Awordvectorspace-sometimes referred toasawordembedding-associates similar wordsina vocabularywithsimilar vectors.

Calibration ensures that probabilistic forecasts meaningfully capture uncertainty by requiring that predicted probabilities align with empirical frequencies. However, many existing calibration methods are specialized for post-hoc recalibration, which can worsen the sharpness of forecasts. Drawing on the insight that calibration can be viewed as a distribution matching task, we introduce kernel-based calibration metrics that unify and generalize popular forms of calibration for both classification and regression. These metrics admit differentiable sample estimates, making it easy to incorporate a calibration objective into empirical risk minimization. Furthermore, we provide intuitive mechanisms to tailor calibration metrics to a decision task, and enforce accurate loss estimation and no regret decisions. Our empirical evaluation demonstrates that employing these metrics as regularizers enhances calibration, sharpness, and decision-making across a range of regression and classification tasks, outperforming methods relying solely on post-hoc recalibration.

In crowd counting, each training image contains multiple people, where each person is annotated by a dot. Existing crowd counting methods need to use a Gaussian to smooth each annotated dot or to estimate the likelihood of every pixel given the annotated point. In this paper, we show that imposing Gaussians to annotations hurts generalization performance. Instead, we propose to use Distribution Matching for crowd COUNTing (DM-Count). In DM-Count, we use Optimal Transport (OT) to measure the similarity between the normalized predicted density map and the normalized ground truth density map. To stabilize OT computation, we include a Total Variation loss in our model. We show that the generalization error bound of DM-Count is tighter than that of the Gaussian smoothed methods. In terms of Mean Absolute Error, DM-Count outperforms the previous state-of-the-art methods by a large margin on two large-scale counting datasets, UCF-QNRF and NWPU, and achieves the state-of-the-art results on the ShanghaiTech and UCF-CC50 datasets. DM-Count reduced the error of the state-of-the-art published result by approximately 16%.

We propose the use of adversarial wireless jamming to regularise the latent space of an autoencoder to match a diagonal Gaussian distribution. We consider the minimisation of a mean squared error distortion, where a jammer attempts to disrupt the recovery of a Gaussian source encoded and transmitted over the adversarial channel. A straightforward consequence of existing theoretical results is the fact that the saddle point of a minimax game - involving such an encoder, its corresponding decoder, and an adversarial jammer - consists of diagonal Gaussian noise output by the jammer. We use this result as inspiration for a novel approach to distribution matching in the latent space, utilising jamming as an auxiliary objective to encourage the aggregated latent posterior to match a diagonal Gaussian distribution. Using this new technique, we achieve distribution matching comparable to standard variational autoencoders and to Wasserstein autoencoders. This approach can also be generalised to other latent distributions.

While in some applications the goal is to "nudge" the pre-trained

This can be written succinctly as Y, b Y | ( X) (18) A.2 Calibration in Classification ECE used for break ties. For each model and dataset, the best performing model is then re-run with 50 random seeds to gather information about standard errors and statistical significance. Kernel Bandwidth We select the RBF kernel bandwidth for training on each dataset using the aforementioned hyperparameter optimization. For each county, we track the weather sequence of each year into a few summary statistics for each month (average/maximum/minimum temperatures, precipitation, cooling/heating degree days). All other hyperparameters are held constant, including the number of training steps.

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Recent advancement in generative models have demonstrated remarkable performance across various data modalities. Beyond their typical use in data synthesis, these models play a crucial role in distribution matching tasks such as latent variable modeling, domain translation, and domain adaptation. Generative Adversarial Networks (GANs) have emerged as the preferred method of distribution matching due to their efficacy in handling high-dimensional data and their flexibility in accommodating various constraints. However, GANs often encounter challenge in training due to their bi-level min-max optimization objective and susceptibility to mode collapse. In this work, we propose a novel approach for distribution matching inspired by the consistency models employed in Continuous Normalizing Flow (CNF). Our model inherits the advantages of CNF models, such as having a straight forward norm minimization objective, while remaining adaptable to different constraints similar to GANs. We provide theoretical validation of our proposed objective and demonstrate its performance through experiments on synthetic and real-world datasets.

Approximate machine unlearning (AMU) enables models to `forget' specific training data through specialized fine-tuning on a retained (and forget) subset of training set. However, processing this large retained subset still dominates computational runtime, while reductions of unlearning epochs also remain a challenge. In this paper, we propose two complementary methods to accelerate arbitrary classification-oriented AMU method. First, \textbf{Blend}, a novel distribution-matching dataset condensation (DC), merges visually similar images with shared blend-weights to significantly reduce the retained set size. It operates with minimal pre-processing overhead and is orders of magnitude faster than state-of-the-art DC methods. Second, our loss-centric method, \textbf{Accelerated-AMU (A-AMU)}, augments the AMU objective to quicken convergence. A-AMU achieves this by combining a steepened primary loss to expedite forgetting with a differentiable regularizer that matches the loss distributions of forgotten and in-distribution unseen data. Our extensive experiments demonstrate that this dual approach of data and loss-centric optimization dramatically reduces end-to-end unlearning latency across both single and multi-round scenarios, all while preserving model utility and privacy. To our knowledge, this is the first work to systematically tackle unlearning efficiency by jointly designing a specialized dataset condensation technique with a dedicated accelerated loss function. Code is available at https://github.com/algebraicdianuj/DC_Unlearning.

Distribution matching (DM) is a versatile domain-invariant representation learning technique that has been applied to tasks such as fair classification, domain adaptation, and domain translation. Non-parametric DM methods struggle with scalability and adversarial DM approaches suffer from instability and mode collapse. While likelihood-based methods are a promising alternative, they often impose unnecessary biases through fixed priors or require explicit density models (e.g., flows) that can be challenging to train. We address this limitation by introducing a novel approach to training likelihood-based DM using expressive score-based prior distributions. Our key insight is that gradient-based DM training only requires the prior's score function -- not its density -- allowing us to train the prior via denoising score matching. This approach eliminates biases from fixed priors (e.g., in VAEs), enabling more effective use of geometry-preserving regularization, while avoiding the challenge of learning an explicit prior density model (e.g., a flow-based prior). Our method also demonstrates better stability and computational efficiency compared to other diffusion-based priors (e.g., LSGM). Furthermore, experiments demonstrate superior performance across multiple tasks, establishing our score-based method as a stable and effective approach to distribution matching. Source code available at https://github.com/inouye-lab/SAUB.