The autoregressive time series model is a popular second-order stationary process, modeling a wide range of real phenomena. However, in applications, autoregressive signals are often corrupted by additive noise. Further, the autoregressive process and the corruptive noise may be highly impulsive, stemming from an infinite-variance distribution. The model estimation techniques that account for additional noise tend to show reduced efficacy when there is very strong noise present in the data, especially when the noise is heavy-tailed. Moreover, identification of a model corrupted with heavy-tailed, particularly infinite-variance noise, can be a very challenging task. In this paper, we propose a novel self-supervised learning method to denoise the additive noise-corrupted autoregressive model. Our approach is motivated by recent work in computer vision and does not require full knowledge of the noise distribution. We use the proposed method to recover exemplary finite- and infinite-variance autoregressive signals, namely, Gaussian- and alpha-stable distributed signals, respectively, from their noise-corrupted versions. The simulation study conducted on both synthetic and semi-synthetic data demonstrates the efficiency of our method compared to several baseline methods, particularly when the corruption is significant and impulsive in nature. Finally, we apply the presented methodology to forecast the pure autoregressive signal from the noise-corrupted data.

We present a novel framework for predicting next actions in soccer possessions by leveraging path signatures to encode their complex spatio-temporal structure. Unlike existing approaches, we do not rely on fixed historical windows and handcrafted features, but rather encode the entire recent possession, thereby avoiding the inclusion of potentially irrelevant or misleading historical information. Path signatures naturally capture the order and interaction of events, providing a mathematically grounded feature encoding for variable-length time series of irregular sampling frequencies without the necessity for manual feature engineering. Our proposed approach outperforms a transformer-based benchmark across various loss metrics and considerably reduces computational cost. Building on these results, we introduce a new possession evaluation metric based on well-established frameworks in soccer analytics, incorporating both predicted action type probabilities and action location. Our metric shows greater reliability than existing metrics in domain-specific comparisons. Finally, we validate our approach through a detailed analysis of the 2017/18 Premier League season and discuss further applications and future extensions.

A central challenge in many areas of science and engineering is to identify model parameters that are consistent with prior knowledge and empirical data. Bayesian inference offers a principled framework for this task, but can be computationally prohibitive when models are defined by stochastic simulators. Simulation-based Inference (SBI) is a suite of methods developed to overcome this limitation, which has enabled scientific discoveries in fields such as particle physics, astrophysics, and neuroscience. The core idea of SBI is to train neural networks on data generated by a simulator, without requiring access to likelihood evaluations. Once trained, inference is amortized: The neural network can rapidly perform Bayesian inference on empirical observations without requiring additional training or simulations. In this tutorial, we provide a practical guide for practitioners aiming to apply SBI methods. We outline a structured SBI workflow and offer practical guidelines and diagnostic tools for every stage of the process -- from setting up the simulator and prior, choosing and training inference networks, to performing inference and validating the results. We illustrate these steps through examples from astrophysics, psychophysics, and neuroscience. This tutorial empowers researchers to apply state-of-the-art SBI methods, facilitating efficient parameter inference for scientific discovery.

Stochastic gradient descent (SGD), one of the most fundamental optimization algorithms in machine learning (ML), can be recast through a continuous-time approximation as a Fokker-Planck equation for Langevin dynamics, a viewpoint that has motivated many theoretical studies. Within this framework, we study the relationship between the quasi-stationary distribution derived from this equation and the initial distribution through the Kullback-Leibler (KL) divergence. As the quasi-steady-state distribution depends on the expected cost function, the KL divergence eventually reveals the connection between the expected cost function and the initialization distribution. By applying this to deep neural network models (DNNs), we can express the bounds of the expected loss function explicitly in terms of the initialization parameters. Then, by minimizing this bound, we obtain an optimal condition of the initialization variance in the Gaussian case. This result provides a concrete mathematical criterion, rather than a heuristic approach, to select the scale of weight initialization in DNNs. In addition, we experimentally confirm our theoretical results by using the classical SGD to train fully connected neural networks on the MNIST and Fashion-MNIST datasets. The result shows that if the variance of the initialization distribution satisfies our theoretical optimal condition, then the corresponding DNN model always achieves lower final training loss and higher test accuracy than the conventional He-normal initialization. Our work thus supplies a mathematically grounded indicator that guides the choice of initialization variance and clarifies its physical meaning of the dynamics of parameters in DNNs.

The ratio of two densities characterizes their differences. We consider learning the density ratio given i.i.d. observations from each of the two distributions. We propose additive tree models for the density ratio along with efficient algorithms for training these models using a new loss function called the balancing loss. With this loss, additive tree models for the density ratio can be trained using algorithms original designed for supervised learning. Specifically, they can be trained from both an optimization perspective that parallels tree boosting and from a (generalized) Bayesian perspective that parallels Bayesian additive regression trees (BART). For the former, we present two boosting algorithms -- one based on forward-stagewise fitting and the other based on gradient boosting, both of which produce a point estimate for the density ratio function. For the latter, we show that due to the loss function's resemblance to an exponential family kernel, the new loss can serve as a pseudo-likelihood for which conjugate priors exist, thereby enabling effective generalized Bayesian inference on the density ratio using backfitting samplers designed for BART. The resulting uncertainty quantification on the inferred density ratio is critical for applications involving high-dimensional and complex distributions in which uncertainty given limited data can often be substantial. We provide insights on the balancing loss through its close connection to the exponential loss in binary classification and to the variational form of f-divergence, in particular that of the squared Hellinger distance. Our numerical experiments demonstrate the accuracy of the proposed approach while providing unique capabilities in uncertainty quantification. We demonstrate the application of our method in a case study involving assessing the quality of generative models for microbiome compositional data.

