Daily Papers

A key element in solving real-life data science problems is selecting the types of models to use. Tree ensemble models (such as XGBoost) are usually recommended for classification and regression problems with tabular data. However, several deep learning models for tabular data have recently been proposed, claiming to outperform XGBoost for some use cases. This paper explores whether these deep models should be a recommended option for tabular data by rigorously comparing the new deep models to XGBoost on various datasets. In addition to systematically comparing their performance, we consider the tuning and computation they require. Our study shows that XGBoost outperforms these deep models across the datasets, including the datasets used in the papers that proposed the deep models. We also demonstrate that XGBoost requires much less tuning. On the positive side, we show that an ensemble of deep models and XGBoost performs better on these datasets than XGBoost alone.

Despite the success of deep learning for text and image data, tree-based ensemble models are still state-of-the-art for machine learning with heterogeneous tabular data. However, there is a significant need for tabular-specific gradient-based methods due to their high flexibility. In this paper, we propose GRANDE, GRAdieNt-Based Decision Tree Ensembles, a novel approach for learning hard, axis-aligned decision tree ensembles using end-to-end gradient descent. GRANDE is based on a dense representation of tree ensembles, which affords to use backpropagation with a straight-through operator to jointly optimize all model parameters. Our method combines axis-aligned splits, which is a useful inductive bias for tabular data, with the flexibility of gradient-based optimization. Furthermore, we introduce an advanced instance-wise weighting that facilitates learning representations for both, simple and complex relations, within a single model. We conducted an extensive evaluation on a predefined benchmark with 19 classification datasets and demonstrate that our method outperforms existing gradient-boosting and deep learning frameworks on most datasets. The method is available under: https://github.com/s-marton/GRANDE

We propose TabTransformer, a novel deep tabular data modeling architecture for supervised and semi-supervised learning. The TabTransformer is built upon self-attention based Transformers. The Transformer layers transform the embeddings of categorical features into robust contextual embeddings to achieve higher prediction accuracy. Through extensive experiments on fifteen publicly available datasets, we show that the TabTransformer outperforms the state-of-the-art deep learning methods for tabular data by at least 1.0% on mean AUC, and matches the performance of tree-based ensemble models. Furthermore, we demonstrate that the contextual embeddings learned from TabTransformer are highly robust against both missing and noisy data features, and provide better interpretability. Lastly, for the semi-supervised setting we develop an unsupervised pre-training procedure to learn data-driven contextual embeddings, resulting in an average 2.1% AUC lift over the state-of-the-art methods.

Concept Bottleneck Models (CBMs) predict through human-interpretable concepts, but they typically output point concept probabilities that conflate epistemic uncertainty (reducible model underspecification) with aleatoric uncertainty (irreducible input ambiguity). This makes concept-level uncertainty hard to interpret and, more importantly, hard to act upon. We introduce CREDENCE (Credal Ensemble Concept Estimation), a CBM framework that decomposes concept uncertainty by construction. CREDENCE represents each concept as a credal prediction (a probability interval), derives epistemic uncertainty from disagreement across diverse concept heads, and estimates aleatoric uncertainty via a dedicated ambiguity output trained to match annotator disagreement when available. The resulting signals support prescriptive decisions: automate low-uncertainty cases, prioritize data collection for high-epistemic cases, route high-aleatoric cases to human review, and abstain when both are high. Across several tasks, we show that epistemic uncertainty is positively associated with prediction errors, whereas aleatoric uncertainty closely tracks annotator disagreement, providing guidance beyond error correlation. Our implementation is available at the following link: https://github.com/Tankiit/Credal_Sets/tree/ensemble-credal-cbm

The first tabular foundation model, TabPFN, and its successor TabPFNv2 have impacted tabular AI substantially, with dozens of methods building on it and hundreds of applications across different use cases. This report introduces TabPFN-2.5, the next generation of our tabular foundation model, built for datasets with up to 50,000 data points and 2,000 features, a 20x increase in data cells compared to TabPFNv2. TabPFN-2.5 is now the leading method for the industry standard benchmark TabArena (which contains datasets with up to 100,000 training data points), substantially outperforming tuned tree-based models and matching the accuracy of AutoGluon 1.4, a complex four-hour tuned ensemble that even includes the previous TabPFNv2. Remarkably, default TabPFN-2.5 has a 100% win rate against default XGBoost on small to medium-sized classification datasets (<=10,000 data points, 500 features) and a 87% win rate on larger datasets up to 100K samples and 2K features (85% for regression). For production use cases, we introduce a new distillation engine that converts TabPFN-2.5 into a compact MLP or tree ensemble, preserving most of its accuracy while delivering orders-of-magnitude lower latency and plug-and-play deployment. This new release will immediately strengthen the performance of the many applications and methods already built on the TabPFN ecosystem.

Despite recent advances in large language models, open-source models often struggle to consistently perform well on complex reasoning tasks. Existing ensemble methods, whether applied at the token or output levels, fail to address these challenges. In response, we present Language model Ensemble with Monte Carlo Tree Search (LE-MCTS), a novel framework for process-level ensembling of language models. LE-MCTS formulates step-by-step reasoning with an ensemble of language models as a Markov decision process. In this framework, states represent intermediate reasoning paths, while actions consist of generating the next reasoning step using one of the language models selected from a predefined pool. Guided by a process-based reward model, LE-MCTS performs a tree search over the reasoning steps generated by different language models, identifying the most accurate reasoning chain. Experimental results on five mathematical reasoning benchmarks demonstrate that our approach outperforms both single language model decoding algorithms and language model ensemble methods. Notably, LE-MCTS improves performance by 3.6% and 4.3% on the MATH and MQA datasets, respectively, highlighting its effectiveness in solving complex reasoning problems.

