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Approximate computing is one of the promising techniques in error-resilient applications to overcome high-density integration challenges, such as energy consumption and performance. Multipliers constitute a significant portion of computer arithmetic units, leading to considerable energy and time consumption. In this paper, we propose low-power and compact approximate compressors for composing approximate Dadda multiplier structures, including compressors, half adders, and full adders, which utilize three-phase partial product compression: truncated, approximation, and exact columns. In approximate columns, we consider approximate compressors derived from the truth table of the exact 4:2 compressor and simplified K-map entries based on the probability of each combination of inputs. An error-correcting module (ECM) is designed to distinguish specific cases and reduce the error metrics. All circuits were simulated using ModelSim and then synthesized using Design Compiler with the 15 nm FinFET technology. When compared to state-of-the-art works, our multipliers exhibit approximately 30%, 43%, and 10% reductions in power, area, and delay, respectively. To evaluate their functionality, we conducted image multiplication and implemented a simple multi-layer perceptron (MLP) neural network using the modified National Institute of Standards and Technology (MNIST) dataset in MATLAB with 0.998 mean structural similarity index metric (MSSIM), 51 dB peak-signal noise ratio (PSNR), and 95% classification accuracy. • Introducing novel ultra-compact approximate compressor structures to reduce design metrics. • Proposing an error-correcting module (ECM) for compensating errors of approximation. • Proposing truncated 8 × 8 Dadda multipliers using the proposed approximate compressors and ECM. • Evaluating the accuracy of approximate multipliers in error-tolerant applications. [ABSTRACT FROM AUTHOR]