Technological advancement has contributed immensely to human life and society. Technologies like industrial robots, artificial intelligence, and machine learning are advancing at a rapid pace. While the evolution of Artificial Intelligence has contributed significantly to the development of personal assistants, automated drones, smart home devices, etc., it has also raised questions about the much-anticipated point in the future where machines may develop intelligence that may be equal to or greater than humans, a term that is popularly known as Technological Singularity. Although technological singularity promises great benefits, past research works on Artificial Intelligence (AI) systems going rogue highlight the downside of Technological Singularity and assert that it may lead to catastrophic effects. Thus, there is a need to identify factors that contribute to technological advancement and may ultimately lead to Technological Singularity in the future. In this paper, we identify factors such as Number of scientific publications in Artificial Intelligence, Number of scientific publications in Machine Learning, Dynamic RAM (Random Access Memory) Price, Number of Transistors, and Speed of Computers’ Processors, and analyze their effects on Technological Singularity using Regression methods (Multiple Linear Regression and Simple Linear Regression). The predictive ability of the models has been validated using PRESS and k-fold cross-validation. Our study shows that academic advancement in AI and ML and Dynamic RAM prices contribute significantly to Technological Singularity. Investigating the factors would help researchers and industry experts comprehend what leads to Technological Singularity and, if needed, how to prevent undesirable outcomes.

Over the last few years, technology has impacted several industries, like medicines, computing, power systems, automobiles, etc. The field of artificial intelligence has significantly led to systems getting smarter and making human lives easy. Intelligent systems are machines with embedded, Internet-connected computers capable of gathering and analyzing data to communicate with other systems. Advancement in technology has led to the emergence of systems like personal assistants, automated drones, smartphones, video games, smart homes, etc. Many of these are not only confined to carrying out tasks but are also capable of interacting with humans [

There is limited research on Technological Singularity. We attempt to explore the domain in yet another way. We identify some factors that can contribute to Technological Singularity.

Most of the research works conducted in the past concerning Technological Singularity consider Technological Singularity as a concept or hypothesis, due to which neither experiments nor quantified results are involved for interpretation. In this paper, we perform an in-depth analysis of the factors considered by using regression methods. We determine three models (equations)

One Multiple Linear Regression (MLR) model using three factors, i.e., Number of scientific publications in Artificial Intelligence, Number of scientific publications in Machine Learning, and Dynamic RAM (Random Access Memory) Price.

Two Simple Linear Regression (SLR) models using one factor each, i.e., Number of Transistors, and Speed of Computers’ Processors

The validation has been performed using the PRESS (predicted residual error sum of squares) and k-fold cross-validation.

The study also finds solutions for the derived equations.

The rest of the paper is organized as follows. Section 2 describes materials and methods. In this section, we list out some related works that have been done in the past and our proposed work. In Section 3, we discuss the experimental analysis. Section 4 discusses the Results. This section also includes performance evaluation and validation. In Section 5, we present the conclusions and future work.

This section has been divided into two subsections. The first subsection lists some of the related works done in the past on the technological singularity. In the second section, we present several factors that can lead to Technological Advancement and hence may be related to Technological Singularity.

A study [

Technological Singularity deals with machines gaining intelligence equal to or more than humans; artificial intelligence underpinning machine learning concepts, natural language processing, deep learning, machine memory, etc. [

This section discusses the datasets essential for our study and the experimental methods adopted to justify our research work.

Since our research work deals with regression analysis of the proposed factors, the data was taken from reliable sources. The datasets for the number of transistors and speed of computer processors have been taken from the data repository ‘Our World in Data by,’ Technological Progress by The Oxford University (

We have already identified a list of factors that may contribute to Technological Singularity. We intend to introduce the factors mentioned in the previous section as variables for two family equations. These factors’ effects on technological singularity will be analyzed using regression methods [

While there is enough data to conduct Multiple Linear Regression (MLR) with a number of publications for Artificial Intelligence and Machine Learning, and Dynamic RAM price due to sufficient data, there is not enough data to conduct MLR for transistors and MIPS. Therefore, transistors and MIPS have been analyzed using Simple Linear Regression, a particular case of MLR. We will here be considering first-order models.

In

In _{i}_{0} intercept.

Our goal is to mimic the behavior of ^{2} depicts sample variance. For conducting the analysis, we need to make the following assumptions:

Explanatory variable and response variable(s) follow a linear relation.

Residuals (

Residuals follow a Normal Distribution.

Residuals have constant variance.

The following steps have been considered for conducting the analysis:

Type 1 error,

The following figure is an illustration of the analysis conducted by us (

Although the Variance Inflation Factor (VIF) detects multicollinearity, multicollinearity does not make sense if there is one variable.