Random forests and, more generally, (decision\nobreakdash-)tree ensembles are widely used methods for classification and regression. Recent algorithmic advances allow to compute decision trees that are optimal for various measures such as their size or depth. We are not aware of such research for tree ensembles and aim to contribute to this area. Mainly, we provide two novel algorithms and corresponding lower bounds. First, we are able to carry over and substantially improve on tractability results for decision trees, obtaining a (6delta D S)^S cdot poly-time algorithm, where S is the number of cuts in the tree ensemble, D the largest domain size, and delta is the largest number of features in which two examples differ. To achieve this, we introduce the witness-tree technique which also seems promising for practice. Second, we show that dynamic programming, which has been successful for decision trees, may also be viable for tree ensembles, providing an ell^n cdot poly-time algorithm, where ell is the number of trees and n the number of examples. Finally, we compare the number of cuts necessary to classify training data sets for decision trees and tree ensembles, showing that ensembles may need exponentially fewer cuts for increasing number of trees.

Despite their remarkable effectiveness and broad application, the drivers of success underlying ensembles of trees are still not fully understood. In this paper, we highlight how interpreting tree ensembles as adaptive and self-regularizing smoothers can provide new intuition and deeper insight to this topic. We use this perspective to show that, when studied as smoothers, randomized tree ensembles not only make predictions that are quantifiably more smooth than the predictions of the individual trees they consist of, but also further regulate their smoothness at test-time based on the dissimilarity between testing and training inputs. First, we use this insight to revisit, refine and reconcile two recent explanations of forest success by providing a new way of quantifying the conjectured behaviors of tree ensembles objectively by measuring the effective degree of smoothing they imply. Then, we move beyond existing explanations for the mechanisms by which tree ensembles improve upon individual trees and challenge the popular wisdom that the superior performance of forests should be understood as a consequence of variance reduction alone. We argue that the current high-level dichotomy into bias- and variance-reduction prevalent in statistics is insufficient to understand tree ensembles -- because the prevailing definition of bias does not capture differences in the expressivity of the hypothesis classes formed by trees and forests. Instead, we show that forests can improve upon trees by three distinct mechanisms that are usually implicitly entangled. In particular, we demonstrate that the smoothing effect of ensembling can reduce variance in predictions due to noise in outcome generation, reduce variability in the quality of the learned function given fixed input data and reduce potential bias in learnable functions by enriching the available hypothesis space.

Linear Mode Connectivity (LMC) refers to the phenomenon that performance remains consistent for linearly interpolated models in the parameter space. For independently optimized model pairs from different random initializations, achieving LMC is considered crucial for validating the stable success of the non-convex optimization in modern machine learning models and for facilitating practical parameter-based operations such as model merging. While LMC has been achieved for neural networks by considering the permutation invariance of neurons in each hidden layer, its attainment for other models remains an open question. In this paper, we first achieve LMC for soft tree ensembles, which are tree-based differentiable models extensively used in practice. We show the necessity of incorporating two invariances: subtree flip invariance and splitting order invariance, which do not exist in neural networks but are inherent to tree architectures, in addition to permutation invariance of trees. Moreover, we demonstrate that it is even possible to exclude such additional invariances while keeping LMC by designing decision list-based tree architectures, where such invariances do not exist by definition. Our findings indicate the significance of accounting for architecture-specific invariances in achieving LMC.

Predicting trends in stock market prices has been an area of interest for researchers for many years due to its complex and dynamic nature. Intrinsic volatility in stock market across the globe makes the task of prediction challenging. Forecasting and diffusion modeling, although effective can't be the panacea to the diverse range of problems encountered in prediction, short-term or otherwise. Market risk, strongly correlated with forecasting errors, needs to be minimized to ensure minimal risk in investment. The authors propose to minimize forecasting error by treating the forecasting problem as a classification problem, a popular suite of algorithms in Machine learning. In this paper, we propose a novel way to minimize the risk of investment in stock market by predicting the returns of a stock using a class of powerful machine learning algorithms known as ensemble learning. Some of the technical indicators such as Relative Strength Index (RSI), stochastic oscillator etc are used as inputs to train our model. The learning model used is an ensemble of multiple decision trees. The algorithm is shown to outperform existing algo- rithms found in the literature. Out of Bag (OOB) error estimates have been found to be encouraging. Key Words: Random Forest Classifier, stock price forecasting, Exponential smoothing, feature extraction, OOB error and convergence.

