To leverage data for the sufficient training of machine learning (ML) models from multiple parties in a confidentiality-preserving way, various collaborative distributed ML (CDML) system designs have been developed, for example, to perform assisted learning, federated learning, and split learning. CDML system designs show different traits, including high agent autonomy, ML model confidentiality, and fault tolerance. Facing a wide variety of CDML system designs with different traits, it is difficult for developers to design CDML systems with traits that match use case requirements in a targeted way. However, inappropriate CDML system designs may result in CDML systems failing their envisioned purposes. We developed a CDML design toolbox that can guide the development of CDML systems. Based on the CDML design toolbox, we present CDML system archetypes with distinct key traits that can support the design of CDML systems to meet use case requirements.

To solve complex tasks, large language models (LLMs) often require multiple rounds of interactions with the user, sometimes assisted by external tools. However, current evaluation protocols often emphasize benchmark performance with single-turn exchanges, neglecting the nuanced interactions among the user, LLMs, and external tools, while also underestimating the importance of natural language feedback from users. These oversights contribute to discrepancies between research benchmark evaluations and real-world use cases. We introduce MINT, a benchmark that evaluates LLMs' ability to solve tasks with multi-turn interactions by (1) using tools and (2) leveraging natural language feedback. To ensure reproducibility, we provide an evaluation framework where LLMs can access tools by executing Python code and receive users' natural language feedback simulated by GPT-4. We repurpose a diverse set of established evaluation datasets focusing on reasoning, coding, and decision-making and carefully curate them into a compact subset for efficient evaluation. Our analysis of 20 open- and closed-source LLMs offers intriguing findings. (a) LLMs generally benefit from tools and language feedback, with performance gains (absolute, same below) of 1-8% for each turn of tool use and 2-17% with natural language feedback. (b) Better single-turn performance does not guarantee better multi-turn performance. (c) Surprisingly, on the LLMs evaluated, supervised instruction-finetuning (SIFT) and reinforcement learning from human feedback (RLHF) generally hurt multi-turn capabilities. We expect MINT can help measure progress and incentivize research in improving LLMs' capabilities in multi-turn interactions, especially for open-source communities where multi-turn human evaluation can be less accessible compared to commercial LLMs with a larger user base.

As large language models increase in capability, researchers have started to conduct surveys of all kinds on these models with varying scientific motivations. In this work, we examine what we can learn from language models' survey responses on the basis of the well-established American Community Survey (ACS) by the U.S. Census Bureau. Using a de-facto standard multiple-choice prompting technique and evaluating 40 different language models, hundreds of thousands of times each on questions from the ACS, we systematically establish two dominant patterns. First, models have significant position and labeling biases, for example, towards survey responses labeled with the letter "A". Second, when adjusting for labeling biases through randomized answer ordering, models across the board trend towards uniformly random survey responses. In fact, binary classifiers can almost perfectly differentiate between models' responses to the ACS and the responses of the US census. Taken together, our findings suggest caution in treating survey responses from language models as equivalent to those of human populations at present time.

Transformers have become the go-to architecture for language and vision tasks, yet their theoretical properties, especially memorization capacity, remain elusive. This paper investigates the memorization abilities of multi-head attention mechanisms, examining how many example sequences they can memorize, as a function of the number of heads and sequence length. Motivated by experimental findings on vision transformers, we introduce novel assumptions about the linear independence of input data, distinct from the commonly used general-position assumption. Under these assumptions, we demonstrate that an attention layer with $H$ heads, dimension $d$, and context size $n < d$, featuring $\Theta(Hd^2)$ parameters, can memorize $\Omega(Hn)$ examples. Our analysis sheds light on how different attention heads handle various example sequences, aided by the softmax operator's saturation property. We validate our findings through experiments on synthetic data.

We propose six axioms concerning when one candidate should defeat another in a democratic election involving two or more candidates. Five of the axioms are widely satisfied by known voting procedures. The sixth axiom is a weakening of Kenneth Arrow's famous condition of the Independence of Irrelevant Alternatives (IIA). We call this weakening Coherent IIA. We prove that the five axioms plus Coherent IIA single out a method of determining defeats studied in our recent work: Split Cycle. In particular, Split Cycle provides the most resolute definition of defeat among any satisfying the six axioms for democratic defeat. In addition, we analyze how Split Cycle escapes Arrow's Impossibility Theorem and related impossibility results.

