A hallmark property of explainable AI models is the ability to teach other agents, communicating knowledge of how to perform a task. While Large Language Models perform complex reasoning by generating explanations for their predictions, it is unclear whether they also make good teachers for weaker agents. To address this, we consider a student-teacher framework between two LLM agents and study if, when, and how the teacher should intervene with natural language explanations to improve the student's performance. Since communication is expensive, we define a budget such that the teacher only communicates explanations for a fraction of the data, after which the student should perform well on its own. We decompose the teaching problem along four axes: (1) if teacher's test time intervention improve student predictions, (2) when it is worth explaining a data point, (3) how the teacher should personalize explanations to better teach the student, and (4) if teacher explanations also improve students on future unexplained data. We first show that teacher LLMs can indeed intervene on student reasoning to improve their performance. Next, inspired by the Theory of Mind abilities of effective teachers, we propose building two few-shot mental models of the student. The first model defines an Intervention Function that simulates the utility of an intervention, allowing the teacher to intervene when this utility is the highest and improving student performance at lower budgets. The second model enables the teacher to personalize explanations for a particular student and outperform unpersonalized teachers. We also demonstrate that in multi-turn interactions, teacher explanations generalize and learning from explained data improves student performance on future unexplained data. Finally, we verify that misaligned teachers can lower student performance to random chance by intentionally misleading them.
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Optimal transport is a fundamental topic that has attracted a great amount of attention from the optimization community in the past decades. In this paper, we consider an interesting discrete dynamic optimal transport problem: can we efficiently update the optimal transport plan when the weights or the locations of the data points change? This problem is naturally motivated by several applications in machine learning. For example, we often need to compute the optimal transport cost between two different data sets; if some changes happen to a few data points, should we re-compute the high complexity cost function or update the cost by some efficient dynamic data structure? We are aware that several dynamic maximum flow algorithms have been proposed before, however, the research on dynamic minimum cost flow problem is still quite limited, to the best of our knowledge. We propose a novel 2D Skip Orthogonal List together with some dynamic tree techniques. Although our algorithm is based on the conventional simplex method, it can efficiently find the variable to pivot within expected $O(1)$ time, and complete each pivoting operation within expected $O(|V|)$ time where $V$ is the set of all supply and demand nodes. Since dynamic modifications typically do not introduce significant changes, our algorithm requires only a few simplex iterations in practice. So our algorithm is more efficient than re-computing the optimal transport cost that needs at least one traversal over all $|E| = O(|V|^2)$ variables, where $|E|$ denotes the number of edges in the network. Our experiments demonstrate that our algorithm significantly outperforms existing algorithms in the dynamic scenarios.
Sparse Bayesian Learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. The hyperparameters in SBL models are crucial for the model's performance, but they are often difficult to estimate due to the non-convexity and the high-dimensionality of the associated objective function. This paper presents a comprehensive framework for hyperparameter estimation in SBL models, encompassing well-known algorithms such as the expectation-maximization (EM), MacKay, and convex bounding (CB) algorithms. These algorithms are cohesively interpreted within an alternating minimization and linearization (AML) paradigm, distinguished by their unique linearized surrogate functions. Additionally, a novel algorithm within the AML framework is introduced, showing enhanced efficiency, especially under low signal noise ratios. This is further improved by a new alternating minimization and quadratic approximation (AMQ) paradigm, which includes a proximal regularization term. The paper substantiates these advancements with thorough convergence analysis and numerical experiments, demonstrating the algorithm's effectiveness in various noise conditions and signal-to-noise ratios.
Distributional Reinforcement Learning (RL) estimates return distribution mainly by learning quantile values via minimizing the quantile Huber loss function, entailing a threshold parameter often selected heuristically or via hyperparameter search, which may not generalize well and can be suboptimal. This paper introduces a generalized quantile Huber loss function derived from Wasserstein distance (WD) calculation between Gaussian distributions, capturing noise in predicted (current) and target (Bellman-updated) quantile values. Compared to the classical quantile Huber loss, this innovative loss function enhances robustness against outliers. Notably, the classical Huber loss function can be seen as an approximation of our proposed loss, enabling parameter adjustment by approximating the amount of noise in the data during the learning process. Empirical tests on Atari games, a common application in distributional RL, and a recent hedging strategy using distributional RL, validate the effectiveness of our proposed loss function and its potential for parameter adjustments in distributional RL.
