After an incredible learning journey over several years, my PhD is finally done! Thank you so much to Mario Wüthrich and Roseanne Harris for supervising, to Stephen Jurisich for all the encouragement and support and to all my wonderful coauthors for all of these papers!
Here is a brief summary taken from the thesis linked in the first comment:
The main theme of this research is to investigate how deep neural networks, originally developed outside of actuarial science, can be adapted to meet the specialized requirements of actuarial modelling. This goal has been accomplished by, on the one hand, adapting and modifying techniques used in the wider machine and deep learning literature for actuarial purposes, and, on the other hand, proposing new approaches that utilize the flexible structure of deep neural networks to produce new types of actuarial models. By using these deep learning techniques adapted for actuarial purposes, actuaries can comply with the requirements of professional standards and guidance while benefiting from the increased accuracy and speed of fitting these models, compared to traditional approaches.
While foundational tools like GLMs are powerful, classifying them as modern AI muddies regulatory waters and blinds us to the representation-learning revolution actively reshaping our world – a revolution characterized not by incremental improvement but by a qualitative transformation in how machines perceive, reason about, and act on reality.
The taxonomy of computational intelligence has sparked a vigorous and necessary debate within the actuarial profession as well as on my LinkedIn feed! This is far more than a squabble over semantics. The words we choose – and the mental models they represent – have profound implications for governance, investment strategy, the evolution of our methods, and our very ability to navigate a world being remade by a new class of technology.
To truly grasp the stakes, let me suggest we must look beyond our own field to the history of science itself, and specifically to the work of philosopher Thomas Kuhn.
Understanding Scientific Revolutions: A Kuhnian Primer
For those uninitiated, Thomas Kuhn’s 1962 book, The Structure of Scientific Revolutions, transformed our understanding of how science progresses. He argued that science doesn’t always advance in a smooth, linear fashion. Instead, it moves through long periods of stability punctuated by radical shifts.
Normal Science: This is the day-to-day work. Scientists operate within an established paradigm—a shared set of assumptions, theories, and methods (like Newtonian physics or, in our world, traditional actuarial modeling). Their work focuses on “puzzle-solving” within the rules of that paradigm.
Anomalies & Crisis: Over time, results emerge that the existing paradigm cannot explain. These are anomalies. As anomalies accumulate, confidence in the old paradigm wavers, leading to a period of crisis.
Paradigm Shift: A new paradigm emerges that can explain the anomalies, offering a fundamentally new way of seeing the world. This paradigm shift is a revolution. The new paradigm isn’t just a better version of the old one; it’s often incommensurable – meaning the two are so different in their core assumptions that they can’t be judged by the same standards. Think of the shift from the Earth-centric astronomy of Ptolemy to the Sun-centric model of Copernicus. Astronomers in the new paradigm were not just getting better answers; they were asking different questions.
Today, actuarial science is in the midst of its own Kuhnian crisis. Our “normal science” of statistical modeling is being challenged by anomalies – models that can “see” images, “read” text, and discover patterns of a complexity we’ve never seen before. I certainly wasn’t aware of models that could do this during my early studies! The “facts on the ground” show that Deep Learning and Large Language Models (LLMs) can simply do different things than prior generations of models. This is our paradigm shift.
The Spectrum of Professional Perspectives
This tension is vividly reflected in a dialogue on an earlier LinkedIn post and blog, which has surfaced diverse viewpoints that illuminate the different facets of this challenge:
Academic Rigor:Max Martinelli (in private communications) grounds his perspective in foundational texts, noting that Russell & Norvig’s definition encompasses any system that “receives percepts from the environment and performs actions.” From this vantage point, even simple linear models qualify as AI. Yet he rightly acknowledges the nuance: the manual, iterative feature engineering common in traditional ratemaking “seems to violate the spirit of the definition.”
Pragmatic Focus:Chris Dolman questions the operational import of these distinctions beyond “marketing or communication problems.” His pragmatic lens rightly focuses on describing a model’s capability rather than debating its categorical boundary.
Industry Reality:Andrew Morgan and Gabriel Ryan highlight the tangible problem of “AI washing”—when traditional techniques are marketed as revolutionary, leading to resource misallocation and unfulfilled expectations.
Causal Complexity:Professor Fei Huang reminds us that even models aimed at “explaining” do not automatically establish causation, adding a crucial layer of consideration for a profession built on understanding risk drivers.
Semantic Evolution:Arthur da Silva captures the temporal nature of these terms by citing Kevin Weil: “AI is whatever hasn’t been done yet… once it’s been done and kind of works, then you call it machine learning.”
The New Paradigm: Representation Learning is the Key Ingredient
My core view is that the revolutionary ingredient fueling this paradigm shift is representation learning. I have been espousing this view since my early paper “AI in Actuarial Science” and built it out in “Believing the Bot”.
