Investment and innovative development of industrial enterprises is driven by the influence on the sensitive indicators of their activity, which characterize technological singularity. Therefore, it is expedient to define them using adequate economic and mathematical methods that will identify the development and growth points that are characterized by the accumulation of information and are a manifestation of singularity. The purpose of the article is to determine the main sensitive indicators of the investment and innovative development of industrial enterprises, which are the points of technological singularity. The article proposes conceptual provisions for evaluating the investment-innovation activity of enterprises as a basis for their development. These provisions consider the activity of economic entities according to three states (functioning, growth, and development); evaluation of investment and innovation activities, both individually and in conjunction with the official statistical reporting of enterprises using a well-founded minimum sufficient system of partial indicators defined through the multidimensional factor analysis and combined into integral and summarizing indicators; determination of technological singularity points as a result of prediction of partial and summarizing indicators' values via the neural networks method. A methodological approach is developed to substantiate the technological singularity points, the managerial influence on which is provided by the development of enterprises. The methodological approach is based on considering the investment-innovation activity nonlinearity, both explicit and latent tendencies of development, situationality and variability of its goals, strategic orientation and possible technological singularity of an enterprise. The proposals submitted were implemented based on statistical reports of the machine-building enterprises for 2014-2018.