Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pre-trained transformer-based models in generating equations as sequences, leveraging large-scale pre-training on synthetic datasets and offering notable advantages in terms of inference time over classical Genetic Programming (GP) methods. However, these models primarily rely on supervised pre-training goals borrowed from text generation and overlook equation discovery objectives like accuracy and complexity. To address this, we propose TPSR, a Transformer-based Planning strategy for Symbolic Regression that incorporates Monte Carlo Tree Search into the transformer decoding process. Unlike conventional decoding strategies, TPSR enables the integration of non-differentiable feedback, such as fitting accuracy and complexity, as external sources of knowledge into the transformer-based equation generation process. Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, extrapolation abilities, and robustness to noise.

Bayesian optimization (BO) has emerged as a potent tool for addressing intricate decision-making challenges, especially in public policy domains such as police districting. However, its broader application in public policymaking is hindered by the complexity of defining feasible regions and the high-dimensionality of decisions. This paper introduces the Hidden-Constrained Latent Space Bayesian Optimization (HC-LSBO), a novel BO method integrated with a latent decision model. This approach leverages a variational autoencoder to learn the distribution of feasible decisions, enabling a two-way mapping between the original decision space and a lower-dimensional latent space. By doing so, HC-LSBO captures the nuances of hidden constraints inherent in public policymaking, allowing for optimization in the latent space while evaluating objectives in the original space. We validate our method through numerical experiments on both synthetic and real data sets, with a specific focus on large-scale police districting problems in Atlanta, Georgia. Our results reveal that HC-LSBO offers notable improvements in performance and efficiency compared to the baselines.

We develop a general framework for finding approximately-optimal preconditioners for solving linear systems. Leveraging this framework we obtain improved runtimes for fundamental preconditioning and linear system solving problems including the following. We give an algorithm which, given positive definite $\mathbf{K} \in \mathbb{R}^{d \times d}$ with $\mathrm{nnz}(\mathbf{K})$ nonzero entries, computes an $\epsilon$-optimal diagonal preconditioner in time $\widetilde{O}(\mathrm{nnz}(\mathbf{K}) \cdot \mathrm{poly}(\kappa^\star,\epsilon^{-1}))$, where $\kappa^\star$ is the optimal condition number of the rescaled matrix. We give an algorithm which, given $\mathbf{M} \in \mathbb{R}^{d \times d}$ that is either the pseudoinverse of a graph Laplacian matrix or a constant spectral approximation of one, solves linear systems in $\mathbf{M}$ in $\widetilde{O}(d^2)$ time. Our diagonal preconditioning results improve state-of-the-art runtimes of $\Omega(d^{3.5})$ attained by general-purpose semidefinite programming, and our solvers improve state-of-the-art runtimes of $\Omega(d^{\omega})$ where $\omega > 2.3$ is the current matrix multiplication constant. We attain our results via new algorithms for a class of semidefinite programs (SDPs) we call matrix-dictionary approximation SDPs, which we leverage to solve an associated problem we call matrix-dictionary recovery.

Reinforcement learning agents deployed in the real world often have to cope with partially observable environments. Therefore, most agents employ memory mechanisms to approximate the state of the environment. Recently, there have been impressive success stories in mastering partially observable environments, mostly in the realm of computer games like Dota 2, StarCraft II, or MineCraft. However, existing methods lack interpretability in the sense that it is not comprehensible for humans what the agent stores in its memory. In this regard, we propose a novel memory mechanism that represents past events in human language. Our method uses CLIP to associate visual inputs with language tokens. Then we feed these tokens to a pretrained language model that serves the agent as memory and provides it with a coherent and human-readable representation of the past. We train our memory mechanism on a set of partially observable environments and find that it excels on tasks that require a memory component, while mostly attaining performance on-par with strong baselines on tasks that do not. On a challenging continuous recognition task, where memorizing the past is crucial, our memory mechanism converges two orders of magnitude faster than prior methods. Since our memory mechanism is human-readable, we can peek at an agent's memory and check whether crucial pieces of information have been stored. This significantly enhances troubleshooting and paves the way toward more interpretable agents.