This is the ability of a model to ingest raw, unstructured data and autonomously learn its own features, or “representations,” of reality. This marks a fundamental departure from the old paradigm.
Consider this concrete actuarial example:
In the old paradigm (GLM), to model auto risk, an actuary must manually hypothesize and engineer features. We must explicitly tell the model to consider “Driver Age,” “Vehicle Type,” and perhaps create an interaction term for “Territory x Vehicle Age,” because we suspect these variables relate in a specific way. The model’s intelligence is constrained by our own imagination.
In the new paradigm (Deep Learning), we can feed a neural network raw telematics data – GPS streams, accelerometer readings, gyroscope data. The model itself might discover a complex, non-linear relationship between subtle braking patterns, the sharpness of turns, and time of day that no human would have hypothesized. It learns the features, creating its own high-dimensional representation of “risky driving.”
This is not only an improvement in accuracy – which deep learning models achieve in many actuarial domains – it is a change in the nature of discovery and modelling! This shift from hand-crafted features to learned representations is in my view the dividing line between traditional ML and the modern AI systems that are driving the current revolution.
Three Distinct Epochs of Algorithmic Intelligence
This paradigm shift becomes even clearer when we view computational history through three distinct phases:
1. The Calculation Era (Pre-2012)
This era was defined by models executing mathematical operations on human-engineered features. Intelligence meant following sophisticated but predetermined rules, a paradigm exemplified by GLMs.
2. The Perception Era (2012-Present)
This phase was sparked by deep learning, which enabled direct learning from raw sensory data. For the first time, models could develop visual understanding (CNNs) and process sequential patterns (RNNs), constructing their own internal representations of reality.
3. The Reasoning & Generative Era (2018-Present)
The current era, supercharged by Transformer architectures, has unlocked emergent synthesis and generation capabilities. Transformers move beyond being mere models; they are engines for compute over anything that can be embedded. By converting text, images, molecules, or user actions into a unified mathematical space (an embedding space), they can reason across domains in a way previously unimaginable. This is a shift from domain-specific analysis to a universal computational framework.
Consequences of the Shift: From Operations to Philosophy
Recognizing this as a true paradigm shift has profound consequences.
Governance: From Regulatory Clarity to Philosophical Challenge
On a practical level, claiming every GLM is AI renders new regulations meaningless through over-inclusion. But the challenge runs deeper. The new paradigm forces us to govern systems whose decision-making processes transcend human interpretability. This opacity is a philosophical one. How do we, as fiduciaries, maintain responsibility over systems whose reasoning we cannot fully comprehend? This is a question the old paradigm never had to ask.
Methodology: From Deductive to Inductive Science
The old paradigm was largely deductive. We started with a human-generated hypothesis (“I believe young drivers in sports cars are riskier”) and used a model to test it. The new paradigm is powerfully inductive. It sifts through vast datasets to discover complex correlative patterns that can inspire new causal investigations. This fundamentally changes the actuarial epistemology – our theory of how we come to know things about risk.
Strategy: Avoiding the Next AI Winter
Clear definitions are vital for credible strategy. The history of this field is littered with “AI winters” – periods of disillusionment and funding collapse caused by capabilities failing to match hype. Lumping GLMs and GPT-4/o3-pro under the same “AI” umbrella invites this same disillusionment. Precise language prevents resource misallocation and builds sustainable, realistic roadmaps for innovation. For instance, while a GLM is king for regulatory rate filing in some jurisdictions, GBMs and Deep Learning models are often superior choices for internal applications like fraud detection or marketing optimization, or for pricing where a pure performance lift is the goal and a formal filing is not required.
The Path Forward: A New Toolkit for a New Era
Navigating this new world requires an updated strategy.
A Practical Taxonomy for Actuarial Practice
Strategic Recommendations
Audit Your Model Portfolio. Classify systems based on whether they learn representations autonomously. This will clarify your true AI governance surface area.
Embrace a New Validation Mindset. Recognize that new models are incommensurable with old ones. Judging a Transformer on its inferential p-values is like judging a car on how well it eats hay. We need new metrics focused on out-of-sample performance, robustness, and the impact of emergent behaviors.
Govern the Ethics of Discovery. The inductive power of AI will uncover patterns that are predictive but may be ethically problematic or based on unfair proxies. We must proactively build ethical frameworks to govern not just our models, but the patterns they discover.
Prepare for Foundation Models. The next shift is from task-specific models to general-purpose foundation models. Actuaries will increasingly fine-tune these massive pre-trained systems rather than building models from scratch. This requires new skills in prompt engineering, model adaptation, and API integration.
Conclusion: Intellectual Honesty in Revolutionary Times
The vigor of this debate confirms we are at a critical juncture. Academic definitions that place GLMs within AI’s historical lineage are valid. Yet to ignore the clear, qualitative chasm between a system that calculates based on our instructions and one that learns to perceive the world on its own is to miss the revolution entirely.
