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The process of drawing electoral district boundaries is known as political redistricting. Within this context, gerrymandering is the practice of drawing these boundaries such that they unfairly favor a particular political party, often leading to unequal representation and skewed electoral outcomes. One of the few ways to detect gerrymandering is by algorithmically sampling redistricting plans. Previous methods mainly focus on sampling from some neighborhood of ``realistic' districting plans, rather than a uniform sample of the entire space. We present a deterministic subexponential time algorithm to uniformly sample from the space of all possible $ k $-partitions of a bounded degree planar graph, and with this construct a sample of the entire space of redistricting plans. We also give a way to restrict this sample space to plans that match certain compactness and population constraints at the cost of added complexity. The algorithm runs in $ 2^{O(\sqrt{n}\log n)} $ time, although we only give a heuristic implementation. Our method generalizes an algorithm to count self-avoiding walks on a square to count paths that split general planar graphs into $ k $ regions, and uses this to sample from the space of all $ k $-partitions of a planar graph.

Recent progress in sentence embedding, which represents the meaning of a sentence as a point in a vector space, has achieved high performance on tasks such as a semantic textual similarity (STS) task. However, sentence representations as a point in a vector space can express only a part of the diverse information that sentences have, such as asymmetrical relationships between sentences. This paper proposes GaussCSE, a Gaussian distribution-based contrastive learning framework for sentence embedding that can handle asymmetric relationships between sentences, along with a similarity measure for identifying inclusion relations. Our experiments show that GaussCSE achieves the same performance as previous methods in natural language inference tasks, and is able to estimate the direction of entailment relations, which is difficult with point representations.

We consider the problem of causal effect estimation with an unobserved confounder, where we observe a proxy variable that is associated with the confounder. Although Proxy causal learning (PCL) uses two proxy variables to recover the true causal effect, we show that a single proxy variable is sufficient for causal estimation if the outcome is generated deterministically, generalizing Control Outcome Calibration Approach (COCA). We propose two kernel-based methods for this setting: the first based on the two-stage regression approach, and the second based on a maximum moment restriction approach. We prove that both approaches can consistently estimate the causal effect, and we empirically demonstrate that we can successfully recover the causal effect on challenging synthetic benchmarks.

Existing trajectory prediction studies intensively leverage generative models. Normalizing flow is one of the genres with the advantage of being invertible to derive the probability density of predicted trajectories. However, mapping from a standard Gaussian by a flow-based model hurts the capacity to capture complicated patterns of trajectories, ignoring the under-represented motion intentions in the training data. To solve the problem, we propose a flow-based model to transform a mixed Gaussian prior into the future trajectory manifold. The model shows a better capacity for generating diverse trajectory patterns. Also, by associating each sub-Gaussian with a certain subspace of trajectories, we can generate future trajectories with controllable motion intentions. In such a fashion, the flow-based model is not encouraged to simply seek the most likelihood of the intended manifold anymore but a family of controlled manifolds with explicit interpretability. Our proposed method is demonstrated to show state-of-the-art performance in the quantitative evaluation of sampling well-aligned trajectories in top-M generated candidates. We also demonstrate that it can generate diverse, controllable, and out-of-distribution trajectories. Code is available at //github.com/mulplue/MGF.

Although motivated by the adaptation of text-to-speech synthesis models, we argue that more generic parameter-efficient fine-tuning (PEFT) is an appropriate framework to do such adaptation. However, catastrophic forgetting remains an issue with PEFT, damaging the pre-trained model's inherent capabilities. We demonstrate that existing Bayesian learning techniques can be applied to PEFT to prevent catastrophic forgetting as long as the parameter shift of the fine-tuned layers can be calculated differentiably. In a principled series of experiments on language modeling and speech synthesis tasks, we utilize established Laplace approximations, including diagonal and Kronecker factored approaches, to regularize PEFT with the low-rank adaptation (LoRA) and compare their performance in pre-training knowledge preservation. Our results demonstrate that catastrophic forgetting can be overcome by our methods without degrading the fine-tuning performance, and using the Kronecker factored approximations produces a better preservation of the pre-training knowledge than the diagonal ones.

