times, the error rates are 25% from errorbackprop vs. 22% rom DN, since DN has already reached 

the ML-optimal solution as early as the first epoch. 

This section discusses about a global view, which is new as 

far as the author is aware, about why error backprop even for 

the easier batch-learning mode suffers from local minima. 

Since error-backprop does not perform acceptably well for 

incremental learning mode, as we can see why also from the 

following discussion, we will concentrate on batch learning 

mode only. Namely, we let the network see the entire training 

set T for each network update. 

Let us first consider a well-known neuronal model that is 

applicable to many CNNs. Suppose a post-synaptic neuron 

with activation zj is connected to its pre-synaptic neurons 

yi, i = 1, 2, ..., n, through synaptic weights wij , by the 

expression: 

Xn

φ( wijyi) = zj (6) 

i=1

1 where φ(y) = is the logistic function. The gradient of 1+e−y

zj with respect to weight vector wj = (w1,j , w2,j , ..., wn,j ) is 

η(y1, y2, ..., yn) , ηy

where η is the partial derivative of φ(y). Thus, according to 

gradient direction, the change of the weight vector wj is along 

the direction of pre-synaptic input vector y. If the error is 

negative, zj should increase. Then the weight vector should 

be incremented by 

wj ← wj + w2y (7) 

where w2 is the learning rate. We use the w2 to relate better 

the optimal Hebbian learning, called LCA, used by DN in 

Section IV. At this point, the following theorem is in order. 

Theorem 2 (Lacks of Error-BackProp): Error-backprop 

lacks (1) energy conservation, (2) an age-dependent learning 

rate, and (3) competition based role-determination. 
Neurons

without

competion

Past

inputs

Bird Cat Dog

Current

input

Fig. 1. Lack of role-determination in hidden neurons. 

Proof: Proof of (1): If pre-synaptic input vectors {y}

are similar, multiple applications of Eq. (7) add many terms 

of {w2y} into the weight vector wj causing it to explode. 

Proof of (2): w2 is typically tuned by an ad hoc way, 

such as a handpicked small value turned by a term called 

momentum, instead of being automatically determined MLoptimality by neuronal firing age to be discussed in Section IV, 

Eq.(11). Proof of (3): Suppose neuron zj is in a hidden area 

of the network hierarchy. This neuron zj updates its presynaptic weight using Eq. (7) regardless zj is role-responsible 

or not for the network error. Likewise, there is a lack of 

role-determination in the area of y1, y2, ..., yn, all of which 

must update using their own gradients. Namely, there is a 

competition-based role-determination in error backprop. 

The meaning (3) of Theorem 2 are illustrated by Fig. 1. 

CNNs do not have a competition mechanism in hidden layers. 

Complete connections initialized with random weights are 

provided for all consecutive areas (also called layers), from 

input area all the way to the output area. If the zj neuron is 

in the output motor area and each output neuron is assigned 

a single class label, the role of zj (“dog” in the figure) is 

determined by human supervised label “dog”. However, let us 

assume instead that zj is in a hidden area, not responsible 

for the “dog” class. zj still updates its input weights using 

the gradient. Likewise, the pre-synaptic area Y , is labeled 

“neurons without competition”. The hidden neurons in this 

area do not have a competition mechanism to decide the role 

of each neuron there. This analysis leads us to the following 

theorem. 

Theorem 3 (Random Roles in Error-BackProp): A set of 

random initial weights in a network assigns random roles to 

all hidden neurons, from which a local minimal point based 

on error-backprop learning inherits this particular random-role 

assignment. Which neurons in each hidden areas take a role 

does not matter, but how hidden neurons share a set of roles 

in each hidden area does matter. 

Proof: Without loss of generality, suppose a maximum in 

the output neuron means a positive classification and weights 

take positive and negative values. Then, a high weight to an 

output neuron zj from a hidden neuron yi means an excitatory 

role to zi and a low weight means a inhibitory role. A zero 

weight means an irrelevant role. The gradient vector computed 

in Eq. (7) means such excitatory-inhibitory input patterns 

from pre-synaptic neurons are added through iterative errorbackprop procedures. Because of the complete connections 

and identical neurons, where a hidden neuron is located in 

the Fig. 1 does not matter, but each input image must have a 

sufficient number of hidden neurons in every hidden area to 

reach the corresponding output neuron. The role assignment 

patterns in initial weights do matter in terms of the fitting error 

rate, the validation error rate, and the test error rate. 