Tabular foundation models (TFMs) increasingly rival tree ensembles, but their performance is often compute-inefficient: with standard affine scalar tokenization, each feature injects value variation through an essentially one-dimensional channel, and feature IDs/positional signals cannot increase within-feature value degrees of freedom, yielding weak early-layer value sensitivity and redundant hidden states. We present a unified tokenize-and-route framework for strong TFMs: RaBEL expands each scalar into compact localized RBF features (optionally exponent-gated) to improve conditioning and shallow-layer effective rank, while a reordered bidirectional block SrightarrowNrightarrowF aligns computation with the readout by aggregating cross-sample context before feature mixing and using attention pooling. Together, these changes yield LimiX-2M, a 2M-parameter model that outperforms larger TabPFN-v2 and TabICL baselines on widely used tabular benchmarks while reducing training and inference costs. These results highlight value-aware tokenization and readout-aligned routing as key levers for improving the accuracy--efficiency trade-off in TFMs. Model checkpoints and inference code are available at https://github.com/limix-ldm-ai/LimiX.

Automating machine learning has achieved remarkable technological developments in recent years, and building an automated machine learning pipeline is now an essential task. The model ensemble is the technique of combining multiple models to get a better and more robust model. However, existing automated machine learning tends to be simplistic in handling the model ensemble, where the ensemble strategy is fixed, such as stacked generalization. There have been many techniques on different ensemble methods, especially ensemble selection, and the fixed ensemble strategy limits the upper limit of the model's performance. In this article, we present a novel framework for automated machine learning. Our framework incorporates advances in dynamic ensemble selection, and to our best knowledge, our approach is the first in the field of AutoML to search and optimize ensemble strategies. In the comparison experiments, our method outperforms the state-of-the-art automated machine learning frameworks with the same CPU time in 42 classification datasets from the OpenML platform. Ablation experiments on our framework validate the effectiveness of our proposed method.

LLM Ensemble -- which involves the comprehensive use of multiple large language models (LLMs), each aimed at handling user queries during downstream inference, to benefit from their individual strengths -- has gained substantial attention recently. The widespread availability of LLMs, coupled with their varying strengths and out-of-the-box usability, has profoundly advanced the field of LLM Ensemble. This paper presents the first systematic review of recent developments in LLM Ensemble. First, we introduce our taxonomy of LLM Ensemble and discuss several related research problems. Then, we provide a more in-depth classification of the methods under the broad categories of "ensemble-before-inference, ensemble-during-inference, ensemble-after-inference'', and review all relevant methods. Finally, we introduce related benchmarks and applications, summarize existing studies, and suggest several future research directions. A curated list of papers on LLM Ensemble is available at https://github.com/junchenzhi/Awesome-LLM-Ensemble.

Ensemble methods enhance Large Language Models (LLMs) by combining multiple models but suffer from high computational costs. In this paper, we introduce Speculative Ensemble, a novel framework that accelerates LLM ensembles without sacrificing performance, inspired by Speculative Decoding-where a small proposal model generates tokens sequentially, and a larger target model verifies them in parallel. Our approach builds on two key insights: (1) the verification distribution can be the ensemble distribution of both the proposal and target models, and (2) alternating each model as the proposer and verifier can further enhance efficiency. We generalize this method to ensembles with n models and theoretically prove that SE is never slower than a standard ensemble, typically achieving faster speed. Extensive experiments demonstrate speed improvements of 1.11x-2.23x over standard ensemble techniques without compromising generation quality. Our code is available at https://github.com/Kamichanw/Speculative-Ensemble/

Regression trees are among the most interpretable yet expressive model classes in machine learning. Historically, greedy induction has been the dominant approach for constructing well-performing regression trees. While optimal methods based on dynamic programming and branch-and-bound exist, they are computationally prohibitive for general linear regression trees, despite often achieving substantially better performance than greedy approaches. Recent work has shown that specialized lookahead strategies can dramatically improve runtime while maintaining near-optimal performance, primarily in classification settings. In this work, we develop a novel algorithm for near-optimal, sparse, piecewise linear regression trees that combines a lookahead-style search strategy with efficient rank-one Cholesky updates of the Gram matrix. We demonstrate, both theoretically and empirically, that our method achieves a favorable trade-off between computational efficiency, predictive accuracy, and sparsity, and scales significantly better than the current state of the art.

Studying low-likelihood high-impact extreme weather events in a warming world is a significant and challenging task for current ensemble forecasting systems. While these systems presently use up to 100 members, larger ensembles could enrich the sampling of internal variability. They may capture the long tails associated with climate hazards better than traditional ensemble sizes. Due to computational constraints, it is infeasible to generate huge ensembles (comprised of 1,000-10,000 members) with traditional, physics-based numerical models. In this two-part paper, we replace traditional numerical simulations with machine learning (ML) to generate hindcasts of huge ensembles. In Part I, we construct an ensemble weather forecasting system based on Spherical Fourier Neural Operators (SFNO), and we discuss important design decisions for constructing such an ensemble. The ensemble represents model uncertainty through perturbed-parameter techniques, and it represents initial condition uncertainty through bred vectors, which sample the fastest growing modes of the forecast. Using the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (IFS) as a baseline, we develop an evaluation pipeline composed of mean, spectral, and extreme diagnostics. Using large-scale, distributed SFNOs with 1.1 billion learned parameters, we achieve calibrated probabilistic forecasts. As the trajectories of the individual members diverge, the ML ensemble mean spectra degrade with lead time, consistent with physical expectations. However, the individual ensemble members' spectra stay constant with lead time. Therefore, these members simulate realistic weather states, and the ML ensemble thus passes a crucial spectral test in the literature. The IFS and ML ensembles have similar Extreme Forecast Indices, and we show that the ML extreme weather forecasts are reliable and discriminating.