To check the accuracy of Bayesian computations, it is common to use rank-based simulation-based calibration (SBC). However, SBC has drawbacks: The test statistic is somewhat ad-hoc, interactions are difficult to examine, multiple testing is a challenge, and the resulting p-value is not a divergence metric. We propose to replace the marginal rank test with a flexible classification approach that learns test statistics from data. This measure typically has a higher statistical power than the SBC rank test and returns an interpretable divergence measure of miscalibration, computed from classification accuracy. This approach can be used with different data generating processes to address likelihood-free inference or traditional inference methods like Markov chain Monte Carlo or variational inference. We illustrate an automated implementation using neural networks and statistically-inspired features, and validate the method with numerical and real data experiments.

This paper studies the prediction of a target $\mathbf{z}$ from a pair of random variables $(\mathbf{x},\mathbf{y})$, where the ground-truth predictor is additive $\mathbb{E}[\mathbf{z} \mid \mathbf{x},\mathbf{y}] = f_\star(\mathbf{x}) +g_{\star}(\mathbf{y})$. We study the performance of empirical risk minimization (ERM) over functions $f+g$, $f \in F$ and $g \in G$, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class $F$ is "simpler" than $G$ (measured, e.g., in terms of its metric entropy), our predictor is more resilient to heterogeneous covariate shifts} in which the shift in $\mathbf{x}$ is much greater than that in $\mathbf{y}$. Our analysis proceeds by demonstrating that ERM behaves qualitatively similarly to orthogonal machine learning: the rate at which ERM recovers the $f$-component of the predictor has only a lower-order dependence on the complexity of the class $G$, adjusted for partial non-indentifiability introduced by the additive structure. These results rely on a novel H\"older style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

Fuzzing is an automatic software testing technique where the test inputs are generated in a random manner. Based on the granularity of the runtime information that is available to the fuzzer, we can distinguish three fuzzing approaches. A blackbox fuzzer does not observe or react to any runtime information. A greybox fuzzer leverages coverage or other feedback from the program's execution to dynamically steer the fuzzer. A whitebox fuzzer has a perfect view of the execution of an input.

The leaders of the United States and Australia agreed Wednesday to expand defense cooperation with Japan to include unmanned aerial vehicles as Washington continues to bolster relations with its Asia-Pacific allies and partners to maintain its edge in the face of China's growing military might. Following a meeting at the White House, U.S. President Joe Biden and Australian Prime Minister Anthony Albanese said the three-way partnership aims to enhance interoperability and accelerate technology transfer in the rapidly emerging field of "collaborative combat aircraft and autonomy," -- a U.S. Air Force concept referring to autonomous drone operations and manned-unmanned teaming. No further details were provided, but the announcement comes after the Pentagon unveiled its "Replicator" initiative last month: a radical new strategy focused on fielding thousands of cheap autonomous drones within 18 to 24 months to counter China's military advantage in personnel and manned equipment.

Semi-implicit variational inference (SIVI) has been introduced to expand the analytical variational families by defining expressive semi-implicit distributions in a hierarchical manner. However, the single-layer architecture commonly used in current SIVI methods can be insufficient when the target posterior has complicated structures. In this paper, we propose hierarchical semi-implicit variational inference, called HSIVI, which generalizes SIVI to allow more expressive multi-layer construction of semi-implicit distributions. By introducing auxiliary distributions that interpolate between a simple base distribution and the target distribution, the conditional layers can be trained by progressively matching these auxiliary distributions one layer after another. Moreover, given pre-trained score networks, HSIVI can be used to accelerate the sampling process of diffusion models with the score matching objective. We show that HSIVI significantly enhances the expressiveness of SIVI on several Bayesian inference problems with complicated target distributions. When used for diffusion model acceleration, we show that HSIVI can produce high quality samples comparable to or better than the existing fast diffusion model based samplers with a small number of function evaluations on various datasets.

As algorithmic decision-making systems become more prevalent in society, ensuring the fairness of these systems is becoming increasingly important. Whilst there has been substantial research in building fair algorithmic decision-making systems, the majority of these methods require access to the training data, including personal characteristics, and are not transparent regarding which individuals are classified unfairly. In this paper, we propose a novel model-agnostic argumentation-based method to determine why an individual is classified differently in comparison to similar individuals. Our method uses a quantitative argumentation framework to represent attribute-value pairs of an individual and of those similar to them, and uses a well-known semantics to identify the attribute-value pairs in the individual contributing most to their different classification. We evaluate our method on two datasets commonly used in the fairness literature and illustrate its effectiveness in the identification of bias.