# DIFF-ERO: A Conformance-Aware Loss for Deep Learning in Process Mining

arXiv: https://arxiv.org/abs/2606.14283 · HTML: https://mlsanity.com/paper/2606.14283/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 33 references that are in the map.
- First posted on arXiv 12 Jun 2026.

## Builds on (most cited first, 20 of 20)

- [Soft-DTW: a Differentiable Loss Function for Time-Series](https://mlsanity.com/paper/1703.01541/) (2017)
- [Learning Latent Permutations with Gumbel-Sinkhorn Networks](https://mlsanity.com/paper/1802.08665/) (2018)
- [Calibrating Sequence likelihood Improves Conditional Language Generation](https://mlsanity.com/paper/2210.00045/) (2022)
- [Predictive Business Process Monitoring with LSTM Neural Networks](https://mlsanity.com/paper/1612.02130/) (2016)
- [Gradient Estimation with Stochastic Softmax Tricks](https://mlsanity.com/paper/2006.08063/) (2020)
- [Classical Structured Prediction Losses for Sequence to Sequence Learning](https://mlsanity.com/paper/1711.04956/) (2017)
- [Loss Functions and Metrics in Deep Learning](https://mlsanity.com/paper/2307.02694/) (2023)
- [Creating Unbiased Public Benchmark Datasets with Data Leakage Prevention for Predictive Process Monitoring](https://mlsanity.com/paper/2107.01905/) (2021)
- [Deep Structured Prediction with Nonlinear Output Transformations](https://mlsanity.com/paper/1811.00539/) (2018)
- [Process Discovery Using Graph Neural Networks](https://mlsanity.com/paper/2109.05835/) (2021)
- [Neuro-Symbolic Predictive Process Monitoring](https://mlsanity.com/paper/2509.00834/) (2025)
- [An Entropic Relevance Measure for Stochastic Conformance Checking in Process Mining](https://mlsanity.com/paper/2007.09310/) (2020)
- [Conformance Checking of Fuzzy Logs against Declarative Temporal Specifications](https://mlsanity.com/paper/2406.12078/) (2024)
- [Knowledge-Driven Modulation of Neural Networks with Attention Mechanism for Next Activity Prediction](https://mlsanity.com/paper/2312.08847/) (2023)
- [Generating Feasible and Plausible Counterfactual Explanations for Outcome Prediction of Business Processes](https://mlsanity.com/paper/2403.09232/) (2024)
- [Can recurrent neural networks learn process model structure?](https://mlsanity.com/paper/2212.06430/) (2022)
- [Guiding the generation of counterfactual explanations through temporal background knowledge for Predictive Process Monitoring](https://mlsanity.com/paper/2403.11642/) (2024)
- [Directly Follows Graphs Go Predictive Process Monitoring With Graph Neural Networks](https://mlsanity.com/paper/2503.03197/) (2025)
- [Attention Please: What Transformer Models Really Learn for Process Prediction](https://mlsanity.com/paper/2408.07097/) (2024)
- [ProCause: Generating Counterfactual Outcomes to Evaluate Prescriptive Process Monitoring Methods](https://mlsanity.com/paper/2509.00797/) (2025)

## Built on by (most cited first, 1 of 1)

- [From Event Logs to Governed Action: A BlueSky Agenda for Agentic Process Mining](https://mlsanity.com/paper/2609.07984/) (2026)

## Abstract (arXiv)

Deep learning has driven many recent advances in process analytics, especially for predictive and prescriptive monitoring. However, standard objectives such as cross-entropy optimize local next-step likelihoods and only implicitly capture control-flow structure. As a result, models can achieve high token-level accuracy while permitting imprecise global behaviour. We introduce DIFF-ERO, a conformance-aware loss function for deep learning models on process data. DIFF-ERO is a differentiable formulation of entropy-based stochastic conformance that incorporates control-flow information during training. Our approach constructs batch-level stochastic transition matrices with soft edge memberships, allowing structural precision and recall signals to directly inform backpropagation. The loss is model-agnostic and can be applied whenever the final representation parametrizes stochastic transitions. We instantiate DIFF-ERO in transformer encoder-decoder pipelines for next-activity prediction and use it jointly with cross-entropy to analyse its theoretical components with respect to convergence. Across benchmarks comparing other loss functions and targets, DIFF-ERO shows improved predictive performance where structure matters most while maintaining parity elsewhere. At the same time, the learned stochastic automaton converges towards the structural ground truth, indicating that the network internalizes process model structure.