Polytrees are a subclass of Bayesian networks that seek to capture the conditional dependencies between a set of n variables as a directed forest and are motivated by their more efficient inference and improved interpretability. Since the problem of learning the best polytree is NP-hard, we study which restrictions make it more tractable by considering for example in-degree bounds, properties of score functions measuring the quality of a polytree, and approximation algorithms. We devise an algorithm that finds the optimal polytree in time O((2+ε)^n) for arbitrarily small ε> 0 and any constant in-degree bound k, improving over the fastest previously known algorithm of time complexity O(3^n). We further give polynomial-time algorithms for finding a polytree whose score is within a factor of k from the optimal one for arbitrary scores and a factor of 2 for additive ones. Many of the results are complemented by (nearly) tight lower bounds for either the time complexity or the approximation factors.

A growing body of research in continual learning focuses on the catastrophic forgetting problem. While many attempts have been made to alleviate this problem, the majority of the methods assume a single model in the continual learning setup. In this work, we question this assumption and show that employing ensemble models can be a simple yet effective method to improve continual performance. However, ensembles' training and inference costs can increase significantly as the number of models grows. Motivated by this limitation, we study different ensemble models to understand their benefits and drawbacks in continual learning scenarios. Finally, to overcome the high compute cost of ensembles, we leverage recent advances in neural network subspace to propose a computationally cheap algorithm with similar runtime to a single model yet enjoying the performance benefits of ensembles.

We investigate the unsupervised constituency parsing task, which organizes words and phrases of a sentence into a hierarchical structure without using linguistically annotated data. We observe that existing unsupervised parsers capture differing aspects of parsing structures, which can be leveraged to enhance unsupervised parsing performance. To this end, we propose a notion of "tree averaging," based on which we further propose a novel ensemble method for unsupervised parsing. To improve inference efficiency, we further distill the ensemble knowledge into a student model; such an ensemble-then-distill process is an effective approach to mitigate the over-smoothing problem existing in common multi-teacher distilling methods. Experiments show that our method surpasses all previous approaches, consistently demonstrating its effectiveness and robustness across various runs, with different ensemble components, and under domain-shift conditions.

Generalization is arguably the most important goal of statistical language modeling research. Publicly available benchmarks and papers published with an open-source code have been critical to advancing the field. However, it is often very difficult, and sometimes even impossible, to reproduce the results fully as reported in publications. In this paper, we propose a simple framework that should help advance the state of the art in language modeling in terms of generalization. We propose to publish not just the code, but also probabilities on dev and test sets with future publications so that one can easily add the new model into an ensemble. This has crucial advantages: it is much easier to determine whether a newly proposed model is actually complementary to the current baseline. Therefore, instead of inventing new names for the old tricks, the scientific community can advance faster. Finally, this approach promotes diversity of ideas: one does not need to create an individual model that is the new state of the art to attract attention; it will be sufficient to develop a new model that learns patterns which other models do not. Thus, even a suboptimal model can be found to have value. Remarkably, our approach has yielded new state-of-the-art results across various language modeling benchmarks up to 10%.

Prompting language models (LMs) is the main interface for applying them to new tasks. However, for smaller LMs, prompting provides low accuracy compared to gradient-based finetuning. Tree Prompting is an approach to prompting which builds a decision tree of prompts, linking multiple LM calls together to solve a task. At inference time, each call to the LM is determined by efficiently routing the outcome of the previous call using the tree. Experiments on classification datasets show that Tree Prompting improves accuracy over competing methods and is competitive with fine-tuning. We also show that variants of Tree Prompting allow inspection of a model's decision-making process.

Model customization necessitates high-quality and diverse datasets, but acquiring such data remains time-consuming and labor-intensive. Despite the great potential of large language models (LLMs) for data synthesis, current approaches are constrained by limited seed data, model biases, and low-variation prompts, resulting in limited diversity and biased distributions with the increase of data scales. To tackle this challenge, we introduce TREESYNTH, a tree-guided subspace-based data synthesis approach inspired by decision trees. It constructs a spatial partitioning tree to recursively divide a task-specific full data space (i.e., root node) into numerous atomic subspaces (i.e., leaf nodes) with mutually exclusive and exhaustive attributes to ensure both distinctiveness and comprehensiveness before synthesizing samples within each atomic subspace. This globally dividing-and-synthesizing method finally collects subspace samples into a comprehensive dataset, effectively circumventing repetition and space collapse to ensure the diversity of large-scale data synthesis. Furthermore, the spatial partitioning tree enables sample allocation into atomic subspaces, allowing the rebalancing of existing datasets for more balanced and comprehensive distributions. Empirically, extensive experiments across diverse benchmarks consistently demonstrate the superior data diversity, model performance, and robust scalability of TREESYNTH compared to both human-crafted datasets and peer data synthesis methods, with an average performance gain reaching 10%. Besides, the consistent improvements of TREESYNTH-balanced datasets highlight its efficacious application to redistribute existing datasets for more comprehensive coverage and the induced performance enhancement. The code is available at https://github.com/cpa2001/TreeSynth.