Humans frequently make decisions with the aid of artificially intelligent (AI) systems. A common pattern is for the AI to recommend an action to the human who retains control over the final decision. Researchers have identified ensuring that a human has appropriate reliance on an AI as a critical component of achieving complementary performance. We argue that the current definition of appropriate reliance used in such research lacks formal statistical grounding and can lead to contradictions. We propose a formal definition of reliance, based on statistical decision theory, which separates the concepts of reliance as the probability the decision-maker follows the AI's prediction from challenges a human may face in differentiating the signals and forming accurate beliefs about the situation. Our definition gives rise to a framework that can be used to guide the design and interpretation of studies on human-AI complementarity and reliance. Using recent AI-advised decision making studies from literature, we demonstrate how our framework can be used to separate the loss due to mis-reliance from the loss due to not accurately differentiating the signals. We evaluate these losses by comparing to a baseline and a benchmark for complementary performance defined by the expected payoff achieved by a rational decision-maker facing the same decision task as the behavioral decision-makers.

Building upon score-based learning, new interest in stochastic localization techniques has recently emerged. In these models, one seeks to noise a sample from the data distribution through a stochastic process, called observation process, and progressively learns a denoiser associated to this dynamics. Apart from specific applications, the use of stochastic localization for the problem of sampling from an unnormalized target density has not been explored extensively. This work contributes to fill this gap. We consider a general stochastic localization framework and introduce an explicit class of observation processes, associated with flexible denoising schedules. We provide a complete methodology, $\textit{Stochastic Localization via Iterative Posterior Sampling}$ (SLIPS), to obtain approximate samples of this dynamics, and as a by-product, samples from the target distribution. Our scheme is based on a Markov chain Monte Carlo estimation of the denoiser and comes with detailed practical guidelines. We illustrate the benefits and applicability of SLIPS on several benchmarks, including Gaussian mixtures in increasing dimensions, Bayesian logistic regression and a high-dimensional field system from statistical-mechanics.

In the pursuit of developing Large Language Models (LLMs) that adhere to societal standards, it is imperative to discern the existence of toxicity in the generated text. The majority of existing toxicity metrics rely on encoder models trained on specific toxicity datasets. However, these encoders are susceptible to out-of-distribution (OOD) problems and depend on the definition of toxicity assumed in a dataset. In this paper, we introduce an automatic robust metric grounded on LLMs to distinguish whether model responses are toxic. We start by analyzing the toxicity factors, followed by examining the intrinsic toxic attributes of LLMs to ascertain their suitability as evaluators. Subsequently, we evaluate our metric, LLMs As ToxiciTy Evaluators (LATTE), on evaluation datasets.The empirical results indicate outstanding performance in measuring toxicity, improving upon state-of-the-art metrics by 12 points in F1 score without training procedure. We also show that upstream toxicity has an influence on downstream metrics.

The past decade has witnessed substantial growth of data-driven speech enhancement (SE) techniques thanks to deep learning. While existing approaches have shown impressive performance in some common datasets, most of them are designed only for a single condition (e.g., single-channel, multi-channel, or a fixed sampling frequency) or only consider a single task (e.g., denoising or dereverberation). Currently, there is no universal SE approach that can effectively handle diverse input conditions with a single model. In this paper, we make the first attempt to investigate this line of research. First, we devise a single SE model that is independent of microphone channels, signal lengths, and sampling frequencies. Second, we design a universal SE benchmark by combining existing public corpora with multiple conditions. Our experiments on a wide range of datasets show that the proposed single model can successfully handle diverse conditions with strong performance.

We propose a summation analog of the paradigm of parallel integration. Using this paradigm, we make some first steps towards an indefinite summation algorithm applicable to summands that rationally depend on the summation index and a P-recursive sequence and its shifts. Under the assumption that the corresponding difference field has no unnatural constants, we are able to compute a bound on the normal part of the denominator of a potential closed form. We can also handle the numerator. Our algorithm is incomplete so far as we cannot predict the special part of the denominator. However, we do have some structural results about special polynomials for the setting under consideration.