Atmospheric Transport Modeling of CO$_2$ with Neural Networks

Accurately describing the distribution of CO$_2$ in the atmosphere with atmospheric tracer transport models is essential for greenhouse gas monitoring and verification support systems to aid implementation of international climate agreements. Large deep neural networks are poised to revolutionize weather prediction, which requires 3D modeling of the atmosphere. While similar in this regard, atmospheric transport modeling is subject to new challenges. Both, stable predictions for longer time horizons and mass conservation throughout need to be achieved, while IO plays a larger role compared to computational costs. In this study we explore four different deep neural networks (UNet, GraphCast, Spherical Fourier Neural Operator and SwinTransformer) which have proven as state-of-the-art in weather prediction to assess their usefulness for atmospheric tracer transport modeling. For this, we assemble the CarbonBench dataset, a systematic benchmark tailored for machine learning emulators of Eulerian atmospheric transport. Through architectural adjustments, we decouple the performance of our emulators from the distribution shift caused by a steady rise in atmospheric CO$_2$. More specifically, we center CO$_2$ input fields to zero mean and then use an explicit flux scheme and a mass fixer to assure mass balance. This design enables stable and mass conserving transport for over 6 months with all four neural network architectures. In our study, the SwinTransformer displays particularly strong emulation skill (90-day $R^2 > 0.99$), with physically plausible emulation even for forward runs of multiple years. This work paves the way forward towards high resolution forward and inverse modeling of inert trace gases with neural networks.

Strong Copyright Protection for Language Models via Adaptive Model Fusion

The risk of language models unintentionally reproducing copyrighted material from their training data has led to the development of various protective measures. In this paper, we propose model fusion as an effective solution to safeguard against copyright infringement. In particular, we introduce Copyright-Protecting Fusion (CP-Fuse), an algorithm that adaptively combines language models to minimize the reproduction of protected materials. CP-Fuse is inspired by the recently proposed Near-Access Free (NAF) framework and additionally incorporates a desirable balancing property that we demonstrate prevents the reproduction of memorized training data. Our results show that CP-Fuse significantly reduces the memorization of copyrighted content while maintaining high-quality text and code generation. Furthermore, we demonstrate how CP-Fuse can be integrated with other techniques for enhanced protection.

Robust Mixture Learning when Outliers Overwhelm Small Groups

We study the problem of estimating the means of well-separated mixtures when an adversary may add arbitrary outliers. While strong guarantees are available when the outlier fraction is significantly smaller than the minimum mixing weight, much less is known when outliers may crowd out low-weight clusters - a setting we refer to as list-decodable mixture learning (LD-ML). In this case, adversarial outliers can simulate additional spurious mixture components. Hence, if all means of the mixture must be recovered up to a small error in the output list, the list size needs to be larger than the number of (true) components. We propose an algorithm that obtains order-optimal error guarantees for each mixture mean with a minimal list-size overhead, significantly improving upon list-decodable mean estimation, the only existing method that is applicable for LD-ML. Although improvements are observed even when the mixture is non-separated, our algorithm achieves particularly strong guarantees when the mixture is separated: it can leverage the mixture structure to partially cluster the samples before carefully iterating a base learner for list-decodable mean estimation at different scales.

Detecting critical treatment effect bias in small subgroups

Randomized trials are considered the gold standard for making informed decisions in medicine, yet they often lack generalizability to the patient populations in clinical practice. Observational studies, on the other hand, cover a broader patient population but are prone to various biases. Thus, before using an observational study for decision-making, it is crucial to benchmark its treatment effect estimates against those derived from a randomized trial. We propose a novel strategy to benchmark observational studies beyond the average treatment effect. First, we design a statistical test for the null hypothesis that the treatment effects estimated from the two studies, conditioned on a set of relevant features, differ up to some tolerance. We then estimate an asymptotically valid lower bound on the maximum bias strength for any subgroup in the observational study. Finally, we validate our benchmarking strategy in a real-world setting and show that it leads to conclusions that align with established medical knowledge.

Privacy-preserving data release leveraging optimal transport and particle gradient descent

We present a novel approach for differentially private data synthesis of protected tabular datasets, a relevant task in highly sensitive domains such as healthcare and government. Current state-of-the-art methods predominantly use marginal-based approaches, where a dataset is generated from private estimates of the marginals. In this paper, we introduce PrivPGD, a new generation method for marginal-based private data synthesis, leveraging tools from optimal transport and particle gradient descent. Our algorithm outperforms existing methods on a large range of datasets while being highly scalable and offering the flexibility to incorporate additional domain-specific constraints.