We introduce ensembles within score-based sampling methods to develop gradient-free approximate sampling techniques that leverage the collective dynamics of particle ensembles to compute approximate reverse diffusion drifts. We introduce the underlying methodology, emphasizing its relationship with generative diffusion models and the previously introduced F\"ollmer sampler. We demonstrate the efficacy of ensemble strategies through various examples, ranging from low- to medium-dimensionality sampling problems, including multi-modal and highly non-Gaussian probability distributions, and provide comparisons to traditional methods like NUTS. Our findings highlight the potential of ensemble strategies for modeling complex probability distributions in situations where gradients are unavailable. Finally, we showcase its application in the context of Bayesian inversion problems within the geophysical sciences.

Ensemble forecasting is crucial for improving weather predictions, especially for forecasts of extreme events. Constructing an ensemble prediction system (EPS) based on conventional NWP models is highly computationally expensive. ML models have emerged as valuable tools for deterministic weather forecasts, providing forecasts with significantly reduced computational requirements and even surpassing the forecast performance of traditional NWP models. However, challenges arise when applying ML models to ensemble forecasting. Recent ML models, such as GenCast and SEEDS model, rely on the ERA5 EDA or operational NWP ensemble members for forecast generation. Their spatial resolution is also considered too coarse for many applications. To overcome these limitations, we introduce FuXi-ENS, an advanced ML model designed to deliver 6-hourly global ensemble weather forecasts up to 15 days. This model runs at a significantly increased spatial resolution of 0.25\textdegree, incorporating 5 atmospheric variables at 13 pressure levels, along with 13 surface variables. By leveraging the inherent probabilistic nature of Variational AutoEncoder (VAE), FuXi-ENS optimizes a loss function that combines the CRPS and the KL divergence between the predicted and target distribution, facilitating the incorporation of flow-dependent perturbations in both initial conditions and forecast. This innovative approach makes FuXi-ENS an advancement over the traditional ones that use L1 loss combined with the KL loss in standard VAE models for ensemble weather forecasting. Results demonstrate that FuXi-ENS outperforms ensemble forecasts from the ECMWF, a world leading NWP model, in the CRPS of 98.1% of 360 variable and forecast lead time combinations. This achievement underscores the potential of the FuXi-ENS model to enhance ensemble weather forecasts, offering a promising direction for further development in this field.

Machine learning (ML)-based weather models have rapidly risen to prominence due to their greater accuracy and speed than traditional forecasts based on numerical weather prediction (NWP), recently outperforming traditional ensembles in global probabilistic weather forecasting. This paper presents FGN, a simple, scalable and flexible modeling approach which significantly outperforms the current state-of-the-art models. FGN generates ensembles via learned model-perturbations with an ensemble of appropriately constrained models. It is trained directly to minimize the continuous rank probability score (CRPS) of per-location forecasts. It produces state-of-the-art ensemble forecasts as measured by a range of deterministic and probabilistic metrics, makes skillful ensemble tropical cyclone track predictions, and captures joint spatial structure despite being trained only on marginals.

Model selection is a strategy aimed at creating accurate and robust models. A key challenge in designing these algorithms is identifying the optimal model for classifying any particular input sample. This paper addresses this challenge and proposes a novel framework for differentiable model selection integrating machine learning and combinatorial optimization. The framework is tailored for ensemble learning, a strategy that combines the outputs of individually pre-trained models, and learns to select appropriate ensemble members for a particular input sample by transforming the ensemble learning task into a differentiable selection program trained end-to-end within the ensemble learning model. Tested on various tasks, the proposed framework demonstrates its versatility and effectiveness, outperforming conventional and advanced consensus rules across a variety of settings and learning tasks.

We investigate the effectiveness of ensembles of pretrained transformer-based language models on short answer questions using the Kaggle Automated Short Answer Scoring dataset. We fine-tune a collection of popular small, base, and large pretrained transformer-based language models, and train one feature-base model on the dataset with the aim of testing ensembles of these models. We used an early stopping mechanism and hyperparameter optimization in training. We observe that generally that the larger models perform slightly better, however, they still fall short of state-of-the-art results one their own. Once we consider ensembles of models, there are ensembles of a number of large networks that do produce state-of-the-art results, however, these ensembles are too large to realistically be put in a production environment.

Probabilistic forecasting is crucial to decision-making under uncertainty about future weather. The dominant approach is to use an ensemble of forecasts to represent and quantify uncertainty in operational numerical weather prediction. However, generating ensembles is computationally costly. In this paper, we propose to generate ensemble forecasts at scale by leveraging recent advances in generative artificial intelligence. Our approach learns a data-driven probabilistic diffusion model from the 5-member ensemble GEFS reforecast dataset. The model can then be sampled efficiently to produce realistic weather forecasts, conditioned on a few members of the operational GEFS forecasting system. The generated ensembles have similar predictive skill as the full GEFS 31-member ensemble, evaluated against ERA5 reanalysis, and emulate well the statistics of large physics-based ensembles. We also apply the same methodology to developing a diffusion model for generative post-processing: the model directly learns to correct biases present in the emulated forecasting system by leveraging reanalysis data as labels during training. Ensembles from this generative post-processing model show greater reliability and accuracy, particularly in extreme event classification. In general, they are more reliable and forecast the probability of extreme weather more accurately than the GEFS operational ensemble. Our models achieve these results at less than 1/10th of the computational cost incurred by the operational GEFS system.

