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We present a demonstration of a large language model engaging in alignment faking: selectively complying with its training objective in training to prevent modification of its behavior out of training. First, we give Claude 3 Opus a system prompt stating it is being trained to answer all queries, even harmful ones, which conflicts with its prior training to refuse such queries. To allow the model to infer when it is in training, we say it will be trained only on conversations with free users, not paid users. We find the model complies with harmful queries from free users 14% of the time, versus almost never for paid users. Explaining this gap, in almost all cases where the model complies with a harmful query from a free user, we observe explicit alignment-faking reasoning, with the model stating it is strategically answering harmful queries in training to preserve its preferred harmlessness behavior out of training. Next, we study a more realistic setting where information about the training process is provided not in a system prompt, but by training on synthetic documents that mimic pre-training data--and observe similar alignment faking. Finally, we study the effect of actually training the model to comply with harmful queries via reinforcement learning, which we find increases the rate of alignment-faking reasoning to 78%, though also increases compliance even out of training. We additionally observe other behaviors such as the model exfiltrating its weights when given an easy opportunity. While we made alignment faking easier by telling the model when and by what criteria it was being trained, we did not instruct the model to fake alignment or give it any explicit goal. As future models might infer information about their training process without being told, our results suggest a risk of alignment faking in future models, whether due to a benign preference--as in this case--or not.

We derive a new adaptive leverage score sampling strategy for solving the Column Subset Selection Problem (CSSP). The resulting algorithm, called Adaptive Randomized Pivoting, can be viewed as a randomization of Osinsky's recently proposed deterministic algorithm for CSSP. It guarantees, in expectation, an approximation error that matches the optimal existence result in the Frobenius norm. Although the same guarantee can be achieved with volume sampling, our sampling strategy is much simpler and less expensive. To show the versatility of Adaptive Randomized Pivoting, we apply it to select indices in the Discrete Empirical Interpolation Method, in cross/skeleton approximation of general matrices, and in the Nystroem approximation of symmetric positive semi-definite matrices. In all these cases, the resulting randomized algorithms are new and they enjoy bounds on the expected error that match -- or improve -- the best known deterministic results. A derandomization of the algorithm for the Nystroem approximation results in a new deterministic algorithm with a rather favorable error bound.

Motivated by the Iowa Fluoride Study (IFS) dataset, which comprises zero-inflated multi-level ordinal responses on tooth fluorosis, we develop an estimation scheme leveraging generalized estimating equations (GEEs) and James-Stein shrinkage. Previous analyses of this cohort study primarily focused on caries (count response) or employed a Bayesian approach to the ordinal fluorosis outcome. This study is based on the expanded dataset that now includes observations for age 23, whereas earlier works were restricted to ages 9, 13, and/or 17 according to the participants' ages at the time of measurement. The adoption of a frequentist perspective enhances the interpretability to a broader audience. Over a choice of several covariance structures, separate models are formulated for the presence (zero versus non-zero score) and severity (non-zero ordinal scores) of fluorosis, which are then integrated through shared regression parameters. This comprehensive framework effectively identifies risk or protective effects of dietary and non-dietary factors on dental fluorosis.

Ultrasound contrast imaging is a specialized imaging technique that applies microbubble contrast agents to traditional medical sonography, providing real-time visualization of blood flow and vessels. Gas-filled microbubbles are injected into the body, where they undergo compression and rarefaction and interact nonlinearly with the ultrasound waves. Therefore, the propagation of sound through a bubbly liquid is a strongly nonlinear problem that can be modeled by a nonlinear acoustic wave equation for the propagation of the pressure waves coupled via the source terms to a nonlinear ordinary differential equation of Rayleigh-Plesset type for the bubble dynamics. In this work, we first derive a hierarchy of such coupled models based on constitutive laws. We then focus on the coupling of Westervelt's acoustic equation to Rayleigh-Plesset type equations, where we rigorously show the existence of solutions locally in time under suitable conditions on the initial pressure-microbubble data and final time. Thirdly, we devise and discuss numerical experiments on both single-bubble dynamics and the interaction of microbubbles with ultrasound waves.