Masked latent prediction has emerged as a leading paradigm in self-supervised learning (SSL), especially for general audio and music representation learning. While recent methods have demonstrated strong performance, the role of the predictor module used at the output of such SSL systems remains mainly overlooked, despite being crucial for solving the pretext task at hand. In particular, this module should be able to deal with the ambiguity inherent in audio content, especially when it is composed of multiple sound sources. This work proposes a novel enhancement: integrating Multiple Choice Learning (MCL) to explicitly model prediction ambiguity and improve representation quality. We build on top of the recently proposed MATPAC system, improving its prediction and unsupervised classification pretext tasks with MCL. We extensively evaluate our method, MATPAC++, through both linear probing across multiple downstream tasks and fine-tuning on AudioSet, employing a unified protocol that enables rigorous and fair comparisons with state-of-the-art SSL approaches. Results show that our proposal achieves state-of-the-art when fine-tuned on AudioSet and overall state-of-the-art scores on downstream tasks. Additionally, we examine domain specialisation by training exclusively on music data, where our model achieves state-of-the-art performance with significantly improved efficiency.

Recently, neural surrogate models have emerged as a compelling alternative to traditional simulation workflows. This is accomplished by modeling the underlying function of scientific simulations, removing the need to run expensive simulations. Beyond just mapping from input parameter to output, surrogates have also been shown useful for inverse problems: output to input parameters. Inverse problems can be understood as search, where we aim to find parameters whose surrogate outputs contain a specified feature. Yet finding these parameters can be costly, especially for high-dimensional parameter spaces. Thus, existing surrogate-based solutions primarily focus on finding a small set of matching parameters, in the process overlooking the broader picture of plausible parameters. Our work aims to model and visualize the distribution of possible input parameters that produce a given output feature. To achieve this goal, we aim to address two challenges: (1) the approximation error inherent in the surrogate model and (2) forming the parameter distribution in an interactive manner. We model error via density estimation, reporting high density only if a given parameter configuration is close to training parameters, measured both over the input and output space. Our density estimate is used to form a prior belief on parameters, and when combined with a likelihood on features, gives us an efficient way to sample plausible parameter configurations that generate a target output feature. We demonstrate the usability of our solution through a visualization interface by performing feature-driven parameter analysis over the input parameter space of three simulation datasets. Source code is available at https://github.com/matthewberger/seeing-the-many

In incremental learning, enhancing the generality of knowledge is crucial for adapting to dynamic data inputs. It can develop generalized representations or more balanced decision boundaries, preventing the degradation of long-term knowledge over time and thus mitigating catastrophic forgetting. Some emerging incremental learning methods adopt an encoder-decoder architecture and have achieved promising results. In the encoder-decoder achitecture, improving the generalization capabilities of both the encoder and decoder is critical, as it helps preserve previously learned knowledge while ensuring adaptability and robustness to new, diverse data inputs. However, many existing continual methods focus solely on enhancing one of the two components, which limits their effectiveness in mitigating catastrophic forgetting. And these methods perform even worse in small-memory scenarios, where only a limited number of historical samples can be stored. To mitigate this limitation, we introduces SEDEG, a two-stage training framework for vision transformers (ViT), focusing on sequentially improving the generality of both Decoder and Encoder. Initially, SEDEG trains an ensembled encoder through feature boosting to learn generalized representations, which subsequently enhance the decoder's generality and balance the classifier. The next stage involves using knowledge distillation (KD) strategies to compress the ensembled encoder and develop a new, more generalized encoder. This involves using a balanced KD approach and feature KD for effective knowledge transfer. Extensive experiments on three benchmark datasets show SEDEG's superior performance, and ablation studies confirm the efficacy of its components. The code is available at https://github.com/ShaolingPu/CIL.

We introduce \textbf{SNAP-UQ}, a single-pass, label-free uncertainty method for TinyML that estimates risk from \emph{depth-wise next-activation prediction}: tiny int8 heads forecast the statistics of the next layer from a compressed view of the previous one, and a lightweight monotone mapper turns the resulting surprisal into an actionable score. The design requires no temporal buffers, auxiliary exits, or repeated forward passes, and adds only a few tens of kilobytes to MCU deployments. Across vision and audio backbones, SNAP-UQ consistently reduces flash and latency relative to early-exit and deep ensembles (typically $\sim$40--60\% smaller and $\sim$25--35\% faster), with competing methods of similar accuracy often exceeding memory limits. In corrupted streams it improves accuracy-drop detection by several AUPRC points and maintains strong failure detection (AUROC $\approx$0.9) in a single pass. Grounding uncertainty in layer-to-layer dynamics yields a practical, resource-efficient basis for on-device monitoring in TinyML.

We introduce TCUQ, a single pass, label free uncertainty monitor for streaming TinyML that converts short horizon temporal consistency captured via lightweight signals on posteriors and features into a calibrated risk score with an O(W ) ring buffer and O(1) per step updates. A streaming conformal layer turns this score into a budgeted accept/abstain rule, yielding calibrated behavior without online labels or extra forward passes. On microcontrollers, TCUQ fits comfortably on kilobyte scale devices and reduces footprint and latency versus early exit and deep ensembles (typically about 50 to 60% smaller and about 30 to 45% faster), while methods of similar accuracy often run out of memory. Under corrupted in distribution streams, TCUQ improves accuracy drop detection by 3 to 7 AUPRC points and reaches up to 0.86 AUPRC at high severities; for failure detection it attains up to 0.92 AUROC. These results show that temporal consistency, coupled with streaming conformal calibration, provides a practical and resource efficient foundation for on device monitoring in TinyML.