Theorem 4 (Percentage Luck of Error-BackProp): 

Suppose a CNN has l > 1 areas, A0, A1, ..., Al, connected 

by a cascade or a variation thereof. A0 takes input frames 

{x ∈ X} and Al is the output area for classification. It has 

a total of m hidden neurons in an area that share a common 

receptive field R in A0. Let the percentage of the m hidden 

neurons do not fire given an input frame x be denoted as 

p(x). Then, the Error-BackProp depends on the average 

p ̄ = Ex∈X{p(x)} to be a reasonably small value, called the 

percentage luck. 

Proof: To guide the proof, we should mention that DNs 

use top-k competition so that each receptive field in each area 

has only k neurons that fires, where k is small, e.g., top-1, for 

each receptive field R. Every receptive field image x ∈ X is 

concrete by which we means that its neurons are only pixels of 

a concrete example of a class C with p ̄ ≈ 50%. Each neuron 

in Al is abstract by which we means that it fires means an 

abstract class C that x belongs to, with p ̄ corresponds to top-1. 

Then, it is necessary for the CNN to convert the most concrete 

representation in A0 with a high p ̄ to the most abstract Al with 

a low p ̄. For example, in Fig. 1, we have l = 2 and there is 

no completion in the hidden area A1. Then error-backprop 

depends on that each neuron in A2 has only few weights from 

the 6 neurons in A1 that are positive, i.e., as its features. 

From Theorems 2 through 4 and their proofs, we can see 

that depending on the luck of role assignment is a critical 

flaw of error-backprop, and so are the system parameters and 

the simple-minded regularization of the learning rate. Because 

of these key reasons, PSUTS plays a critical role to select the 

luckiest network from many unlucky ones after error backprop. 

The more networks have trained by error backprop, the more 

likely the luckiest one has a good role-assignment to start with. 

There has been no lack of papers that claim to justify error 

backprop does not over fit, e.g., variance based stochastic 

gradient descent [31], saddle-free deep network [32], drop 

out [33], implicit regularization during gradient flow [34]. 
They all address only local issues of neural networks trained 

by error backprop and did not mention PSUTS. The theory 

here addresses, for the first time in a journal submission, the 

global role-assignment problem of random weights that no 

local arguments can deal with. That seems to be why PSUTS 

is necessary by error backprop, but PSUTS is controversially 

fraudulent in terms of research ethics—test sets are meant to 

test a reported system, not are supposed to be used to decide 

which network to report from many. 

IV. DEVELOPMENTAL ERRORS 

Apparently, brains do not use PUSTS, as every human child 

must normally develop in a human environment to make the 

living. Cresceptron [14] and later DN [15] were inspired by 

the interactive mode that brains learn though lifetime. 

A. Developmental Errors 

In contrast to PSUTS we define and reported developmental 

errors that includes all errors occurred through lifetime of each 

learning network: 

Definition 7 (Developmental error): The developmental errors of a developmental network N = (X, Y,Z, M) with sensory area X, skull closed hidden area Y and motor area Z and 

memory M, runs through lifetime by sampling at discrete time 

indices t = 0, 1, 2, ... as N(t) = (X(t), Y (t), Z(t), M(t)). 

Start at inception t = 0 with supervised sensory input 

x0 ∈ X(0), initial state z0 ∈ Z(0), and randomly initialized 

weigh vector y0 ∈ Y (0), and initial memory m0 ∈ M(0). 

At each time t = 1, 2, ..., the network N recursively and 

incrementally updates: 

(xt, yt, zt, mt) = f(xt−1, yt−1, zt−1, mt−1) (8) 

where f is the Developmental Program (DP) of N. If zt ∈

Z(t) is supervised by the teacher, the network complies and 

the error et is recorded, but if the supervised motor vector 

has error, the error should be treated as teacher’s. Otherwise, 

the learner is not motor-supervised and N generates a motor 

vector zt and is observed by the teacher and its deviation from ∗ the desired z is recorded as error et. The lifetime average t

error from time 0 to time t is defined as 

Xt 1

e ̄(t) , ei. (9) t

i=0

Namely, the developmental error, unless stated otherwise 

for a particular time period, is the average lifetime error. 

