A 2025 survey in the forests of Laos, Vietnam, and Cambodia uncovered several rare and endangered animals. A pig-tailed macaque is caught on camera in a Cambodian forest. Breakthroughs, discoveries, and DIY tips sent six days a week. The results of a new camera-trap survey in Southeast Asia is revealing a bevy of hidden biodiversity tucked within the Annamites mountain range . This largely unexplored wildlife hotspot has a forest stretching 683 miles (1,100 kilometers) across the countries of Laos, Vietnam, and Cambodia.

The $β$-VAE is a foundational framework for unsupervised disentanglement, using $β$ to regulate the trade-off between latent factorization and reconstruction fidelity. Empirically, however, disentanglement performance exhibits a pervasive non-monotonic trend: benchmarks such as MIG and SAP typically peak at intermediate $β$ and collapse as regularization increases. We demonstrate that this collapse is a fundamental information-theoretic failure, where strong Kullback-Leibler pressure promotes marginal independence at the expense of the latent channel's semantic informativeness. By formalizing this mechanism in a linear-Gaussian setting, we prove that for $β> 1$, stationarity-induced dynamics trigger a spectral contraction of the encoder gain, driving latent-factor mutual information to zero. To resolve this, we introduce the $λβ$-VAE, which decouples regularization pressure from informational collapse via an auxiliary $L_2$ reconstruction penalty $λ$. Extensive experiments on dSprites, Shapes3D, and MPI3D-real confirm that $λ> 0$ stabilizes disentanglement and restores latent informativeness over a significantly broader range of $β$, providing a principled theoretical justification for dual-parameter regularization in variational inference backbones.

As machine learning models increasingly impact society, their opaque nature poses challenges to trust and accountability, particularly in fairness contexts. Understanding how individual features influence model outcomes is crucial for building interpretable and equitable models. While feature importance metrics for accuracy are well-established, methods for assessing feature contributions to fairness remain underexplored. We propose two model-agnostic approaches to measure fair feature importance. First, we propose to compare model fairness before and after permuting feature values. This simple intervention-based approach decouples a feature and model predictions to measure its contribution to training. Second, we evaluate the fairness of models trained with and without a given feature. This occlusion-based score enjoys dramatic computational simplification via minipatch learning. Our empirical results reflect the simplicity and effectiveness of our proposed metrics for multiple predictive tasks. Both methods offer simple, scalable, and interpretable solutions to quantify the influence of features on fairness, providing new tools for responsible machine learning development.

We study online learning in the random-order model, where the multiset of loss functions is chosen adversarially but revealed in a uniformly random order. Building on the batch-to-online conversion by Dong and Yoshida (2023), we show that if an offline algorithm admits a $(1+\varepsilon)$-approximation guarantee and the effect of $\varepsilon$ on its average sensitivity is characterized by a function $φ(\varepsilon)$, then an adaptive choice of $\varepsilon$ yields a small-loss regret bound of $\tilde O(φ^{\star}(\mathrm{OPT}_T))$, where $φ^{\star}$ is the concave conjugate of $φ$, $\mathrm{OPT}_T$ is the offline optimum over $T$ rounds, and $\tilde O$ hides polylogarithmic factors in $T$. Our method requires no regularity assumptions on loss functions, such as smoothness, and can be viewed as a generalization of the AdaGrad-style tuning applied to the approximation parameter $\varepsilon$. Our result recovers and strengthens the $(1+\varepsilon)$-approximate regret bounds of Dong and Yoshida (2023) and yields small-loss regret bounds for online $k$-means clustering, low-rank approximation, and regression. We further apply our framework to online submodular function minimization using $(1\pm\varepsilon)$-cut sparsifiers of submodular hypergraphs, obtaining a small-loss regret bound of $\tilde O(n^{3/4}(1 + \mathrm{OPT}_T^{3/4}))$, where $n$ is the ground-set size. Our approach sheds light on the power of sparsification and related techniques in establishing small-loss regret bounds in the random-order model.

In many safety-critical settings, probabilistic ML systems have to make predictions subject to algebraic constraints, e.g., predicting the most likely trajectory that does not cross obstacles. These real-world constraints are rarely convex, nor the densities considered are (log-)concave. This makes computing this constrained maximum a posteriori (MAP) prediction efficiently and reliably extremely challenging. In this paper, we first investigate under which conditions we can perform constrained MAP inference over continuous variables exactly and efficiently and devise a scalable message-passing algorithm for this tractable fragment. Then, we devise a general constrained MAP strategy that interleaves partitioning the domain into convex feasible regions with numerical constrained optimization. We evaluate both methods on synthetic and real-world benchmarks, showing our approaches outperform constraint-agnostic baselines, and scale to complex densities intractable for SoTA exact solvers.

