Many problems in machine learning involve bilevel optimization (BLO), including hyperparameter optimization, meta-learning, and dataset distillation. Bilevel problems consist of two nested sub-problems, called the outer and inner problems, respectively. In practice, often at least one of these sub-problems is overparameterized. In this case, there are many ways to choose among optima that achieve equivalent objective values. Inspired by recent studies of the implicit bias induced by optimization algorithms in single-level optimization, we investigate the implicit bias of gradient-based algorithms for bilevel optimization. We delineate two standard BLO methods -- cold-start and warm-start -- and show that the converged solution or long-run behavior depends to a large degree on these and other algorithmic choices, such as the hypergradient approximation. We also show that the inner solutions obtained by warm-start BLO can encode a surprising amount of information about the outer objective, even when the outer parameters are low-dimensional. We believe that implicit bias deserves as central a role in the study of bilevel optimization as it has attained in the study of single-level neural net optimization.

As language models (LMs) scale, they develop many novel behaviors, good and bad, exacerbating the need to evaluate how they behave. Prior work creates evaluations with crowdwork (which is time-consuming and expensive) or existing data sources (which are not always available). Here, we automatically generate evaluations with LMs. We explore approaches with varying amounts of human effort, from instructing LMs to write yes/no questions to making complex Winogender schemas with multiple stages of LM-based generation and filtering. Crowdworkers rate the examples as highly relevant and agree with 90-100% of labels, sometimes more so than corresponding human-written datasets. We generate 154 datasets and discover new cases of inverse scaling where LMs get worse with size. Larger LMs repeat back a dialog user's preferred answer ("sycophancy") and express greater desire to pursue concerning goals like resource acquisition and goal preservation. We also find some of the first examples of inverse scaling in RL from Human Feedback (RLHF), where more RLHF makes LMs worse. For example, RLHF makes LMs express stronger political views (on gun rights and immigration) and a greater desire to avoid shut down. Overall, LM-written evaluations are high-quality and let us quickly discover many novel LM behaviors.

Variational autoencoders (VAEs) are powerful tools for learning latent representations of data used in a wide range of applications. In practice, VAEs usually require multiple training rounds to choose the amount of information the latent variable should retain. This trade-off between the reconstruction error (distortion) and the KL divergence (rate) is typically parameterized by a hyperparameter $\beta$. In this paper, we introduce Multi-Rate VAE (MR-VAE), a computationally efficient framework for learning optimal parameters corresponding to various $\beta$ in a single training run. The key idea is to explicitly formulate a response function that maps $\beta$ to the optimal parameters using hypernetworks. MR-VAEs construct a compact response hypernetwork where the pre-activations are conditionally gated based on $\beta$. We justify the proposed architecture by analyzing linear VAEs and showing that it can represent response functions exactly for linear VAEs. With the learned hypernetwork, MR-VAEs can construct the rate-distortion curve without additional training and can be deployed with significantly less hyperparameter tuning. Empirically, our approach is competitive and often exceeds the performance of multiple $\beta$-VAEs training with minimal computation and memory overheads.

神经网络经常将许多无关的概念包装到一个神经元中 - 一种令人困惑的现象被称为“多疾病”，这使解释性更具挑战性。本文提供了一个玩具模型，可以完全理解多义，这是由于模型在“叠加”中存储其他稀疏特征的结果。我们证明了相变的存在，与均匀多型的几何形状的令人惊讶的联系以及与对抗性例子联系的证据。我们还讨论了对机械解释性的潜在影响。

影响功能有效地估计了删除单个训练数据点对模型学习参数的影响。尽管影响估计值与线性模型的剩余重新进行了良好的重新对齐，但最近的作品表明，在神经网络中，这种比对通常很差。在这项工作中，我们通过将其分解为五个单独的术语来研究导致这种差异的特定因素。我们研究每个术语对各种架构和数据集的贡献，以及它们如何随网络宽度和培训时间等因素而变化。尽管实际影响函数估计值可能是非线性网络中保留对方的重新培训的差异，但我们表明它们通常是对不同对象的良好近似值，我们称其为近端Bregman响应函数（PBRF）。由于PBRF仍然可以用来回答许多激励影响功能的问题，例如识别有影响力或标记的示例，因此我们的结果表明，影响功能估计的当前算法比以前的错误分析所暗示的更有用的结果。