For more detailed information about the process of errors 

{et | t ≥ 0}, other statistical characterizations can be utilized, 

such as standard deviation, variance, and ranked statistics such 

as minimum, 25%, 50% (median), 75%, and maximum errors. 

Because Cresceptron and DN have a dynamic number of 

neurons up to a system memory limit, each new context 

ct , (xt, yt, zt) (10) 

may be significantly different from the nearest matched learned 

weight vectors of all hidden neurons. If that happens and 

there are still new hidden neuron that have not fired, a new 

hidden neuron is spawned that perfectly memorize this new 

context regardless its randomly initialized weights. When all 

the available hidden neurons have fired at least once, the DN 

will update the top-k matched neurons optimally in the sense 

of maximum likelihood (ML), as proven in [13]. For more 

specific time periods, such as the period from time t1 to t2

during which only disjoint tests were made by the teacher and 

the learning agent is not motor-supervised, the average error 

is denoted as e ̄(t1 : t2). Therefore, e ̄(t) means e ̄(0 : t). 

Note that a developmental system has two input areas from 

the environment, sensory X and motor Z. Since there is 

hardly any sensory input x ∈ X that exactly duplicates at 

two different time indices, almost all sensory inputs from X

are sensory-disjoint. During motor-supervised learning, if the 

teacher supervises its motor area Z and the learner complies. 

Since a teacher can take an error, the motor-error that the 

teacher made is also recorded as motor error from the learner 

but due to the teacher. 

B. Competition 

As discussed above, error backprop learning is without completion. The main purpose of competition is to automatically 

assign roles among hidden neurons. Below, we consider two 

cases, sensory networks that are simpler and sensorimotor 

networks which are more complex but much more powerful 

and brain-like. 

1) Sensory networks: Let us first consider the case of feedforward networks as illustrated in Fig. 2. Fig. 2(a) shows a 

situation where the number of samples in X is larger than 

the number of hidden neurons, which is typical and natural. 

Otherwise, if there are sufficient hidden neurons, each hidden 

neuron can simply memorize a single sample x ∈ X. 

This means that the total number of hidden neurons must 

be shared through incremental learning, where each sample 

image-label pair (x, s) ∈ X ×S arrives incrementally through 

time, t = 0, 1, 2, .... This is the case with Cresceptron which 

conducts incremental learning by dealing with image-label 

pairs one at a time and update incrementally. 

Every layer in Cresceptron consists of a image-feature 

kernel, which is very different from those in DN where 

each hidden neuron represents a sensorimotor feature to be 

discussed later. By image-feature, we mean that each hidden 

neuron is centered at an image pixel. Competitions take place 

within the column for a receptive field centered at each pixel at 

the resolution of the layer. The resolution reduces from lower 

layer to higher layer through was called resolution reduction 

(drop-out). 

The competition in incremental learning is represented by 

incrementally assigning a new neuronal plane (convolution 

plane) where the new kernel memorizes the new input pattern 

if the best matched neuron in a column does not match 

sufficiently well. Suppose images x ∈ X arrives sequentially, 

the top-1 competition in the hidden layer in Fig. 2(a) enables 

each hidden neuron to respond to multiple features, indicated 

by the typically multiple upward arrows, one from each image, 

pointing to a hidden neuron. This amounts to incremental 
Neurons

with top-1

competion

Neurons

with top-1

competion

Past

inputs

Current

input

Bird Cat Dog

I win!

0.4 0.3

0.3

0.3

0.2 0.4

0.2 0.6

0.3

Neurons

without

competion

Past

inputs

More!

More! More!

More!

More!

Bird Cat Dog

Current

input

Completely

not their job!

(a) (b)

Fig. 2. How competition automatically assigns roles among hidden neurons without a central controller: The case for automatically construct a mapping 

f : X 7→ S. (a) Each hidden neuron must win-and-fire for multiple inputs. (b) Error-backprop from the “dog” motor neuron asks some hidden neurons to 

help but the current input feature is not their job. 

clustering based on top-k competition. The weight vector of 

each hidden Y neuron corresponds to a cluster in the X space. 

