Point Processes: A Crash Course - The Foundation Inference Model Program

This section gives the minimum background needed to use FIM-PP and is adapted from Berghaus et al. (2026).

What FIM-PP Infers¶

FIM-PP is a Foundation Inference Model for marked temporal point processes. A marked temporal point process is a sequence of event times

\{(t_i, \kappa_i)\}_{i=1}^n

(1)

where each event arrives at time $t_i$ and carries a discrete mark $\kappa_i$ describing its type.

The goal is to infer the conditional intensity

\lambda(t, \kappa \mid \mathcal{H}_t),

(2)

which describes how likely an event of type $\kappa$ is to occur at time $t$ given the history $\mathcal{H}_t$ .

Rather than training a new neural point-process model for every dataset, FIM-PP is pretrained on a broad synthetic distribution of point processes and then used in-context on new event data.

Figure 1:FIM-PP encodes context paths and attends to them when estimating the conditional intensity of a target history.

Hawkes Processes as the Training Prior¶

The released checkpoint is trained on a broad family of Hawkes-style processes. For each mark $k$ , the conditional intensity is of the form

\lambda_k(t \mid \mathcal{H}_t) = \mu_k(t) + \sum_{(t_i, \kappa_i) \in \mathcal{H}_t} z_{k\kappa_i}\,\gamma_{k\kappa_i}(t-t_i),

(3)

where

$\mu_k(t)$ is a base intensity,
$\gamma_{k\kappa_i}$ is an interaction kernel, and
$z_{k\kappa_i}$ determines whether the interaction is excitatory, inhibitory, or absent.

This gives FIM-PP a strong prior over interpretable point-process dynamics while still allowing the pretrained model to generalize beyond the exact synthetic processes seen during training.

Inputs and Outputs¶

The released FIM-PP checkpoint expects a context/inference split:

context_event_times, context_event_types, context_seq_lengths
inference_event_times, inference_event_types, inference_seq_lengths
intensity_evaluation_times

Given these tensors, the model returns predicted Hawkes intensity parameters together with evaluated intensity curves. If ground-truth functions are provided, it can also return target intensity values and losses for comparison.

Zero-Shot Use vs Fine-Tuning¶

Zero-shot: Use the pretrained checkpoint directly on a new dataset and inspect the predicted intensity curves or downstream next-event behavior.
Fine-tuning: Continue training the pretrained checkpoint on a target dataset using scripts/hawkes/fim_finetune.py. This is useful when the target domain contains recurring patterns that are weakly represented by the synthetic prior.

The released checkpoint is configured for up to 22 marks.

Figure 2:Example intensity estimates from the FIM-PP paper on synthetic and real-world data.

Practical Recommendation¶

For user-facing workflows, prefer the standardized Hugging Face path:

from transformers import AutoModel

model = AutoModel.from_pretrained("FIM4Science/fim-pp", trust_remote_code=True)

This is the primary path documented in the companion tutorial notebook. The lower-level fallback FIMHawkes.load_model(...) remains useful for debugging local checkpoints.

References¶

Berghaus, D., Seifner, P., Cvejoski, K., Ojeda, C., & Sánchez, R. J. (2026). In-Context Learning of Temporal Point Processes with Foundation Inference Models. The Fourteenth International Conference on Learning Representations. https://openreview.net/forum?id=h9HwUAODFP