Our task is not to discard the old paradigm – GLMs remain indispensable, elegant tools for the right problems. Rather, our duty is to name the new paradigm accurately, to understand its profound and sometimes unsettling implications, and to build the intellectual and ethical frameworks required to wield its power responsibly. It is time to see the world through the new lens.
A sincere thank you to Max Martinelli, Professor Fei Huang, Chris Dolman, Andrew Morgan, Gabriel Ryan, Davide Radwan, and Arthur da Silva for enriching this crucial discourse. Your perspectives strengthen our collective understanding as we navigate these transformative times.
As an actuary and researcher working at the intersection of actuarial science and artificial intelligence, I’ve been exploring how we can enhance our traditional actuarial toolkit with modern deep learning approaches while maintaining our professional standards and ethical principles. Let me share my current thinking on this evolution of our profession.
The Fusion of Classical and Modern Methods
A key insight that has emerged from my research is the distinction between general AI applications, like large language models, and specific AI tools designed for core actuarial tasks. While LLMs generate significant buzz, I believe the more profound impact in the short and medium term on actuarial work will come from specialized deep learning models adapted for insurance applications.
The LocalGLMnet architecture (Richman & Wüthrich, 2023a) represents one approach to creating inherently interpretable neural networks. By maintaining the same model structure as a GLM while allowing coefficients to vary smoothly with inputs, this architecture provides both interpretability and strong predictive performance. The LocalGLMnet is thus one example of how deep learning can be specialized for actuarial purposes.
The Canadian Institute of Actuaries’ research on mortality table construction (Goulet et al., 2022) provides a fascinating case study of this evolution. When comparing Whittaker-Henderson graduation to neural network approaches, we see that deep learning models can capture more complex relationships while still maintaining the essential characteristics that actuaries expect from mortality tables. The key insight is that we don’t need to choose between traditional actuarial principles and modern methodologies – we can synthesize both approaches to create more powerful and reliable models. This is the approach we took in a recent talk at ASSA’s 2024 Convention – deck attached below.
The core innovation we presented was the incorporation of Whittaker-Henderson (WH) smoothing directly into a neural network architecture through the loss function. This creates what could be called a “smoothness-aware” deep learning model that respects classical actuarial principles while leveraging modern computational capabilities.
This work represents a broader paradigm shift in actuarial science – one where we don’t simply replace traditional methods with black-box deep learning, but rather thoughtfully integrate classical actuarial principles into modern architectures. The presentation shows how this can be done while maintaining:
Professional standards for model interpretability
Actuarial judgment in parameter selection
Smooth and credible mortality patterns
Transfer learning capabilities across populations
This work demonstrates how thoughtful integration of classical actuarial principles with modern deep learning can produce models that are both more powerful and more aligned with actuarial professional standards. It provides a template for similar syntheses in other areas of actuarial work.
Classical actuarial principles, like credibility theory, shouldn’t be discarded as we adopt modern methods. Instead, in our recent work on the Credibility Transformer (Richman, Scognamiglio & Wüthrich, 2024), we show how traditional actuarial concepts can be integrated into state-of-the-art deep learning architectures, enhancing their performance and interpretability. This synthesis of old and new represents an exciting path forward for our profession.
Professional Considerations and Challenges
However, the adoption of AI methods raises important professional considerations. In recent work with Roseanne Harris and Mario Wüthrich (Harris et al., 2024), we examine how actuaries can embrace AI tools while remaining committed to professional and ethical principles that have long distinguished our field. Key requirements include:
Ensuring model understandability and interpretability
Avoiding bias and discrimination in model outputs
Maintaining strong governance frameworks
Adapting professional education to cover new methodologies
Exercising appropriate professional judgment
The actuarial profession is at an inflection point. As discussed in my recent essay (Richman, 2024), choices made about embracing AI and ML in the next few years will determine if we thrive or merely survive in the age of AI. The promising results from applying neural networks to mortality modeling in the Canadian Institute of Actuaries’ research (Goulet et al., 2022), where I contributed to developing new approaches, show how we can adapt powerful tools to meet actuarial standards of practice.
The AI-Enhanced Actuary
Looking ahead, I envision what I call the “AI-enhanced actuary” – a professional who leverages both classical actuarial expertise and AI capabilities to:
Build more accurate and efficient models
Incorporate new data sources
Automate routine tasks
Focus on high-level strategic decisions
Ensure ethical implementation of AI systems
This evolution represents a natural progression that builds upon our foundation of mathematical and statistical techniques while embracing new methodological advances. The integration of AI into actuarial practice creates opportunities for innovation while maintaining our core professional values.