As a new research area, quantum software testing lacks systematic testing benchmarks to assess testing techniques' effectiveness. Recently, some open-source benchmarks and mutation analysis tools have emerged. However, there is insufficient evidence on how various quantum circuit characteristics (e.g., circuit depth, number of quantum gates), algorithms (e.g., Quantum Approximate Optimization Algorithm), and mutation characteristics (e.g., mutation operators) affect the most mutant detection in quantum circuits. Studying such relations is important to systematically design faulty benchmarks with varied attributes (e.g., the difficulty in detecting a seeded fault) to facilitate assessing the cost-effectiveness of quantum software testing techniques efficiently. To this end, we present a large-scale empirical evaluation with more than 700K faulty benchmarks (quantum circuits) generated by mutating 382 real-world quantum circuits. Based on the results, we provide valuable insights for researchers to define systematic quantum mutation analysis techniques. We also provide a tool to recommend mutants to users based on chosen characteristics (e.g., a quantum algorithm type) and the required difficulty of killing mutants. Finally, we also provide faulty benchmarks that can already be used to assess the cost-effectiveness of quantum software testing techniques.
The restricted mean survival time (RMST) model has been garnering attention as a way to provide a clinically intuitive measure: the mean survival time. RMST models, which use methods based on pseudo time-to-event values and inverse probability censoring weighting, can adjust covariates. However, no approach has yet been introduced that considers random effects for clusters. In this paper, we propose a new random-effect RMST. We present two methods of analysis that consider variable effects by i) using a generalized mixed model with pseudo-values and ii) integrating the estimated results from the inverse probability censoring weighting estimating equations for each cluster. We evaluate our proposed methods through computer simulations. In addition, we analyze the effect of a mother's age at birth on under-five deaths in India using states as clusters.
Large language models (LLMs) have been extensively used as the backbones for general-purpose agents, and some economics literature suggest that LLMs are capable of playing various types of economics games. Following these works, to overcome the limitation of evaluating LLMs using static benchmarks, we propose to explore competitive games as an evaluation for LLMs to incorporate multi-players and dynamicise the environment. By varying the game history revealed to LLMs-based players, we find that most of LLMs are rational in that they play strategies that can increase their payoffs, but not as rational as indicated by Nash Equilibria (NEs). Moreover, when game history are available, certain types of LLMs, such as GPT-4, can converge faster to the NE strategies, which suggests higher rationality level in comparison to other models. In the meantime, certain types of LLMs can win more often when game history are available, and we argue that the winning rate reflects the reasoning ability with respect to the strategies of other players. Throughout all our experiments, we observe that the ability to strictly follow the game rules described by natural languages also vary among the LLMs we tested. In this work, we provide an economics arena for the LLMs research community as a dynamic simulation to test the above-mentioned abilities of LLMs, i.e. rationality, strategic reasoning ability, and instruction-following capability.
Causality can be described in terms of a structural causal model (SCM) that carries information on the variables of interest and their mechanistic relations. For most processes of interest the underlying SCM will only be partially observable, thus causal inference tries to leverage any exposed information. Graph neural networks (GNN) as universal approximators on structured input pose a viable candidate for causal learning, suggesting a tighter integration with SCM. To this effect we present a theoretical analysis from first principles that establishes a novel connection between GNN and SCM while providing an extended view on general neural-causal models. We then establish a new model class for GNN-based causal inference that is necessary and sufficient for causal effect identification. Our empirical illustration on simulations and standard benchmarks validate our theoretical proofs.
Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.
Graph neural networks (GNNs) are a popular class of machine learning models whose major advantage is their ability to incorporate a sparse and discrete dependency structure between data points. Unfortunately, GNNs can only be used when such a graph-structure is available. In practice, however, real-world graphs are often noisy and incomplete or might not be available at all. With this work, we propose to jointly learn the graph structure and the parameters of graph convolutional networks (GCNs) by approximately solving a bilevel program that learns a discrete probability distribution on the edges of the graph. This allows one to apply GCNs not only in scenarios where the given graph is incomplete or corrupted but also in those where a graph is not available. We conduct a series of experiments that analyze the behavior of the proposed method and demonstrate that it outperforms related methods by a significant margin.
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.
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