Point Processes: A Crash Course

Point Processes: A Crash Course#

This section gives the minimum background needed to use FIM-PP and is adapted from [BSC+26].

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

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

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

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

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.

_images/fim_pp_architecture_figure.png

Fig. 2 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

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

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.

_images/intensity_comparison_synth_vs_retweet.png

Fig. 3 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.

Bibliography#

[BSC+26]

David Berghaus, Patrick Seifner, Kostadin Cvejoski, Cesar Ojeda, and Ramses J Sanchez. In-context learning of temporal point processes with foundation inference models. In The Fourteenth International Conference on Learning Representations. 2026. URL: https://openreview.net/forum?id=h9HwUAODFP.

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