Generative AI models like ChatGPT are making significant inroads in the legal sector. They assist in drafting legal documents, predicting legal outcomes, and automating routine tasks. However, the phenomenon known as 'hallucinations' presents a unique challenge.

Hallucinations in AI refer to instances where the model generates outputs not based on its input or training data. In the context of the legal sector, such hallucinations can have serious consequences. A hallucination might lead to incorrect legal advice, inaccurate prediction of case outcomes, or errors in legal documents.

Pre-training Strategies:

1. Quality and diversity of training data: Legal AI models need to be trained on a large and diverse set of legal documents, cases, and regulations. The quality of data is crucial. It should be free from errors and should represent different jurisdictions, legal areas, and case scenarios the model might encounter.
2. Fine-tuning with specific legal data: After initial training, the model should be fine-tuned with data specific to the tasks it will perform. For instance, if the model is to be used for contract law, it should be fine-tuned with a variety of contract cases and legal documents.
3. Architectural modifications: Experimenting with different model architectures might help reduce hallucinations. Some architectures might be more prone to hallucinations in the context of legal texts. Techniques such as attention mechanisms, transformers, and memory networks may prove useful.

Post-training Strategies:

1. Output review and filtering: Due to the high stakes involved in the legal sector, a robust review system is vital. This could involve human review of AI outputs, automated systems using rules or heuristics based on legal principles, or a combination of both.
2. Ensemble methods: Using an ensemble of AI models can reduce the likelihood of hallucinations. If one model makes a mistake, the others may correct it. This could be particularly useful in complex legal predictions.
3. Uncertainty estimation: Legal AI models should provide an estimation of uncertainty with their predictions. High uncertainty might indicate a hallucination. Techniques such as Monte Carlo Dropout or Bayesian Neural Networks could be applied.

The legal sector stands to benefit immensely from generative AI models. However, the risk of hallucinations necessitates careful deployment and robust mitigation strategies. By adopting these methods, we can harness the power of AI in law while minimizing the risk of serious errors.