In Fig. 2(a), k = 1 for top-k competition in Y . 

Likewise, suppose top-1 competition in the next higher 

layer, say Z, namely each time only one Z neuron is supervised to fire at 1 and all other Z neurons do not fire, resulting 

the connection patterns from the second layer Y to the next 

higher layer Z. 

The Candid Covariance-free Incremental (CCI) Lobe Component Analysis (LCA) in Weng 2009 [28] proved that such 

automatic assignment of roles through competition results 

in a dually optimal neuronal layer, optimal spatially and 

optimal temporally. Optimal spatially means the CCI LCA 

incrementally computes the first principal component features 

of the receptive field. Optimal temporally means that the 

principal component vector has the least expected distance 

to its target—the optimal estimator in the sense of minimum 

variance to the true principal component vector. 

Intuitively, regardless what random weights each hidden 

neuron starts with, as soon as it is spawn to fire, its firing 

age a = 1. Its random weight vector is multiplied by the 

zero retention rate w1 = 1 − 1/a = 0 and this learning rate 

w2 = s1/a = 1 so that the new weight vector before becomes 

the first input rx with r = 1 for the firing winner. 

1 1 v ← (1 − )v + rx. (11) 

a a

It has been proven that the above expression incrementally 

computes the first principal component as v. The learning rate 

w2 = is the optimal and age-dependent learning rate. CCI a

LCA is a framework for dually optimal Hebbian learning. The 

property “candid” corresponds to the property that sum of the 

1 1 − 1 learning rate w2 = and the retention rate w1 = is a a

always 1 to keep the “energy” of response r weighted input 

x unchanged (e.g., not to explode or vanish). This dually 

optimality resolves the three problems in Theorem 2. 

Fig. 2(b) shows how the three neurons in the Z area updates 

their weights so that the weight from the second area to the 

third area become the probability of firing, conditioned on the 

firing of the post-synaptic neuron in area Z (Dog, Cat, Bird, 

etc.). The CCI LAC guarantees that the sum of weights for 

each Z neuron sum to 1. This automatic role assignment optimally solves the random roles in error-backprop established 

by Theorem 3. 

However, optimal network for incrementally constructing a 

mapping f : X 7→ S is too restricted, since f : X 7→ S is 

only what brains can do, but not all brains can do. For the 

latter, we must address sensorimotor networks. 

2) Sensorimotor networks: The main reason that Marvin 

Minsky [3] complained that neural network is scruffy was 

because conventional neural networks lacked not only the 

optimality described above for sensory networks, but also 

lacked the Emergent Universal Turing Machines (EUTM) that 

is ML-optimal [13]. 

First, each neuron in the brain not only corresponds to a 

sensory feature as illustrated in Fig. 2, but also a sensorimotor 

feature. By sensorimotor feature, we mean that the firing of 

each hidden neuron in Fig. 2 is determined not just by the 

current image σ represented by a sensory vector x ∈ X, but 

also the state q represented by a motor vector z ∈ Z. It is 

well known that a biological brain contains not only bottomup inputs from x ∈ X but also top-down inputs from z ∈ Z. 

In summary, each hidden neuron represents a sensorimotor 

feature in a complex brain-like network. 

1
C. FA as sensorimotor mapping 

This sensorimotor feature is easier to understand if we use 

symbols. Let us borrow the idea of Finite Automaton (FA). In 

an FA, transitions are represented by function δ : Q×Σ 7→ Q, 

where Σ is the set of input symbols and Q the set of states. 

Each transition is represented by 

f 0 (q, σ) −→ q

Weng [13] extended the definition an FA so that it outputs 

its state so the resulting FA becomes an Agent FA (AFA). 

Further, Weng [13] extended the action q to the machinery of 

Turing machine so that action q includes output symbol to the 

Turing tape and the head motion of the read-write head of a 

Turing machine. With this extension, Weng [13] proved that 

any Turing machine is an AFA. 