Hidden yet quantifiable: A lower bound for confounding strength using randomized trials

In the era of fast-paced precision medicine, observational studies play a major role in properly evaluating new treatments in clinical practice. Yet, unobserved confounding can significantly compromise causal conclusions drawn from non-randomized data. We propose a novel strategy that leverages randomized trials to quantify unobserved confounding. First, we design a statistical test to detect unobserved confounding with strength above a given threshold. Then, we use the test to estimate an asymptotically valid lower bound on the unobserved confounding strength. We evaluate the power and validity of our statistical test on several synthetic and semi-synthetic datasets. Further, we show how our lower bound can correctly identify the absence and presence of unobserved confounding in a real-world setting.

Can semi-supervised learning use all the data effectively? A lower bound perspective

Prior works have shown that semi-supervised learning algorithms can leverage unlabeled data to improve over the labeled sample complexity of supervised learning (SL) algorithms. However, existing theoretical analyses focus on regimes where the unlabeled data is sufficient to learn a good decision boundary using unsupervised learning (UL) alone. This begs the question: Can SSL algorithms simultaneously improve upon both UL and SL? To this end, we derive a tight lower bound for 2-Gaussian mixture models that explicitly depends on the labeled and the unlabeled dataset size as well as the signal-to-noise ratio of the mixture distribution. Surprisingly, our result implies that no SSL algorithm can improve upon the minimax-optimal statistical error rates of SL or UL algorithms for these distributions. Nevertheless, we show empirically on real-world data that SSL algorithms can still outperform UL and SL methods. Therefore, our work suggests that, while proving performance gains for SSL algorithms is possible, it requires careful tracking of constants.

How robust accuracy suffers from certified training with convex relaxations

Adversarial attacks pose significant threats to deploying state-of-the-art classifiers in safety-critical applications. Two classes of methods have emerged to address this issue: empirical defences and certified defences. Although certified defences come with robustness guarantees, empirical defences such as adversarial training enjoy much higher popularity among practitioners. In this paper, we systematically compare the standard and robust error of these two robust training paradigms across multiple computer vision tasks. We show that in most tasks and for both $\mathscr{l}_\infty$-ball and $\mathscr{l}_2$-ball threat models, certified training with convex relaxations suffers from worse standard and robust error than adversarial training. We further explore how the error gap between certified and adversarial training depends on the threat model and the data distribution. In particular, besides the perturbation budget, we identify as important factors the shape of the perturbation set and the implicit margin of the data distribution. We support our arguments with extensive ablations on both synthetic and image datasets.

PILLAR: How to make semi-private learning more effective

In Semi-Supervised Semi-Private (SP) learning, the learner has access to both public unlabelled and private labelled data. We propose a computationally efficient algorithm that, under mild assumptions on the data, provably achieves significantly lower private labelled sample complexity and can be efficiently run on real-world datasets. For this purpose, we leverage the features extracted by networks pre-trained on public (labelled or unlabelled) data, whose distribution can significantly differ from the one on which SP learning is performed. To validate its empirical effectiveness, we propose a wide variety of experiments under tight privacy constraints ($\epsilon = 0.1$) and with a focus on low-data regimes. In all of these settings, our algorithm exhibits significantly improved performance over available baselines that use similar amounts of public data.

Strong inductive biases provably prevent harmless interpolation

Classical wisdom suggests that estimators should avoid fitting noise to achieve good generalization. In contrast, modern overparameterized models can yield small test error despite interpolating noise -- a phenomenon often called "benign overfitting" or "harmless interpolation". This paper argues that the degree to which interpolation is harmless hinges upon the strength of an estimator's inductive bias, i.e., how heavily the estimator favors solutions with a certain structure: while strong inductive biases prevent harmless interpolation, weak inductive biases can even require fitting noise to generalize well. Our main theoretical result establishes tight non-asymptotic bounds for high-dimensional kernel regression that reflect this phenomenon for convolutional kernels, where the filter size regulates the strength of the inductive bias. We further provide empirical evidence of the same behavior for deep neural networks with varying filter sizes and rotational invariance.