The analysis conducted may be explained in the following steps:

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In this section, we will be discussing the equations, analyzing the model by inspecting the validity of the model, and finding the solution to the equations. We also perform a comparative analysis concerning some previous works that have been done regarding Technological Singularity.

Based on the factors considered and the analysis conducted, we have identified three equations. The first equation has factors like the number of publications in ML, the number of publications in AI, and Dynamic RAM price, which is analyzed using Multiple Linear Regression. The second equation considers the number of microprocessor transistors and has been analyzed using Simple Linear Regression. Finally, the third equation considers Million Instructions Per Second (MIPS) and is analyzed using Simple Linear Regression. The equations are depicted as follows:

To perform validation, we rely on two popular methods, i.e., PRESS statistic and k-fold cross-validation.

PRESS refers to the predicted residual error sum of squares. This statistic is a form of cross-validation used in regression analysis for providing a summary measure of the fit of a model to a sample of observations that were not themselves used to estimate the model. It is given by the summation of squares of the prediction residuals for those observations.

The lowest values of PRESS indicate the best structures. If a model is overfitted, small residuals for observations will be included in the model-fitting, but large residuals for observations will be excluded. Thus, the smaller the PRESS value, the better the model’s predictive ability.

The slopes are unknown to accompany bias due to shrinkage. Hence, the prediction would not be accurate; rather, it would not be viable to compute the Y values based on these biased values. However, the low Akaike Information Criterion (AIC) value is indicative of a good prediction. The AIC values are used for estimating the likelihood of a model for predicting/estimating future values. The best model has the minimum AIC value among all other models. Hence it provides a means for model selection. Also, the model explains 92.47% of the variance in Y, which is reasonably good. The Bayesian Information Criterion (BIC) is closely related to AIC. Adding parameters for model fitting may often lead to overfitting. BIC resolves this by introducing a penalty term for the number of parameters in the model. The BIC value is not as low as AIC, but this value implies that our model may not be the most parsimonious.

We observe that the Mean Square Error (MSE) is also high, with a value of 1451.15. Hence, the model parameters are relevant. However, using the predicted residual error sum of squares (PRESS), we observe that the value of K increases with K increasing from 0 to 0.11 and beyond (

From

Equations | Type | PRESS value |
---|---|---|

MLR | 46.4213 | |

SLR | 46.7899 | |

SLR | 634.9394 |

Due to multicollinearity in

CI = Point Estimate

Margin of Error = Standard Error

CI for b0 with 95% confidence: −31.81850

CI for b1 with 95% confidence: 4.28581

CI for b0 with 95% confidence:

12.1780

CI for b1 with 95% confidence: −3.9230

Cross-validation is a resampling procedure used for evaluating machine learning models on a limited data sample. K refers to the number of groups that a given data sample is to be split into. In k-fold cross-validation, the available dataset is partitioned into k number of disjoint subsets, which are of equal size. The number of resulting subsets is known as folds. The partitioning is done by randomly sampling the dataset without any replacement.

To validate the models, we perform the k-fold validation and also observe the values for

The Mean Square Percentage Error (MSPE) is based on the value of k. From

Root Mean Square Percentage

We directly compute the RMSPE over the validation data and get the percentage error.

The validation metrics used for

Similarly, the validation metrics used for

MSE measures the average/mean squared error of our predictions. RMSE Root Mean Square Error is very similar to MSE. MSPE measures the mean square percentage error. MSPE summarizes the predictive ability of a model. RMPSE is the Square Root of MSPE. The variation in Validation means RMPSE for

Kurzweil’s foresight of the technological Singularity predicts its occurrence in 2045 [

Denote ln(AI) by X, ln(ML) by Y and ln(RAM) by Z

The above linear inequality may be expressed in a three-dimensional solution space. The solution space for the above equation may be depicted as follows (

Denote ln(AI) by X, ln(ML) by Y and ln(RAM) by Z

The above linear inequality may be expressed in a three-dimensional solution space. The colored region lies in the solution space of the equation derived. The solution space for the above equation may be depicted as follows (

^{1.1} = −31.81850+4.28581(lx)

For years: 2005–2030

This implies, e

Hence,

e

^{1.1} = 12.1780 −3.9230 (lx)

For Years: 2005–2030

Also,

This implies,

e

Hence,

In this section, we present a comparative analysis of our research work concerning some previous research works.

