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Homogeneous and isotropic solutions to the relativistic Euler equations are known to be unstable on a Minkowski background. However, for FLRW models with a fast expansion rate, relativistic fluids stabilize. This scenario suggests a transition between stable and unstable behavior, somewhere along a family of spacetimes parametrized by their expansion rate. In this talk we will discuss this phase transition for various equations of state, focusing on the regime of linear and decelerated expansion. This is based on recent analytical results, complemented by numerical analysis.

• Speaker: Max Ofner (Vienna)
• Monday 03 March 2025, 15:00-16:00
• Venue: MR13.
• Series: Partial Differential Equations seminar; organiser: Dr Greg Taujanskas.

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Abstract not available

• Speaker: Jeremy Hahn (Cambridge)
• Wednesday 05 March 2025, 16:00-17:00
• Venue: CMS, MR15.
• Series: Differential Geometry and Topology Seminar; organiser: Oscar Randal-Williams.

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From water adsorption on a hematite surface to 2D graphene networks on copper, the talk will focus on various surface studies performed at the I09 beamline of Diamond Light Source, the UK’s national synchrotron facility. The I09 beamline is a unique two-colour beamline utilising X-ray Standing Waves (XSW) which, as will be showcased, can probe element-specific adsorption heights, h, with high precision (Δh ≈ 0.02 Å).

• Speaker: Fulden Eratam, Diamond Light Source, Harwell
• Thursday 13 March 2025, 15:00-16:00
• Venue: Mott Seminar Room, Cavendish Laboratory.
• Series: Physics and Chemistry of Solids Group; organiser: Stephen Walley.

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Impact sensitivity (literally, how hard do you need to hit a material to cause it to initiate) is a critically important safety metric and performance indicator for explosives. It’s a challenging property to measure experimentally, however, which has fuelled the need for physical models to understand the link between structure and material property. While predicting property from structure is valuable, perhaps an even greater prize is having the ability to run the process in reverse, i.e. to predict structures likely to present with a desired property. In this talk I will outline, (i) how we can link impact sensitivity to structure through a first-principles physical model, and (ii) how we can broaden out the pool of structures studied through a supervised machine learning study, using features derived from the physical model. The output from this work are tools that can guide the discovery, design and synthesis of safer explosives.

• Speaker: Professor Carole Morrison, University of Edinburgh
• Wednesday 12 March 2025, 14:30-15:30
• Venue: Unilever Lecture Theatre, Yusuf Hamied Department of Chemistry.
• Series: Theory - Chemistry Research Interest Group; organiser: Lisa Masters.

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Abstract not available

• Speaker: Callum Pearman
• Friday 09 May 2025, 16:00-17:00
• Venue: Tea Room, Old House.
• Series: Bullard Laboratories Tea Time Talks; organiser: David Al-Attar.

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=== Hybrid talk ===

Join Zoom Meeting https://cam-ac-uk.zoom.us/j/87143365195?pwd=SELTNkOcfVrIE1IppYCsbooOVqenzI.1

Meeting ID: 871 4336 5195

Passcode: 541180

Note unusual time

• Speaker: Francisco Ferreira Ruiz (Royal Holloway, University of London)
• Wednesday 12 March 2025, 17:00-18:00
• Venue: MR14 Centre for Mathematical Sciences.
• Series: Formalisation of mathematics with interactive theorem provers ; organiser: Anand Rao Tadipatri.

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If E is an elliptic curve over Q with split multiplicative reduction at p, then the p-adic L-function associated with E vanishes at s=1 independently of whether the complex L-function vanishes. In this case, one has an “exceptional zero formula” relating the first derivative of the p-adic L-function to the complex L-function multiplied by a certain L-invariant. This L-invariant can be interpreted in several ways—on the automorphic side for example, L-invariants parameterise part of the p-adic local Langlands correspondence for GL(2)(Q_p).

In this talk, I will discuss an exceptional zero formula for (not necessarily essentially self-dual) regular algebraic, cuspidal automorphic representations of GL(3) which are Steinberg at p. The formula involves an automorphic L-invariant constructed by Gehrmann. Joint work with Daniel Barrera and Chris Williams.

• Speaker: Andrew Graham (Oxford)
• Tuesday 18 February 2025, 14:30-15:30
• Venue: MR13.
• Series: Number Theory Seminar; organiser: Rong Zhou.

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In Navier-Stokes (NS) turbulence, large-scale turbulent flows determine small-scale flows; in other words, small-scale flows are synchronized to large-scale flows. In 3D turbulence, previous numerical studies suggest that the critical length separating these two scales is determined by the Kolmogorov length. In this talk, I will introduce our theoretical framework for characterizing synchronization phenomena [1]. Specifically, it provides a computational method for the exponential rate of convergence to the synchronized state, and identifies the critical length based on the NS equations via the “transverse” Lyapunov exponent. I will also discuss the synchronization property of 2D NS turbulence and how it differs from the 3D case [2]. These insights into synchronization and critical length scales are essential for developing machine-learning closure models for turbulence, in particular their stable reproducibility [3]. Finally, I will illustrate how “generalized” synchronization is crucial for predicting chaotic dynamics [4].

[1] M. Inubushi, Y. Saiki, M. U. Kobayashi, and S. Goto, Characterizing small-scale dynamics of Navier-Stokes turbulence with transverse Lyapunov exponents: A data assimilation approach, Phys. Rev. Lett. 131, 254001 (2023).

[2] M. Inubushi and C. P. Caulfield (in preparation).

[3] S. Matsumoto, M. Inubushi, and S. Goto, Stable reproducibility of turbulence dynamics by machine learning, Phys. Rev. Fluids 9, 104601 (2024).

[4] A. Ohkubo and M. Inubushi, Reservoir computing with generalized readout based on generalized synchronization, Sci. Rep. 14, 30918 (2024).

• Speaker: Professor Masanobu Inubushi, Tokyo University of Science
• Friday 14 February 2025, 16:00-17:00
• Venue: MR2.
• Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.

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Abstract not available

• Speaker: Jeremy Hahn (Cambridge)
• Wednesday 05 March 2025, 10:30-11:30
• Venue: CMS, MR15.
• Series: Differential Geometry and Topology Seminar; organiser: Oscar Randal-Williams.

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Dario Klingenberg: Using nonlinear optimisation to investigate shear turbulence

Much research has focused on understanding how flows transition to turbulence. However, an equally important question is how, once established, turbulence is sustained. Interestingly, the same methods used for the transition problem are also useful in the turbulent setting, despite the stark differences between the two. In this work, I will use nonlinear optimisation to find the initial perturbation that, over a given time horizon, experiences the highest energy growth in channel flow with a friction Reynolds number of 180. Although the precise form of the initial condition depends on this time horizon, and also the initial energy available to it, it turns out that over a wide range in this parameter space, optimals with very similar dynamics arise. Interestingly, many important aspects of these dynamics are consistent with observations made in real turbulence. Based on these results, it is argued that nonlinear optimals are a conceptually simple and valuable concept to investigate turbulence.

Philipp Vieweg: Large-scale flow structures and their induced mixing in horizontally extended forced stratified shear flows

Covering about 70% of Earth’s surface, the oceans represent the biggest heat sink in climate and weather models. However, our understanding of the oceans’ inherent turbulent processes is still far from complete. Here, we study an idealised or simplified configuration that is stably stratified and continuously forced. The basic configuration has been introduced by Smith et al. (Journal of Fluid Mechanics 910, A42 (2021)) for small numerical domains and may be susceptible to Kelvin-Helmholtz instabilities. We extend these results to horizontally extended domains by conducting direct numerical simulations using the GPU -accelerated open-source spectral element solver NekRS.

On the one hand, we analyse the formation and convergence of large-scale flow structures in extended domains. Due to the anisotropic nature of the flow, this involves separate treatments of the stream-wise and span-wise direction. On the other hand, we analyse the impact of these flow structures on their induced mixing of the two layers of fluid.

Based on these structural and statistical analyses of stratified turbulent flows, this research contributes to advancing our current understanding of oceanic flows and allowing for improved predictions using global simulations that involve turbulence modelling.

James Shemilt: Viscoplastic dynamics of mucus transport during coughing

Coughing is a mechanism by which excess mucus is cleared from the lungs’ airways. In obstructive lung diseases such as cystic fibrosis, the rheology of mucus changes, including its yield stress increasing, and coughing can become a central mechanism for mucus clearance. I will present thin-film modelling of a viscoplastic liquid layer driven by high-speed confined air flow, which is a model for mucus transport during a cough that accounts for the yield stress of mucus. Numerical solutions of the thin-film equations, and travelling-wave solutions, are used to quantify how the liquid’s yield stress alters the dynamics. Criteria are determined for finite-time blow-up of solutions, where the liquid layer reaches the upper wall of the channel. I will also discuss how these theoretical results compare with experiments in which viscoplastic liquid layers are exposed to high-speed air flow.

Fabio Pino: Stability and Dynamics of Evaporating/Condensing Liquid Film Flows

Pulsating heat pipes (PHPs) have emerged as an effective heat transfer device for small-scale electronics. Their enhanced thermal performance relies on the periodic evaporation and condensation of a liquid film lining the pipe walls. However, an incomplete understanding of the phase change mechanism limits its broader application.

This research addresses this gap by investigating the linear and nonlinear stability of a 3D evaporating/condensing liquid film over an inclined plate. To reduce the complexity of the governing equations, we will develop a liquid film integral boundary layer model. This model will capture key liquid film dynamics, including phase change, inertia, and thermo-capillarity. The integral model’s validation will involve comparing the linear stability properties with the solution to the linearised full governing equations and assessing nonlinear dynamics against COMSOL simulations of the governing equations.

Based on the integral model, the continuation and bifurcation analysis of steady-state solutions will reveal how the liquid film’s behaviour develops as the evaporation rate or the Reynolds number varies. This analysis will identify key transitions and stability shifts affecting system performance. In addition, we will investigate the transient behaviour of disturbances via a nonlinear, nonmodal stability analysis. This approach will uncover nonlinear mechanisms that drive instabilities, such as the impact of temperature variations on the solid substrate during the evaporation or condensation phase.

The findings of this research will provide deeper insight into liquid film dynamics and develop a predictive reduced-order model for PHP systems. Additionally, these will be critical for designing optimal control laws based on liquid film stability properties, enhancing the evaporation/condensation mechanism, and guiding the design of more stable and efficient PHP configurations.

Gergely Buza: Rigorization of model reduction in fluid dynamics

The emergence of data-driven methods has fueled a newfound interest in the utilization of nonlinear tools from dynamical systems theory. In fluid dynamics, prominent examples are Koopman eigenfunctions (through dynamic mode decomposition) and spectral submanifolds. Due to their immense popularity, both of these techniques have been studied extensively, to the point that most aspects regarding their implementation are now fully fleshed out. However, there is one issue that has remained mostly untouched, and it is perhaps the most pressing one — the mathematical foundation of these tools. While the theory is well understood in the case of finite-dimensional systems, fluid dynamics is inherently infinite-dimensional, which calls for a more careful assessment. The talk will provide existence and uniqueness results for spectral submanifolds, smooth invariant foliations and Koopman eigenfunctions in the full, infinite-dimensional phase space of the Navier-Stokes system, alongside avenues to make the approximation procedure rigorous.

• Speaker: Post-doc talks, DAMTP
• Friday 21 February 2025, 14:00-17:00
• Venue: MR2.
• Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.

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Recently, we optimized small (vDZP), deeply contracted AO basis sets in molecular DFT calculations using standard ECPs for all elements up to radon1. This strategy is further- more applied to a minimal set of AOs which — as a totally new ingredient — is made adap- tive, i.e., radially different for symmetry distinct atoms in a molecule. The ”breathing” of the AOs in the molecular environment is parameterized efficiently by on-the-fly computed effec- tive atomic charges (obtained by a new EEQ charge model) and coordination numbers. This so-called q-vSZP set2 provides in typical DFT applications results of about or better than DZ quality. It forms the basis of our third-generation tight-binding model g-xTB (g=general). This includes non-local Fock-exchange as well as other new, many-center Hamiltonian terms (e.g., atomic correction potentials, ACP ). It aims at general purpose applicability in chem- istry and more closely approaches DFT accuracy (actually ωB97M-V/aTZ3) than previous semi-empirical methods at only slightly increased computational cost (factor of 1.5 compared to GFN2 xTB). It will be consistently available for all elements Z=1-103 with f-electrons in cluded for lanathanides/actinides. The talk describes key improvements of the underlying TB theory as well as extensive benchmarking on a wide range of standard thermochemistry sets. [1] M. Müller, A. Hansen, S. Grimme, J. Chem. Phys. 158 (2023), 014103 [2] M. Müller, A. Hansen, S. Grimme, J. Chem. Phys. 159 (2023), 164108. Revision: JPC A , doi:10.1021/acs.jpca.4c06989 [3] N. Mardirossian and M. Head-Gordon, J. Chem. Phys. 144 (2016), 214110

• Speaker: Professor Stefan Grimme, University of Bonn
• Wednesday 05 March 2025, 14:30-15:30
• Venue: Unilever Lecture Theatre, Yusuf Hamied Department of Chemistry.
• Series: Theory - Chemistry Research Interest Group; organiser: Lisa Masters.

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In Navier-Stokes (NS) turbulence, large-scale turbulent flows determine small-scale flows; in other words, small-scale flows are synchronized to large-scale flows. In 3D turbulence, previous numerical studies suggest that the critical length separating these two scales is determined by the Kolmogorov length. In this talk, I will introduce our theoretical framework for characterizing synchronization phenomena [1]. Specifically, it provides a computational method for the exponential rate of convergence to the synchronized state, and identifies the critical length based on the NS equations via the “transverse” Lyapunov exponent. I will also discuss the synchronization property of 2D NS turbulence and how it differs from the 3D case [2]. These insights into synchronization and critical length scales are essential for developing machine-learning closure models for turbulence, in particular their stable reproducibility [3]. Finally, I will illustrate how “generalized” synchronization is crucial for predicting chaotic dynamics [4].

[1] M. Inubushi, Y. Saiki, M. U. Kobayashi, and S. Goto, Characterizing small-scale dynamics of Navier-Stokes turbulence with transverse Lyapunov exponents: A data assimilation approach, Phys. Rev. Lett. 131, 254001 (2023).

[2] M. Inubushi and C. P. Caulfield (in preparation).

[3] S. Matsumoto, M. Inubushi, and S. Goto, Stable reproducibility of turbulence dynamics by machine learning, Phys. Rev. Fluids 9, 104601 (2024).

[4] A. Ohkubo and M. Inubushi, Reservoir computing with generalized readout based on generalized synchronization, Sci. Rep. 14, 30918 (2024).

• Speaker: Professor Masanobu Inubushi, Tokyo University of Science
• Friday 14 February 2025, 16:00-17:00
• Venue: MR2.
• Series: Fluid Mechanics (DAMTP); organiser: Professor Grae Worster.

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Aerosols are unique microcompartments central to areas as diverse as climate and air pollution, disease transmission, and chemical synthesis. Resolving their roles in each of these areas is challenging. For instance, the surface composition of aerosol droplets is key to predicting cloud droplet number concentrations, understanding atmospheric pollutant transformation, and interpreting observations of accelerated droplet chemistry. However, direct measurement of the surface properties of aerosol droplets is challenging, even though such measurements are necessary, as surface-bulk partitioning is strongly affected by the droplet’s surface area-to-volume ratio. In this presentation, we will discuss new advances to characterise the equilibrium and dynamic surface properties of picolitre volume droplets, gaining important insights that bear directly on our understanding of how cloud droplets form in the atmosphere and how chemical reactions may proceed in finite-volume systems. We will also describe a new mass spectrometry approach enabling sensitive, high throughput chemical analysis of picolitre droplets, facilitating more robust studies of the factors governing chemical reactivity in microcompartments.

Bio: Bryan Bzdek is Proleptic Associate Professor in the School of Chemistry, University of Bristol. He earned a B.S. degree in Chemistry at Bucknell University and a Ph.D. in Chemistry at the University of Delaware. He performed postdoctoral studies with Jonathan P. Reid, and then began his independent career at the University of Bristol in 2017 as a NERC Independent Research Fellow. His research on the physical and analytical chemistry of aerosols spans applications in atmospheric science and health. He is a recipient of the Kenneth T. Whitby (2024) Award from the American Association for Aerosol Research, the Marlow Prize (2023) from the Royal Society of Chemistry, and the Philip Leverhulme Prize (2022) from the Leverhulme Trust. During the COVID -19 pandemic, his research altered UK government guidance in the performing arts and the NHS infection prevention and control manual. He also gave many print and radio interviews about aerosols and COVID -19 to organisations including US public radio, BBC , CBS, and CNN .

RSC 2023 Faraday Early Career Prize: Marlow Prize Winner

• Speaker: Dr Bryan Bzdek, University of Bristol
• Tuesday 25 February 2025, 14:00-15:00
• Venue: Pfizer Lecture Theatre, Department of Chemistry.
• Series: Physical Chemistry Research Interest Group; organiser: David Madden.

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Due to its importance in the construction of ships, wood was one of the first substances to have the velocity dependence of its resistance to impact quantified. This was achieved in England and France early in the 19th century. Techniques for measuring the high-rate mechanical properties of wood were developed around the start of the 20th century. These studies involved drop-weight and pendulum machines to quantify the dynamic fracture toughness of timbers and were mostly performed by the US Forestry Service. It was not until 1977 that the first high-rate compression stress-strain curves of wood were obtained using the Kolsky bar, despite this device having been developed in Britain in the 1940s. It took until the mid-1990s and the desire to use wood to cushion the drop-impact of vessels used to transport dangerous waste that Kolsky bar studies of wood began in earnest in Britain, the Czech Republic and Russia. Even so, to date fewer than 100 such studies have been published compared to nearly 5,000 for metals. The seminar will summarize the effects of anisotropy, stress state, multiple repeat loading, moisture content, temperature, and density on the high-rate properties of a wide range of woods. The seminar will finish with suggestions for what needs doing in the future. A review paper on this topic has recently been accepted for publication in ‘Journal of Dynamic Behavior of Materials’.

• Speaker: Stephen Walley, PCS Group, Cavendish Laboratory
• Thursday 01 May 2025, 15:00-16:00
• Venue: Mott Seminar Room, Cavendish Laboratory.
• Series: Physics and Chemistry of Solids Group; organiser: Stephen Walley.

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Better understanding of the origin and behaviour of fatigue cracks should lead to improved engineering design and alloying strategies for structural metals. The surface stresses caused by persistent slip bands, including a zone of infinite tensile stress at the edge of each band, seem an inevitable consequence of elastic non-linearity and hard to combat, except perhaps by the present expensive methods of shot-peening or surface removal. But the underlying process of jog movement to eliminate screw dislocation dipoles should be susceptible to control. It is important to understand better the main engineering problem: is design against persistent slip the metallurgist’s answer to crack-proof rotating machinery?

• Speaker: Mick Brown, Cavendish Laboratory
• Thursday 08 May 2025, 15:00-16:00
• Venue: Mott Seminar Room, Cavendish Laboratory.
• Series: Physics and Chemistry of Solids Group; organiser: Stephen Walley.

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Alan Turing is best remembered as one of the leading code breakers of Bletchley Park during World War II. It was Turing’s brilliant insights and mathematical mind that helped to break Enigma, the apparently unbreakable code used by the German military. We present a history of both Alan Turing and the Enigma machine, leading to this triumph of mathematical ingenuity.

• Speaker: James Grime, Institute of Continuing Education
• Monday 03 March 2025, 19:15-21:00
• Venue: Lightfoot Room, Divinity School, St John's College, Cambridge, CB2 1TP.
• Series: Cambridge Statistics Discussion Group (CSDG); organiser: Peter Watson.

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Abstract not available

• Speaker: Wendelin Werner (Cambridge)
• Tuesday 11 February 2025, 14:00-15:00
• Venue: MR12.
• Series: Probability; organiser: ww295.

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Elliptic curves are one of the simplest non-trivial objects in algebraic geometry, which are pervasive in modern number theory, but also see applications in point counting algorithms and public key cryptography. Due to their geometric nature, formalising a working definition typically requires a lot of technical machinery, let alone any non-trivial results. Yet, the Lean community has managed to formalise two of the most fundamental theorems in the theory of elliptic curves, with scope for many more projects. In this talk, I will explain these theorems, and how we inadvertently discovered new proofs in our formalisation attempts.

=== Hybrid talk ===

Join Zoom Meeting https://cam-ac-uk.zoom.us/j/87143365195?pwd=SELTNkOcfVrIE1IppYCsbooOVqenzI.1

Meeting ID: 871 4336 5195

Passcode: 541180

• Speaker: David Angdinata (University College London)
• Thursday 13 February 2025, 17:00-18:00
• Venue: MR14 Centre for Mathematical Sciences.
• Series: Formalisation of mathematics with interactive theorem provers ; organiser: Anand Rao Tadipatri.

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Sea ice plays a key role in Earth’s climate system and exhibits significant seasonal variability as it advances and retreats across the Arctic and Antarctic every year. The production of sea ice forecasts provides great scientific and practical value to stakeholders across the polar regions, informing shipping, conservation, logistics, and the daily lives of inhabitants of local communities. Machine learning offers a promising means by which to develop such forecasts, capturing the nonlinear dynamics and subtle spatiotemporal patterns at play as effectively—if not more effectively—than conventional physics-based models. In particular, the ability of deep generative models to produce probabilistic forecasts which acknowledge the inherent stochasticity of sea ice processes and represent uncertainty by design make them a sensible choice for the task of sea ice forecasting. Diffusion models, a class of deep generative models, present a strong option given their state-of-the-art performance on computer vision tasks and their strong track record when adapted to spatiotemporal modelling tasks in weather and climate domains. In this talk, I will present preliminary results from a IceNet-like [1] diffusion model trained to autoregressively forecast daily, 6.25 km resolution sea ice concentration in the Bellingshausen Sea along the Antarctic Peninsula. I will also touch on the downstream applications for these forecasts, from conservation to marine route planning, which are under development at the British Antarctic Survey (BAS). I welcome ideas and suggestions for improvement and look forward to discussing opportunities for collaboration within and beyond BAS .

[1] Andersson, Tom R., et al. “Seasonal Arctic sea ice forecasting with probabilistic deep learning.” Nature communications 12.1 (2021): 5124. https://www.nature.com/articles/s41467-021-25257-4

• Speaker: Andrew McDonald, University of Cambridge and British Antarctic Survey
• Wednesday 12 February 2025, 13:00-14:00
• Venue: BAS Seminar Room 2; https://ukri.zoom.us/j/96472472041.
• Series: British Antarctic Survey - Polar Oceans seminar series; organiser: Dr Birgit Rogalla.

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In a supervised learning setting, a model fitting algorithm is unstable if small perturbations to the input (the training data) can often lead to large perturbations in the output (say, predictions returned by the fitted model). Algorithmic stability is a desirable property with many important implications such as generalization and robustness, but testing the stability property empirically is known to be impossible in the setting of complex black-box models. In this work, we establish that bagging any black-box regression algorithm automatically ensures that stability holds, with no assumptions on the algorithm or the data. Furthermore, we construct a new framework for defining stability in the context of classification, and show that using bagging to estimate our uncertainty about the output label will again allow stability guarantees for any black-box model. This work is joint with Jake Soloff and Rebecca Willett.

Evaluating a black-box algorithm: stability, risk, and model comparisons

When we run a complex algorithm on real data, it is standard to use a holdout set, or a cross-validation strategy, to evaluate its behavior and performance. When we do so, are we learning information about the algorithm itself, or only about the particular fitted model(s) that this particular data set produced? In this talk, we will establish fundamental hardness results on the problem of empirically evaluating properties of a black-box algorithm, such as its stability and its average risk, in the distribution-free setting. This work is joint with Yuetian Luo and Byol Kim.

A wine reception in the Central Core will follow this lecture

• Speaker: Rina Foygel Barber (Chicago)
• Thursday 13 March 2025, 16:00-17:00
• Venue: Centre for Mathematical Sciences MR2.
• Series: Peter Whittle Lecture; organiser: HoD Secretary, DPMMS.

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