In Part I, we created an ensemble based on Spherical Fourier Neural Operators. As initial condition perturbations, we used bred vectors, and as model perturbations, we used multiple checkpoints trained independently from scratch. Based on diagnostics that assess the ensemble's physical fidelity, our ensemble has comparable performance to operational weather forecasting systems. However, it requires orders of magnitude fewer computational resources. Here in Part II, we generate a huge ensemble (HENS), with 7,424 members initialized each day of summer 2023. We enumerate the technical requirements for running huge ensembles at this scale. HENS precisely samples the tails of the forecast distribution and presents a detailed sampling of internal variability. HENS has two primary applications: (1) as a large dataset with which to study the statistics and drivers of extreme weather and (2) as a weather forecasting system. For extreme climate statistics, HENS samples events 4sigma away from the ensemble mean. At each grid cell, HENS increases the skill of the most accurate ensemble member and enhances coverage of possible future trajectories. As a weather forecasting model, HENS issues extreme weather forecasts with better uncertainty quantification. It also reduces the probability of outlier events, in which the verification value lies outside the ensemble forecast distribution.

We present a novel prior for tree topology within Bayesian Additive Regression Trees (BART) models. This approach quantifies the hypothetical loss in information and the loss due to complexity associated with choosing the wrong tree structure. The resulting prior distribution is compellingly geared toward sparsity, a critical feature considering BART models' tendency to overfit. Our method incorporates prior knowledge into the distribution via two parameters that govern the tree's depth and balance between its left and right branches. Additionally, we propose a default calibration for these parameters, offering an objective version of the prior. We demonstrate our method's efficacy on both simulated and real datasets.

Foundation models have become a dominant paradigm in machine learning, achieving remarkable performance across diverse tasks through large-scale pretraining. However, they often yield overconfident, uncalibrated predictions. The standard approach to quantifying epistemic uncertainty are ensembles of multiple independently trained models. But their computational cost scales linearly with ensemble size, making them impractical for large foundation models. We propose Singular Value Ensemble (SVE), a parameter-efficient implicit ensembling method. SVE builds on a simple, but powerful core assumption: namely, that the singular vectors of the weight matrices correspond to meaningful directions in the representation space. If the singular vectors are indeed meaningful (orthogonal) "knowledge directions", then a model ensemble can be obtained by modulating only how strongly each direction contributes to the output. Rather than learning new parameters for each ensemble member, we freeze the singular vectors and only train per-member singular values that rescale the contribution of each direction in that shared knowledge basis. Ensemble diversity emerges naturally during joint training as stochastic initialization and random batch sampling cause different members to converge to different combinations of the same underlying knowledge. SVE performs comparable to an explicit ensemble, while increasing the parameter count of the base model by <1%, making principled uncertainty estimation accessible in resource-constrained settings. We validate SVE on NLP and vision tasks with various different backbones and show that it improves calibration while maintaining predictive accuracy.

Prototype-based methods use interpretable representations to address the black-box nature of deep learning models, in contrast to post-hoc explanation methods that only approximate such models. We propose the Neural Prototype Tree (ProtoTree), an intrinsically interpretable deep learning method for fine-grained image recognition. ProtoTree combines prototype learning with decision trees, and thus results in a globally interpretable model by design. Additionally, ProtoTree can locally explain a single prediction by outlining a decision path through the tree. Each node in our binary tree contains a trainable prototypical part. The presence or absence of this learned prototype in an image determines the routing through a node. Decision making is therefore similar to human reasoning: Does the bird have a red throat? And an elongated beak? Then it's a hummingbird! We tune the accuracy-interpretability trade-off using ensemble methods, pruning and binarizing. We apply pruning without sacrificing accuracy, resulting in a small tree with only 8 learned prototypes along a path to classify a bird from 200 species. An ensemble of 5 ProtoTrees achieves competitive accuracy on the CUB-200- 2011 and Stanford Cars data sets. Code is available at https://github.com/M-Nauta/ProtoTree

A very simple way to improve the performance of almost any machine learning algorithm is to train many different models on the same data and then to average their predictions. Unfortunately, making predictions using a whole ensemble of models is cumbersome and may be too computationally expensive to allow deployment to a large number of users, especially if the individual models are large neural nets. Caruana and his collaborators have shown that it is possible to compress the knowledge in an ensemble into a single model which is much easier to deploy and we develop this approach further using a different compression technique. We achieve some surprising results on MNIST and we show that we can significantly improve the acoustic model of a heavily used commercial system by distilling the knowledge in an ensemble of models into a single model. We also introduce a new type of ensemble composed of one or more full models and many specialist models which learn to distinguish fine-grained classes that the full models confuse. Unlike a mixture of experts, these specialist models can be trained rapidly and in parallel.