Weng [13] proved that a DN is ML-optimal and has a low 

time complexity O(1) suited for real-time computation. The 

ML-optimality is conditioned on the Three Conditions: (1) 

task-nonspecific and incremental learning, (2) a training experience, and (3) a limited number of hidden neurons. Namely, 

under the same Three Conditions, every DN is performance 

equivalent, free of local minima; one network is sufficient. 

V. CONCLUSIONS 

Although public has received claims that deep learning with 

error backprop has approached or even exceeded human level 

performance on certain tasks (e.g., classification for static 

images), this paper raises PSUTS which seems to question 

such claims. The author hopes that the exposure of PSUTS 

improves AI credibility and its future development. Fig. 7 of 

[30] experimentally showed the ML-optimal DN leads to a 

much smaller developmental error by training only a single 

network although the ML-optimality is not to minimize it. 

REFERENCES 

[1] A. M. Turing, “Computing machinery and intelligence,” Mind, vol. 59, 

pp. 433–460, October 1950. 

[2] S. Russell and P. Norvig, Artificial Intelligence: A Modern Approach. 

Upper Saddle River, New Jersey: Prentice-Hall, 3rd ed., 2010. 

[3] M. Minsky, “Logical versus analogical or symbolic versus connectionist 

or neat versus scruffy,” AI Magazine, vol. 12, no. 2, pp. 34–51, 1991. 

[4] J. Weng, T. S. Huang, and N. Ahuja, Motion and Structure from Image 

Sequences. New York: Springer-Verlag, 1993. 

[5] K. Fukushima, S. Miyake, and T. Ito, “Neocognitron: A neural network 

model for a mechanism of visual pattern recognition,” IEEE Trans. 

Systems, Man and Cybernetics, vol. 13, no. 5, pp. 826–834, 1983. 

[6] P. J. Werbos, The Roots of Backpropagation: From Ordered Derivatives 

to Neural Networks and Political Forecasting. Chichester: Wiley, 1994. 

[7] T. Serre, T. Poggio, M. Riesenhuber, L. Wolf, and S. Bileschi, “Highperformance vision system exploiting key features of visual cortex,” US 

Patent, vol. US7606777B2, Sept. 1 2006. 

[8] L. Fei-Fei, R. Fergus, and P. Perona, “One-shot learning of object 

categories,” IEEE Trans. Pattern Analysis and Machine Intelligence, 

vol. 28, no. 4, pp. 594–611, 2006. 

[9] Y. LeCun, L. Bottou, Y. Bengio, and P. Haffner, “Gradient-based learning 

applied to document recognition,” Proceedings of IEEE, vol. 86, no. 11, 

pp. 2278–2324, 1998. 

[10] A. Krizhevsky, I. Sutskever, and G. Hinton, “Imagenet classification with 

deep convolutional neural networks,” in Advances in Neural Information 

Processing Systems 25, pp. 1106–1114, 2012. 

[11] Y. LeCun, L. Bengio, and G. Hinton, “Deep learning,” Nature, vol. 521, 

pp. 436–444, 2015. 

[12] J. Weng, J. McClelland, A. Pentland, O. Sporns, I. Stockman, M. Sur, 

and E. Thelen, “Autonomous mental development by robots and animals,” Science, vol. 291, no. 5504, pp. 599–600, 2001. 

[13] J. Weng, “Brain as an emergent finite automaton: A theory and three 

theorems,” International Journal of Intelligent Science, vol. 5, no. 2, 

pp. 112–131, 2015. 

[14] J. Weng, N. Ahuja, and T. S. Huang, “Learning recognition and 

segmentation using the Cresceptron,” International Journal of Computer 

Vision, vol. 25, pp. 109–143, Nov. 1997. 

[15] J. Weng, “Why have we passed “neural networks do not abstract well”?,” 

Natural Intelligence: the INNS Magazine, vol. 1, no. 1, pp. 13–22, 2011. 

[16] C. M. Super, “Environmental effects on motor development: A case of 

Africa infant precocity,” Developmental Medicine and Child Neurology, 

vol. 18, pp. 561–567, 1976. 

[17] K. A. Thoroughman and J. A. Taylor, “Rapid reshaping of human motor 

generalization,” Jounal of Neuroscience, vol. 25, no. 39, pp. 8948–8953, 

2005. 