命题模型计数或#SAT是计算布尔公式满足分配数量的问题。来自不同应用领域的许多问题，包括许多离散的概率推理问题，可以将#SAT求解器解决的模型计数问题转化为模型计数问题。但是，确切的#sat求解器通常无法扩展到工业规模实例。在本文中，我们提出了Neuro＃，这是一种学习分支启发式方法，以提高特定问题家族中的实例的精确#sat求解器的性能。我们通过实验表明，我们的方法减少了类似分布的持有实例的步骤，并将其推广到同一问题家族的更大实例。它能够在具有截然不同的结构的许多不同问题家族上实现这些结果。除了步骤计数的改进外，Neuro＃还可以在某些问题家族的较大实例上在较大的实例上实现壁式锁定速度的订单，尽管开头查询了模型。

可逆的神经网络（Inns）已被用于设计生成模型，实现节省内存梯度计算，并解决逆问题。在这项工作中，我们展示了普通二手纪念架构遭受爆炸逆，因此易于变得数值不可逆转。在广泛的Inn用例中，我们揭示了包括在分配和分配的变化（OOD）数据的变化公式的不适用性的失败，用于节省内存返回的不正确渐变，以及无法从标准化流量模型中采样。我们进一步推出了普通架构原子构建块的双嘴唇特性。这些见解对旅馆的稳定性然后提供了前进的方法来解决这些故障。对于本地可释放足够的任务，如记忆保存的倒退，我们提出了一种灵活且高效的常规器。对于必要的全球可逆性的问题，例如在ood数据上应用标准化流动，我们展示了设计稳定的旅馆构建块的重要性。

We decompose the evidence lower bound to show the existence of a term measuring the total correlation between latent variables. We use this to motivate the β-TCVAE (Total Correlation Variational Autoencoder) algorithm, a refinement and plug-in replacement of the β-VAE for learning disentangled representations, requiring no additional hyperparameters during training. We further propose a principled classifier-free measure of disentanglement called the mutual information gap (MIG). We perform extensive quantitative and qualitative experiments, in both restricted and non-restricted settings, and show a strong relation between total correlation and disentanglement, when the model is trained using our framework.

We propose an efficient method for approximating natural gradient descent in neural networks which we call Kronecker-factored Approximate Curvature (K-FAC). K-FAC is based on an efficiently invertible approximation of a neural network's Fisher information matrix which is neither diagonal nor low-rank, and in some cases is completely non-sparse. It is derived by approximating various large blocks of the Fisher (corresponding to entire layers) as being the Kronecker product of two much smaller matrices. While only several times more expensive to compute than the plain stochastic gradient, the updates produced by K-FAC make much more progress optimizing the objective, which results in an algorithm that can be much faster than stochastic gradient descent with momentum in practice. And unlike some previously proposed approximate natural-gradient/Newton methods which use high-quality non-diagonal curvature matrices (such as Hessian-free optimization), K-FAC works very well in highly stochastic optimization regimes. This is because the cost of storing and inverting K-FAC's approximation to the curvature matrix does not depend on the amount of data used to estimate it, which is a feature typically associated only with diagonal or low-rank approximations to the curvature matrix.

Current language models are considered to have sub-human capabilities at natural language tasks like question-answering or writing code. However, language models are not trained to perform well at these tasks, they are trained to accurately predict the next token given previous tokes in tokenized text. It is not clear whether language models are better or worse than humans at next token prediction. To try to answer this question, we performed two distinct experiments to directly compare humans and language models on this front: one measuring top-1 accuracy and the other measuring perplexity. In both experiments, we find humans to be consistently \emph{worse} than even relatively small language models like GPT3-Ada at next-token prediction.