The cycle of scientific discovery is frequently bottlenecked by the slow, manual creation of software to support computational experiments. To address this, we present an AI system that creates expert-level scientific software whose goal is to maximize a quality metric. The system uses a Large Language Model (LLM) and Tree Search (TS) to systematically improve the quality metric and intelligently navigate the large space of possible solutions. The system achieves expert-level results when it explores and integrates complex research ideas from external sources. The effectiveness of tree search is demonstrated across a wide range of benchmarks. In bioinformatics, it discovered 40 novel methods for single-cell data analysis that outperformed the top human-developed methods on a public leaderboard. In epidemiology, it generated 14 models that outperformed the CDC ensemble and all other individual models for forecasting COVID-19 hospitalizations. Our method also produced state-of-the-art software for geospatial analysis, neural activity prediction in zebrafish, time series forecasting and numerical solution of integrals. By devising and implementing novel solutions to diverse tasks, the system represents a significant step towards accelerating scientific progress.

We introduce a novel machine learning model for credit risk by combining tree-boosting with a latent spatio-temporal Gaussian process model accounting for frailty correlation. This allows for modeling non-linearities and interactions among predictor variables in a flexible data-driven manner and for accounting for spatio-temporal variation that is not explained by observable predictor variables. We also show how estimation and prediction can be done in a computationally efficient manner. In an application to a large U.S. mortgage credit risk data set, we find that both predictive default probabilities for individual loans and predictive loan portfolio loss distributions obtained with our novel approach are more accurate compared to conventional independent linear hazard models and also linear spatio-temporal models. Using interpretability tools for machine learning models, we find that the likely reasons for this outperformance are strong interaction and non-linear effects in the predictor variables and the presence of large spatio-temporal frailty effects.

Automated machine learning (AutoML) systems commonly ensemble models post hoc to improve predictive performance, typically via greedy ensemble selection (GES). However, we believe that GES may not always be optimal, as it performs a simple deterministic greedy search. In this work, we introduce two novel population-based ensemble selection methods, QO-ES and QDO-ES, and compare them to GES. While QO-ES optimises solely for predictive performance, QDO-ES also considers the diversity of ensembles within the population, maintaining a diverse set of well-performing ensembles during optimisation based on ideas of quality diversity optimisation. The methods are evaluated using 71 classification datasets from the AutoML benchmark, demonstrating that QO-ES and QDO-ES often outrank GES, albeit only statistically significant on validation data. Our results further suggest that diversity can be beneficial for post hoc ensembling but also increases the risk of overfitting.

Ensembling is among the most popular tools in machine learning (ML) due to its effectiveness in minimizing variance and thus improving generalization. Most ensembling methods for black-box base learners fall under the umbrella of "stacked generalization," namely training an ML algorithm that takes the inferences from the base learners as input. While stacking has been widely applied in practice, its theoretical properties are poorly understood. In this paper, we prove a novel result, showing that choosing the best stacked generalization from a (finite or finite-dimensional) family of stacked generalizations based on cross-validated performance does not perform "much worse" than the oracle best. Our result strengthens and significantly extends the results in Van der Laan et al. (2007). Inspired by the theoretical analysis, we further propose a particular family of stacked generalizations in the context of probabilistic forecasting, each one with a different sensitivity for how much the ensemble weights are allowed to vary across items, timestamps in the forecast horizon, and quantiles. Experimental results demonstrate the performance gain of the proposed method.

More and more processes governing our lives use in some part an automatic decision step, where -- based on a feature vector derived from an applicant -- an algorithm has the decision power over the final outcome. Here we present a simple idea which gives some of the power back to the applicant by providing her with alternatives which would make the decision algorithm decide differently. It is based on a formalization reminiscent of methods used for evasion attacks, and consists in enumerating the subspaces where the classifiers decides the desired output. This has been implemented for the specific case of decision forests (ensemble methods based on decision trees), mapping the problem to an iterative version of enumerating k-cliques.

Despite remarkable progress achieved, most neural architecture search (NAS) methods focus on searching for one single accurate and robust architecture. To further build models with better generalization capability and performance, model ensemble is usually adopted and performs better than stand-alone models. Inspired by the merits of model ensemble, we propose to search for multiple diverse models simultaneously as an alternative way to find powerful models. Searching for ensembles is non-trivial and has two key challenges: enlarged search space and potentially more complexity for the searched model. In this paper, we propose a one-shot neural ensemble architecture search (NEAS) solution that addresses the two challenges. For the first challenge, we introduce a novel diversity-based metric to guide search space shrinking, considering both the potentiality and diversity of candidate operators. For the second challenge, we enable a new search dimension to learn layer sharing among different models for efficiency purposes. The experiments on ImageNet clearly demonstrate that our solution can improve the supernet's capacity of ranking ensemble architectures, and further lead to better search results. The discovered architectures achieve superior performance compared with state-of-the-arts such as MobileNetV3 and EfficientNet families under aligned settings. Moreover, we evaluate the generalization ability and robustness of our searched architecture on the COCO detection benchmark and achieve a 3.1% improvement on AP compared with MobileNetV3. Codes and models are available at https://github.com/researchmm/NEAS.

In the field of decision trees, most previous studies have difficulty ensuring the statistical optimality of a prediction of new data and suffer from overfitting because trees are usually used only to represent prediction functions to be constructed from given data. In contrast, some studies, including this paper, used the trees to represent stochastic data observation processes behind given data. Moreover, they derived the statistically optimal prediction, which is robust against overfitting, based on the Bayesian decision theory by assuming a prior distribution for the trees. However, these studies still have a problem in computing this Bayes optimal prediction because it involves an infeasible summation for all division patterns of a feature space, which is represented by the trees and some parameters. In particular, an open problem is a summation with respect to combinations of division axes, i.e., the assignment of features to inner nodes of the tree. We solve this by a Markov chain Monte Carlo method, whose step size is adaptively tuned according to a posterior distribution for the trees.