Author and Year | Proposed work | Methodology/parameters | Results | |
---|---|---|---|---|

Warwick [ |
Recommended an Approach to achieve Technological Singularity | Human Enhancement-Whole Body or Brain Transplant | Enhancements through neural implants may be a way of achieving Technological Singularity (not supported by experimental analysis) | |

Walsh [ |
Proposed that Singularity may never happen | Arguments: The Fast Thinking Dog Argument, The Anthropocentric Argument, The Limits of Intelligence Argument, The Computational Complexity Argument, etc. | The world may never witness a technological singularity; however, it may have an impact on the economy and society (not supported by experimental analysis) | |

Yampolskiy [ |
Proposed that Technological Singularity may happen sooner than anticipated | Counter Arguments: Fast Thinking Dog, The Anthropocentric Argument, The Limits of Intelligence Argument, The Computational Complexity Argument, etc | AI can recursively self-improve with respect to speed, communication, duplicability, cognitive ability, etc. (not supported by experimental analysis) | |

Last [ |
Proposed a Cosmic Evolutionary Philosophy and a Dialectical Approach to Technological Singularity | Disordered phenomenon, thermodynamics, thermodynamics, structural transformations, totality, etc | Dialectical Approach to Technological singularity could become the center of future theories of totality. | |

Silichev et al. [ |
Propounded that Artificial Intelligence can lead to Technological Singularity | Classification of Artificial Intelligence into six levels (1–4, weak AI), (5–6, strong AI) | Level 6 witnesses machine intelligence surpassing human intelligence (not supported by experimental analysis) | |

Iastremska et al. [ |
Proposed investment and industrial development as means of Technological Singularity | Statistical Analysis, Multilevel Perceptron for forecasting generalized integral index | Eight enterprises at a low level (42.1%), Eleven in medium level (57.89%) | |

Priyadarshini et al. [ |
Suggested Presence of Technological Singularity in the Cyberspace (Cyber Singularity) | Intelligent Entities in Cyberspace that are self-learning, self-healing, self-organizing, etc., |
Singularity exists in Cyberspace (supported by set theory) | |

Our proposed work, 2020 | Analyzing the factors of Technological Singularity, using Regression Methods | MLR for |
Equation 1 is the best model for the prediction of Technological Singularity, followed by |

In this study, we identified three equations, which are regression models supporting our research.

Based on the analysis conducted, we can say that Model 1 (

PRESS value: Comparing the PRESS values for the equations (models), we find that the PRESS value for model 1 is the least followed by models 2 and 3, respectively. As we know, the smaller the PRESS value, the better the model’s predictive ability. Hence Model 1’s predictive ability is the best.

The solution space for Model 1 is represented in a three-dimensional space. Comparing the solutions for Model 2 and Model 3, we find that the solutions for Model 3 are too small concerning the other models, which verifies our judgment of Model 3 being the least suitable.

The RMSE and RMSPE values, as evaluation criteria, indicate that the performance of Model 1 and Model 2 is significantly better than Model 3.

Some Limitations of the study are as follows:

The predictor variable is treated as being continuous. It is hard to infer what a real-valued prediction means. Hence, predictions must be reported with Confidence Intervals (Mean Response or Single Response).

Model 1 was treated using Ridge Regression, i.e., variables less significant were shrunk to a greater extent than the more significant variables. This is known to induce bias in the model. MSE, as large as 1451.15, is indicative of that. The BIC value is not as low, but this value implies that our model may not be the most parsimonious model.

Consider Model 1,

Mathematically, when

Additionally, the study has been carried out using the R-programming language, which has some limitations of its own. R utilizes more memory. Hence it is not ideal for handling big data. The packages and the programming language confined to R are relatively slow. Moreover, the algorithms are spread across packages, which is challenging as well as time-consuming.

The fascinating field of Artificial Intelligence promises innovations and advancement in multiple realms of technology. However, it also brings the anticipation of an unseen tomorrow, which may witness machines gaining intelligence greater than or equal to humans, and the society does not entirely benefit from it. Hence, there is a need to identify specific factors that may contribute to this technology advancement so that appropriate measures may be taken if such a situation arises. This paper identified additional factors that can lead to Technological Singularity and analyzed them using regression methods. We derived three models, i.e., one Multiple Linear Regression Model (MLR) and two Simple Linear Regression (SLR) models, and analyzed their predictive abilities. We justified that an MLR based on Artificial Intelligence and Machine Learning Research and Dynamic Random-Access Memory (RAM) price has the best predictive ability using validation methods. This study validates that research in AI and ML (publications) along with Dynamic RAM prices can contribute immensely to Technological Singularity as compared to other factors like Microprocessor Transistors and MIPS. In the future, we would like to explore more Artificial Intelligence methods for analyzing the performance of the models and comparing them with the conducted study. Although we attempted to analyze five factors for this study, several other factors may act as a driving force towards Technological Singularity. It would be interesting to explore the effect of Quantum computing’s processing power on Technological Singularity.