Tipping points are thresholds at which a system, often abruptly and irreversibly, transitions from a stable state to a contrasting one. Crossing such critical boundaries poses a risk to Earth system stability and may have catastrophic consequences. This is especially relevant, as current climate change is destabilizing Earth subsystems, potentially bringing them closer to tipping points. Thus, it is important to be able to detect approaching tipping points in the Earth’s system, which can be achieved through calibration on palaeo-records. Recently, new deep learning (DL) methods have been established that are able to confidently and quantitatively identify different types of critical transitions characterised by their abruptness and (ir)reversibility. Based on this, we develop a new (simplified) DL classifier focusing on the quantitative detection of catastrophic tipping points (fold bifurcations) in the Earth system. Our approach reduces computational demand and improves performance, especially for short timeseries. We first test the new classifier's performance on synthetic data and subsequently on different existing Cenozoic proxy records. Our DL results are compared to the results from previous studies applying generic early warning signals (EWS), which can detect approaching transitions qualitatively but cannot distinguish bifurcation types (abruptness and (ir)reversibility of the transition). Our DL classifier enables us to identify how abrupt and (ir)reversible an approaching transition is, which is important for tipping point risk assessment and mitigation. Results are generally consistent between generic EWS from previous studies and our DL approach and fit with what is known from the geological context. We note that some results are dependent on the length of the classifier used and the time interval investigated before the bifurcation. We implement an out-of-distribution (OOD) detection method to reduce the misclassification of non-catastrophic bifurcations as catastrophic tipping points. Combined with the binary DL classifier, this approach enables reliable, quantitative detection of catastrophic tipping points in Earth system records.