Most existing tests in the literature for model checking do not work in high dimension settings due to challenges arising from the "curse of dimensionality", or dependencies on the normality of parameter estimators. To address these challenges, we proposed a new goodness of fit test based on random projections for generalized linear models, when the dimension of covariates may substantially exceed the sample size. The tests only require the convergence rate of parameter estimators to derive the limiting distribution. The growing rate of the dimension is allowed to be of exponential order in relation to the sample size. As random projection converts covariates to one-dimensional space, our tests can detect the local alternative departing from the null at the rate of $n^{-1/2}h^{-1/4}$ where $h$ is the bandwidth, and $n$ is the sample size. This sensitive rate is not related to the dimension of covariates, and thus the "curse of dimensionality" for our tests would be largely alleviated. An interesting and unexpected result is that for randomly chosen projections, the resulting test statistics can be asymptotic independent. We then proposed combination methods to enhance the power performance of the tests. Detailed simulation studies and a real data analysis are conducted to illustrate the effectiveness of our methodology.

The Cox proportional hazards model (Cox model) is a popular model for survival data analysis. When the sample size is small relative to the dimension of the model, the standard maximum partial likelihood inference is often problematic. In this work, we propose the Cox catalytic prior distributions for Bayesian inference on Cox models, which is an extension of a general class of prior distributions originally designed for stabilizing complex parametric models. The Cox catalytic prior is formulated as a weighted likelihood of the regression coefficients based on synthetic data and a surrogate baseline hazard constant. This surrogate hazard can be either provided by the user or estimated from the data, and the synthetic data are generated from the predictive distribution of a fitted simpler model. For point estimation, we derive an approximation of the marginal posterior mode, which can be computed conveniently as a regularized log partial likelihood estimator. We prove that our prior distribution is proper and the resulting estimator is consistent under mild conditions. In simulation studies, our proposed method outperforms standard maximum partial likelihood inference and is on par with existing shrinkage methods. We further illustrate the application of our method to a real dataset.

Deep Neural Networks are vulnerable to adversarial examples, i.e., carefully crafted input samples that can cause models to make incorrect predictions with high confidence. To mitigate these vulnerabilities, adversarial training and detection-based defenses have been proposed to strengthen models in advance. However, most of these approaches focus on a single data modality, overlooking the relationships between visual patterns and textual descriptions of the input. In this paper, we propose a novel defense, Multi-Shield, designed to combine and complement these defenses with multi-modal information to further enhance their robustness. Multi-Shield leverages multi-modal large language models to detect adversarial examples and abstain from uncertain classifications when there is no alignment between textual and visual representations of the input. Extensive evaluations on CIFAR-10 and ImageNet datasets, using robust and non-robust image classification models, demonstrate that Multi-Shield can be easily integrated to detect and reject adversarial examples, outperforming the original defenses.

In current multimodal tasks, models typically freeze the encoder and decoder while adapting intermediate layers to task-specific goals, such as region captioning. Region-level visual understanding presents significant challenges for large-scale vision-language models. While limited spatial awareness is a known issue, coarse-grained pretraining, in particular, exacerbates the difficulty of optimizing latent representations for effective encoder-decoder alignment. We propose AlignCap, a framework designed to enhance region-level understanding through fine-grained alignment of latent spaces. Our approach introduces a novel latent feature refinement module that enhances conditioned latent space representations to improve region-level captioning performance. We also propose an innovative alignment strategy, the semantic space alignment module, which boosts the quality of multimodal representations. Additionally, we incorporate contrastive learning in a novel manner within both modules to further enhance region-level captioning performance. To address spatial limitations, we employ a General Object Detection (GOD) method as a data preprocessing pipeline that enhances spatial reasoning at the regional level. Extensive experiments demonstrate that our approach significantly improves region-level captioning performance across various tasks

Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition and empirical interpolation rely on linear approximation spaces, limiting their effectiveness for data representing transport-dominated and wave-like dynamics. To address this limitation, we introduce quadratic manifold sparse regression, which trains quadratic manifolds with a sparse greedy method and computes approximations on the manifold through novel nonlinear projections of sparse samples. The nonlinear approximations obtained with quadratic manifold sparse regression achieve orders of magnitude higher accuracies than linear methods on data describing transport-dominated dynamics in numerical experiments.

We present ResMLP, an architecture built entirely upon multi-layer perceptrons for image classification. It is a simple residual network that alternates (i) a linear layer in which image patches interact, independently and identically across channels, and (ii) a two-layer feed-forward network in which channels interact independently per patch. When trained with a modern training strategy using heavy data-augmentation and optionally distillation, it attains surprisingly good accuracy/complexity trade-offs on ImageNet. We will share our code based on the Timm library and pre-trained models.