Heavy tails is a common feature of filtering distributions that results from the nonlinear dynamical and observation processes as well as the uncertainty from physical sensors. In these settings, the Kalman filter and its ensemble version - the ensemble Kalman filter (EnKF) - that have been designed under Gaussian assumptions result in degraded performance. t-distributions are a parametric family of distributions whose tail-heaviness is modulated by a degree of freedom $\nu$. Interestingly, Cauchy and Gaussian distributions correspond to the extreme cases of a t-distribution for $\nu = 1$ and $\nu = \infty$, respectively. Leveraging tools from measure transport (Spantini et al., SIAM Review, 2022), we present a generalization of the EnKF whose prior-to-posterior update leads to exact inference for t-distributions. We demonstrate that this filter is less sensitive to outlying synthetic observations generated by the observation model for small $\nu$. Moreover, it recovers the Kalman filter for $\nu = \infty$. For nonlinear state-space models with heavy-tailed noise, we propose an algorithm to estimate the prior-to-posterior update from samples of joint forecast distribution of the states and observations. We rely on a regularized expectation-maximization (EM) algorithm to estimate the mean, scale matrix, and degree of freedom of heavy-tailed \textit{t}-distributions from limited samples (Finegold and Drton, arXiv preprint, 2014). Leveraging the conditional independence of the joint forecast distribution, we regularize the scale matrix with an $l1$ sparsity-promoting penalization of the log-likelihood at each iteration of the EM algorithm. By sequentially estimating the degree of freedom at each analysis step, our filter can adapt its prior-to-posterior update to the tail-heaviness of the data. We demonstrate the benefits of this new ensemble filter on challenging filtering problems.

Stiff systems of ordinary differential equations (ODEs) and sparse training data are common in scientific problems. This paper describes efficient, implicit, vectorized methods for integrating stiff systems of ordinary differential equations through time and calculating parameter gradients with the adjoint method. The main innovation is to vectorize the problem both over the number of independent times series and over a batch or "chunk" of sequential time steps, effectively vectorizing the assembly of the implicit system of ODEs. The block-bidiagonal structure of the linearized implicit system for the backward Euler method allows for further vectorization using parallel cyclic reduction (PCR). Vectorizing over both axes of the input data provides a higher bandwidth of calculations to the computing device, allowing even problems with comparatively sparse data to fully utilize modern GPUs and achieving speed ups of greater than 100x, compared to standard, sequential time integration. We demonstrate the advantages of implicit, vectorized time integration with several example problems, drawn from both analytical stiff and non-stiff ODE models as well as neural ODE models. We also describe and provide a freely available open-source implementation of the methods developed here.

The 2022 National Defense Strategy of the United States listed climate change as a serious threat to national security. Climate intervention methods, such as stratospheric aerosol injection, have been proposed as mitigation strategies, but the downstream effects of such actions on a complex climate system are not well understood. The development of algorithmic techniques for quantifying relationships between source and impact variables related to a climate event (i.e., a climate pathway) would help inform policy decisions. Data-driven deep learning models have become powerful tools for modeling highly nonlinear relationships and may provide a route to characterize climate variable relationships. In this paper, we explore the use of an echo state network (ESN) for characterizing climate pathways. ESNs are a computationally efficient neural network variation designed for temporal data, and recent work proposes ESNs as a useful tool for forecasting spatio-temporal climate data. Like other neural networks, ESNs are non-interpretable black-box models, which poses a hurdle for understanding variable relationships. We address this issue by developing feature importance methods for ESNs in the context of spatio-temporal data to quantify variable relationships captured by the model. We conduct a simulation study to assess and compare the feature importance techniques, and we demonstrate the approach on reanalysis climate data. In the climate application, we select a time period that includes the 1991 volcanic eruption of Mount Pinatubo. This event was a significant stratospheric aerosol injection, which we use as a proxy for an artificial stratospheric aerosol injection. Using the proposed approach, we are able to characterize relationships between pathway variables associated with this event.

Estimating the counterfactual outcome of treatment is essential for decision-making in public health and clinical science, among others. Often, treatments are administered in a sequential, time-varying manner, leading to an exponentially increased number of possible counterfactual outcomes. Furthermore, in modern applications, the outcomes are high-dimensional and conventional average treatment effect estimation fails to capture disparities in individuals. To tackle these challenges, we propose a novel conditional generative framework capable of producing counterfactual samples under time-varying treatment, without the need for explicit density estimation. Our method carefully addresses the distribution mismatch between the observed and counterfactual distributions via a loss function based on inverse probability weighting. We present a thorough evaluation of our method using both synthetic and real-world data. Our results demonstrate that our method is capable of generating high-quality counterfactual samples and outperforms the state-of-the-art baselines.

Motivated by a recent literature on the double-descent phenomenon in machine learning, we consider highly over-parameterized models in causal inference, including synthetic control with many control units. In such models, there may be so many free parameters that the model fits the training data perfectly. We first investigate high-dimensional linear regression for imputing wage data and estimating average treatment effects, where we find that models with many more covariates than sample size can outperform simple ones. We then document the performance of high-dimensional synthetic control estimators with many control units. We find that adding control units can help improve imputation performance even beyond the point where the pre-treatment fit is perfect. We provide a unified theoretical perspective on the performance of these high-dimensional models. Specifically, we show that more complex models can be interpreted as model-averaging estimators over simpler ones, which we link to an improvement in average performance. This perspective yields concrete insights into the use of synthetic control when control units are many relative to the number of pre-treatment periods.