Meeting Professional Standards
A critical aspect of this evolution is ensuring that new methods comply with professional standards. Recent work has shown how we can adapt deep learning approaches to meet key requirements:
Model understanding through inherently interpretable architectures
Prevention of unwanted bias through specialized constraints
Uncertainty quantification through modern techniques
Reproducibility through appropriate model design
The Future Path
The actuarial profession has always evolved with new methodological developments. The current AI revolution offers us the chance to enhance our capabilities while remaining true to our professional principles. The key will be thoughtfully embracing these new tools, ensuring they serve our ultimate goal of managing risk and uncertainty for the benefit of society.
Goulet, S., Balona, C., Richman, R., & Bennet, S. (2022). Canadian mortality table construction alternative methods: Generalized additive model and neural network model. Canadian Institute of Actuaries.
A major challenge in actuarial modelling is how to deal with categorical variables with many levels (i.e. high cardinality). This is often encountered when one has a rating factor like car model, which can take on one of thousands of values, some of which have significant exposure and others with exposure close to zero.
In a new paper with Mario Wüthrich, we show how to incorporate these variables into neural networks using different types of regularized embeddings, including using variational inference. We also consider both the case of standalone variables, as well as the case of variables with a natural hierarchy, which lend themselves to being modelled with recurrent neural networks or Transformers. On a synthetic dataset, the proposed methods provide a significant gain in performance compared to other techniques.
We show the problem we are trying to solve in the image below, which illustrates how the most detailed covariate in the synthetic dataset – Vehicle Detail – can produce observed values vastly different from the true value due to sampling error.
A special thank you to Michael Mayer, PhD for input into the paper and interesting discussions on the topic!
In these past days I had the privilege of presenting on the topic of “Explainable deep learning for actuarial modelling” to Munich Re‘s actuarial and data science teams. In this talk I covered several explainable deep learning methods: the CAXNN, LocalGLMnet and ICEnet models.
My slides are attached below if this is of interest.
I am pleased to share a new paper on adding smoothness and monotonicity constraints to neural networks. This is a joint work with Mario Wüthrich.
In this paper, we propose a novel method for enforcing smoothness and monotonicity constraints within deep learning models used for actuarial tasks, such as pricing. The method is called ICEnet, which stands for Individual Conditional Expectation network. It’s based on augmenting the original data with pseudo-data that reflect the structure of the variables that need to be constrained. We show how to design and train the ICEnet using a compound loss function that balances accuracy and constraints, and we provide example applications using real-world datasets. The structure of the ICEnet is shown in the following figure.
Applying the model produces predictions that are smooth and vary with risk factors in line with intuition. Below is an example where applying constraints forces a neural network to produce predictions of claims frequency that increase with population density and vehicle power.
I’m excited to share our latest research paper on using the LocalGLMnet, an explainable deep learning model, to forecast mortality rates for multiple populations. This paper is joint work with Francesca Perla, Salvatore Scognamiglio and Mario Wüthrich.
Mortality forecasting is crucial for actuarial applications in life insurance and pensions, as well as for demographic planning. However, most existing machine learning models for this task are not transparent. We wanted to bridge this gap by adapting the LocalGLMnet, which preserves the interpretable structure of generalized linear models while allowing for variable selection and interaction identification.
We applied our model to data from the Human Mortality Database (HMD) and the United States Mortality Database, and found that it produced highly accurate forecasts that can be explained by autoregressive time-series models of mortality rates. We also showed how regularizing and denoising our model can improve its performance even further.
The image below shows a comparison of forecasting results between different models for the HMD.
The fantastic new resource from Mario Wüthrich and Michael Merz on statistical learning for actuarial work has just been published by Springer. This is open access and freely available here:
The Institute and Faculty of Actuaries (IFoA) has been key to my journey as an actuary, providing my initial professional education and, subsequently, many great opportunities to contribute and learn more along the way. This made receiving the 2022 Outstanding Achievement award from the IFoA’s GI Board yesterday very special:
The award was given in connection with my research into applying machine and deep learning within actuarial work. My hope is that more actuaries within the vibrant community attending the 2022 GIRO conference will be motivated to apply these techniques in their own work.
Thank you again to the #GIRO2022 organizing committee and the #ifoa for a fantastic event!
Last week was the ASSA 2022 Convention held in Cape Town, South Africa. We were delighted to hear that our paper “LASSO Regularization within the LocalGLMnet Architecture” won the RGA Prize for the Best Convention Paper and the Swiss Re Prize for the Best Paper on Risk or Reinsurance.
I’m most appreciative of the Actuarial Society of South Africa (ASSA)’s making this award and hope that actuaries will start to use the method proposed for interpretable machine learning. Thanks very much to Professor Mario Wüthrich for this project!
I was also pleased to hear that another paper, Mind the Gap – Safely Incorporating Deep Learning Models into the Actuarial Toolkit, was highly commended by ASSA’s Research Committee. This paper can be found here:
