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Gibbs posteriors are proportional to a prior distribution multiplied by an exponentiated loss function, with a key tuning parameter weighting information in the loss relative to the prior and providing a control of posterior uncertainty. Gibbs posteriors provide a principled framework for likelihood-free Bayesian inference, but in many situations, including a single tuning parameter inevitably leads to poor uncertainty quantification. In particular, regardless of the value of the parameter, credible regions have far from the nominal frequentist coverage even in large samples. We propose a sequential extension to Gibbs posteriors to address this problem. We prove the proposed sequential posterior exhibits concentration and a Bernstein-von Mises theorem, which holds under easy to verify conditions in Euclidean space and on manifolds. As a byproduct, we obtain the first Bernstein-von Mises theorem for traditional likelihood-based Bayesian posteriors on manifolds. All methods are illustrated with an application to principal component analysis.

Model-based reinforcement learning has drawn considerable interest in recent years, given its promise to improve sample efficiency. Moreover, when using deep-learned models, it is potentially possible to learn compact models from complex sensor data. However, the effectiveness of these learned models, particularly their capacity to plan, i.e., to improve the current policy, remains unclear. In this work, we study MuZero, a well-known deep model-based reinforcement learning algorithm, and explore how far it achieves its learning objective of a value-equivalent model and how useful the learned models are for policy improvement. Amongst various other insights, we conclude that the model learned by MuZero cannot effectively generalize to evaluate unseen policies, which limits the extent to which we can additionally improve the current policy by planning with the model.

The distribution-free chain ladder of Mack justified the use of the chain ladder predictor and enabled Mack to derive an estimator of conditional mean squared error of prediction for the chain ladder predictor. Classical insurance loss models, i.e. of compound Poisson type, are not consistent with Mack's distribution-free chain ladder. However, for a sequence of compound Poisson loss models indexed by exposure (e.g. number of contracts), we show that the chain ladder predictor and Mack's estimator of conditional mean squared error of prediction can be derived by considering large exposure asymptotics. Hence, quantifying chain ladder prediction uncertainty can be done with Mack's estimator without relying on the validity of the model assumptions of the distribution-free chain ladder.

Binwise Variance Scaling (BVS) has recently been proposed as a post hoc recalibration method for prediction uncertainties of machine learning regression problems that is able of more efficient corrections than uniform variance (or temperature) scaling. The original version of BVS uses uncertainty-based binning, which is aimed to improve calibration conditionally on uncertainty, i.e. consistency. I explore here several adaptations of BVS, in particular with alternative loss functions and a binning scheme based on an input-feature (X) in order to improve adaptivity, i.e. calibration conditional on X. The performances of BVS and its proposed variants are tested on a benchmark dataset for the prediction of atomization energies and compared to the results of isotonic regression.

We call into question the recently popularized method of direct model editing as a means of correcting factual errors in LLM generations. We contrast model editing with three similar but distinct approaches that pursue better defined objectives: (1) retrieval-based architectures, which decouple factual memory from inference and linguistic capabilities embodied in LLMs; (2) concept erasure methods, which aim at preventing systemic bias in generated text; and (3) attribution methods, which aim at grounding generations into identified textual sources. We argue that direct model editing cannot be trusted as a systematic remedy for the disadvantages inherent to LLMs, and while it has proven potential in improving model explainability, it opens risks by reinforcing the notion that models can be trusted for factuality. We call for cautious promotion and application of model editing as part of the LLM deployment process, and for responsibly limiting the use cases of LLMs to those not relying on editing as a critical component.

We describe a polynomial time algorithm that takes as input a polygon with axis-parallel sides but irrational vertex coordinates, and outputs a set of as few rectangles as possible into which it can be dissected by axis-parallel cuts and translations. The number of rectangles is the rank of the Dehn invariant of the polygon. The same method can also be used to dissect an axis-parallel polygon into a simple polygon with the minimum possible number of edges. When rotations or reflections are allowed, we can approximate the minimum number of rectangles to within a factor of two.

Data-driven approximations of ordinary differential equations offer a promising alternative to classical methods of discovering a dynamical system model, particularly in complex systems lacking explicit first principles. This paper focuses on a complex system whose dynamics is described with a system of such equations, coupled through a complex network. Numerous real-world systems, including financial, social, and neural systems, belong to this class of dynamical models. We propose essential elements for approximating these dynamical systems using neural networks, including necessary biases and an appropriate neural architecture. Emphasizing the differences from static supervised learning, we advocate for evaluating generalization beyond classical assumptions of statistical learning theory. To estimate confidence in prediction during inference time, we introduce a dedicated null model. By studying various complex network dynamics, we demonstrate that the neural approximations of dynamics generalize across complex network structures, sizes, and statistical properties of inputs. Our comprehensive framework enables accurate and reliable deep learning approximations of high-dimensional, nonlinear dynamical systems.

A core principle in statistical learning is that smoothness of target functions allows to break the curse of dimensionality. However, learning a smooth function seems to require enough samples close to one another to get meaningful estimate of high-order derivatives, which would be hard in machine learning problems where the ratio between number of data and input dimension is relatively small. By deriving new lower bounds on the generalization error, this paper formalizes such an intuition, before investigating the role of constants and transitory regimes which are usually not depicted beyond classical learning theory statements while they play a dominant role in practice.

Non-convex optimization is ubiquitous in modern machine learning. Researchers devise non-convex objective functions and optimize them using off-the-shelf optimizers such as stochastic gradient descent and its variants, which leverage the local geometry and update iteratively. Even though solving non-convex functions is NP-hard in the worst case, the optimization quality in practice is often not an issue -- optimizers are largely believed to find approximate global minima. Researchers hypothesize a unified explanation for this intriguing phenomenon: most of the local minima of the practically-used objectives are approximately global minima. We rigorously formalize it for concrete instances of machine learning problems.

Compared with cheap addition operation, multiplication operation is of much higher computation complexity. The widely-used convolutions in deep neural networks are exactly cross-correlation to measure the similarity between input feature and convolution filters, which involves massive multiplications between float values. In this paper, we present adder networks (AdderNets) to trade these massive multiplications in deep neural networks, especially convolutional neural networks (CNNs), for much cheaper additions to reduce computation costs. In AdderNets, we take the $\ell_1$-norm distance between filters and input feature as the output response. The influence of this new similarity measure on the optimization of neural network have been thoroughly analyzed. To achieve a better performance, we develop a special back-propagation approach for AdderNets by investigating the full-precision gradient. We then propose an adaptive learning rate strategy to enhance the training procedure of AdderNets according to the magnitude of each neuron's gradient. As a result, the proposed AdderNets can achieve 74.9% Top-1 accuracy 91.7% Top-5 accuracy using ResNet-50 on the ImageNet dataset without any multiplication in convolution layer.