We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only assumes that its singular vectors are generic. It is a vast generalization of the i.i.d. Gaussian design typically considered in the theoretical literature, and is motivated by the fact that real data often have a complex correlation structure so that methods relying on i.i.d. assumptions can be highly suboptimal. Building on the paradigm of spectrally-initialized iterative optimization, this paper proposes optimal spectral estimators and combines them with an approximate message passing (AMP) algorithm, establishing rigorous performance guarantees for these two algorithmic steps. Both the spectral initialization and the subsequent AMP meet existing conjectures on the fundamental limits to estimation -- the former on the optimal sample complexity for efficient weak recovery, and the latter on the optimal errors. Numerical experiments suggest the effectiveness of our methods and accuracy of our theory beyond orthogonally invariant data.

Iterative self-improvement fine-tunes an autoregressive large language model (LLM) on reward-verified outputs generated by the LLM itself. In contrast to the empirical success of self-improvement, the theoretical foundation of this generative, iterative procedure in a practical, finite-sample setting remains limited. We make progress toward this goal by modeling each round of self-improvement as maximum-likelihood fine-tuning on a reward-filtered distribution and deriving finite-sample guarantees for the expected reward. Our analysis reveals an explicit feedback loop where better models accept more data per iteration, supporting sustained self-improvement while explaining eventual saturation of such improvement. Adopting a task-centric view by considering reasoning tasks with multiple difficulty levels, we further prove quantifiable conditions on model initialization, task difficulty, and sample budget where easy-to-hard curricula provably achieve better guarantees than training on fixed mixtures of tasks. Our analyses are validated via Monte-Carlo simulations and controlled experiments on graph-based reasoning tasks.

Current instance segmentation models achieve high performance on average predictions, but lack principled uncertainty quantification: their outputs are not calibrated, and there is no guarantee that a predicted mask is close to the ground truth. To address this limitation, we introduce a conformal prediction algorithm to generate adaptive confidence sets for instance segmentation. Given an image and a pixel coordinate query, our algorithm generates a confidence set of instance predictions for that pixel, with a provable guarantee for the probability that at least one of the predictions has high Intersection-Over-Union (IoU) with the true object instance mask. We apply our algorithm to instance segmentation examples in agricultural field delineation, cell segmentation, and vehicle detection. Empirically, we find that our prediction sets vary in size based on query difficulty and attain the target coverage, outperforming existing baselines such as Learn Then Test, Conformal Risk Control, and morphological dilation-based methods. We provide versions of the algorithm with asymptotic and finite sample guarantees.

Conditional Value-at-Risk (CVaR) is a central tail-risk measure in stochastic structural mechanics, yet its accurate evaluation under high-dimensional, spatially correlated material uncertainty remains computationally prohibitive for classical Monte Carlo methods. Leveraging bounded-expectation reformulations of CVaR compatible with quantum amplitude estimation, we develop a quantum-enhanced inference framework that casts CVaR evaluation as a statistically consistent, confidence-constrained maximum-likelihood amplitude estimation problem. The proposed method extends iterative quantum amplitude estimation (IQAE) by embedding explicit maximum-likelihood inference within a rigorously controlled interval-tracking architecture. To ensure global correctness under finite-shot noise and the non-injective oscillatory response induced by Grover amplification, we introduce a stabilized inference scheme incorporating multi-hypothesis feasibility tracking, periodic low-depth disambiguation, and a bounded restart mechanism governed by an explicit failure-probability budget. This formulation preserves the quadratic oracle-complexity advantage of amplitude estimation while providing finite-sample confidence guarantees and reduced estimator variance. The framework is demonstrated on benchmark problems with spatially correlated lognormal Young's modulus fields generated using a Nystrom low-rank Gaussian kernel model. Numerical results show that the proposed estimator achieves substantially lower oracle complexity than classical Monte Carlo CVaR estimation at comparable confidence levels, while maintaining rigorous statistical reliability. This work establishes a practically robust and theoretically grounded quantum-enhanced methodology for tail-risk quantification in stochastic continuum mechanics.

We introduce WildCat, a high-accuracy, low-cost approach to compressing the attention mechanism in neural networks. While attention is a staple of modern network architectures, it is also notoriously expensive to deploy due to resource requirements that scale quadratically with the input sequence length $n$. WildCat avoids these quadratic costs by only attending over a small weighted coreset. Crucially, we select the coreset using a fast but spectrally-accurate subsampling algorithm -- randomly pivoted Cholesky -- and weight the elements optimally to minimise reconstruction error. Remarkably, given bounded inputs, WildCat approximates exact attention with super-polynomial $O(n^{-\sqrt{\log(\log(n))}})$ error decay while running in near-linear $O(n^{1+o(1)})$ time. In contrast, prior practical approximations either lack error guarantees or require quadratic runtime to guarantee such high fidelity. We couple this advance with a GPU-optimized PyTorch implementation and a suite of benchmark experiments demonstrating the benefits of WildCat for image generation, image classification, and language model KV cache compression.