[18] G. Rizzotti, L. Riggio, I. Dascola, and C. Umilta, “Reorienting attention 

across the horizontal and vertical meridians: evidence in favor of a 

premotor theory of attention,” Neuropsychologia, vol. 25, pp. 31–40, 

1987. 

[19] T. Moore, K. M. Armstrong, and M. Fallah, “Visuomotor origins of 

covert spatial attention,” Neuron, vol. 40, pp. 671–683, 2003. 

[20] J. M. Iverson, “Developing language in a developing body: the relationship between motor development and language development,” Journal 

of child language, vol. 37, no. 2, pp. 229–261, 2010. 

[21] J. Weng and M. Luciw, “Brain-like emergent spatial processing,” IEEE 

Trans. Autonomous Mental Development, vol. 4, no. 2, pp. 161–185, 

2012. 

[22] J. Weng, M. Luciw, and Q. Zhang, “Brain-like temporal processing: 

Emergent open states,” IEEE Trans. Autonomous Mental Development, 

vol. 5, no. 2, pp. 89 – 116, 2013. 

[23] J. Weng, Z. Zheng, X. Wu, and J. Castro-Garcia, “Auto-programming 

for general purposes: Theory and experiments,” in Proc. International 

Joint Conference on Neural Networks, (Glasgow, UK), pp. 1–8, July 

19-24 2020. 

[24] J. Weng, “Autonomous programming for general purposes: Theory,” 

International Journal of Huamnoid Robotics, vol. 17, pp. 1–36, August 

2020. 

[25] J. Weng, “Conscious intelligence requires developmental autonomous 

programming for general purposes,” in Proc. IEEE International Conference on Development and Learning and Epigenetic Robotics, (Valparaiso, Chile), pp. 1–7, Oct. 26-27 2020. 

[26] J. Weng, Natural and Artificial Intelligence: Introduction to Computational Brain-Mind. Okemos, Michigan: BMI Press, second ed., 2019. 

[27] A. Karpathy, G. Toderici, S. Shetty, T. Leung, R. Sukthankar, and 

L. Fei-Fei, “Large-scale video classification with convolutional neural 

networks,” in Proc. Computer Vision and Pattern Recognition, (Columbus, Ohio), pp. +1–8, June 24-27, 2014. 

[28] J. Weng and M. Luciw, “Dually optimal neuronal layers: Lobe component analysis,” IEEE Trans. Autonomous Mental Development, vol. 1, 

no. 1, pp. 68–85, 2009. 

[29] T. Serre, L. Wolf, S. Bileschi, M. Riesenhuber, and T. Poggio, “Robust 

object recognition with cortex-like mechanisms,” IEEE Trans. Pattern 

Analysis and Machine Intelligence, vol. 29, no. 3, pp. 411–426, 2007. 

[30] Z. Zheng and J. Weng, “Mobile device based outdoor navigation 

with on-line learning neural network: a comparison with convolutional 

neural network,” in Proc. 7th Workshop on Computer Vision in Vehicle 

Technology (CVVT 2016) at CVPR 2016, (Las Vega), pp. 11–18, June 

269 2016. 

[31] P. Sermanet, K. Kavukcuoglu, S. Chintala, and Y. LeCun, “No more 

pesky learning rates,” in Proc. International Conference on Machine 

learning, (Atlanta, GA), pp. 343–351, June 16-21 2013. 

[32] Y. N. Dauphin, R. Pascanu, C. Gulcehre, K. Cho, S. Ganguli, and 

Y. Bengio, “Identifying and attacking the saddle point problem in 

high-dimensional non-convex optimization,” in Advances in Neural 

Information Processing Systems, (Montreal, Canada), pp. 2933–2941, 

Curran Associates, Inc., 2014. 

[33] N. Srivastava, G. E. Hinton, K. Krizhevsky, I. Sutskever, and 

R. Salakhutdinov, “Dropout: A simple way to prevent neural networks 

from overtting,” Journal of Machine Learning Research, vol. 15, no. 1, 

pp. 1929–1958, 2014. 

[34] T. Poggio, “Theoretical issues in deep networks,” Proceedings of thr 

National Academy of Sciences, vol. 117, no. 48, pp. 30039–30045, 2020.