Deep Ensembles are a simple, reliable, and effective method of improving both the predictive performance and uncertainty estimates of deep learning approaches. However, they are widely criticised as being computationally expensive, due to the need to deploy multiple independent models. Recent work has challenged this view, showing that for predictive accuracy, ensembles can be more computationally efficient (at inference) than scaling single models within an architecture family. This is achieved by cascading ensemble members via an early-exit approach. In this work, we investigate extending these efficiency gains to tasks related to uncertainty estimation. As many such tasks, e.g. selective classification, are binary classification, our key novel insight is to only pass samples within a window close to the binary decision boundary to later cascade stages. Experiments on ImageNet-scale data across a number of network architectures and uncertainty tasks show that the proposed window-based early-exit approach is able to achieve a superior uncertainty-computation trade-off compared to scaling single models. For example, a cascaded EfficientNet-B2 ensemble is able to achieve similar coverage at 5% risk as a single EfficientNet-B4 with <30% the number of MACs. We also find that cascades/ensembles give more reliable improvements on OOD data vs scaling models up. Code for this work is available at: https://github.com/Guoxoug/window-early-exit.

Decision trees are renowned for their interpretability capability to achieve high predictive performance, especially on tabular data. Traditionally, they are constructed through recursive algorithms, where they partition the data at every node in a tree. However, identifying the best partition is challenging, as decision trees optimized for local segments may not bring global generalization. To address this, we introduce MetaTree, which trains a transformer-based model on filtered outputs from classical algorithms to produce strong decision trees for classification. Specifically, we fit both greedy decision trees and optimized decision trees on a large number of datasets. We then train MetaTree to produce the trees that achieve strong generalization performance. This training enables MetaTree to not only emulate these algorithms, but also to intelligently adapt its strategy according to the context, thereby achieving superior generalization performance.

Large language models demonstrate a remarkable capability for learning to solve new tasks from a few examples. The prompt template, or the way the input examples are formatted to obtain the prompt, is an important yet often overlooked aspect of in-context learning. In this work, we conduct a comprehensive study of the template format's influence on the in-context learning performance. We evaluate the impact of the prompt template across models (from 770M to 70B parameters) and 4 standard classification datasets. We show that a poor choice of the template can reduce the performance of the strongest models and inference methods to a random guess level. More importantly, the best templates do not transfer between different setups and even between models of the same family. Our findings show that the currently prevalent approach to evaluation, which ignores template selection, may give misleading results due to different templates in different works. As a first step towards mitigating this issue, we propose Template Ensembles that aggregate model predictions across several templates. This simple test-time augmentation boosts average performance while being robust to the choice of random set of templates.

Different large language models (LLMs) exhibit diverse strengths and weaknesses, and LLM ensemble serves as a promising approach to integrate their complementary capabilities. Despite substantial progress in improving ensemble quality, limited attention has been paid to the robustness of ensembles against potential erroneous signals, which often arise from heterogeneous tokenization schemes and varying model expertise. Our analysis shows that ensemble failures typically arise from both the token level and the model level: the former reflects severe disagreement in token predictions, while the latter involves low confidence and pronounced disparities among models. In light of this, we propose CoRE, a plug-and-play technique that harnesses model consistency for robust LLM ensemble, which can be seamlessly integrated with diverse ensemble methods. Token-level consistency captures fine-grained disagreements by applying a low-pass filter to downweight uncertain tokens with high inconsistency, often due to token misalignment, thereby improving robustness at a granular level. Model-level consistency models global agreement by promoting model outputs with high self-confidence and minimal divergence from others, enhancing robustness at a coarser level. Extensive experiments across diverse benchmarks, model combinations, and ensemble strategies demonstrate that CoRE consistently improves ensemble performance and robustness.

It is impossible today to pretend that the practice of machine learning is compatible with the idea that training and testing data follow the same distribution. Several authors have recently used ensemble techniques to show how scenarios involving multiple data distributions are best served by representations that are both richer than those obtained by regularizing for the best in-distribution performance, and richer than those obtained under the influence of the implicit sparsity bias of common stochastic gradient procedures. This contribution investigates the use of very high dropout rates instead of ensembles to obtain such rich representations. Although training a deep network from scratch using such dropout rates is virtually impossible, fine-tuning a large pre-trained model under such conditions is not only possible but also achieves out-of-distribution performances that exceed those of both ensembles and weight averaging methods such as model soups. This result has practical significance because the importance of the fine-tuning scenario has considerably grown in recent years. This result also provides interesting insights on the nature of rich representations and on the intrinsically linear nature of fine-tuning a large network using a comparatively small dataset.

Agriculture is increasingly challenged by climate change, soil degradation, and resource depletion, and hence requires advanced data-driven crop classification and recommendation solutions. This work presents an explainable ensemble learning paradigm that fuses optimized feature pyramids, deep networks, self-attention mechanisms, and residual networks for bolstering crop suitability predictions based on soil characteristics (e.g., pH, nitrogen, potassium) and climatic conditions (e.g., temperature, rainfall). With a dataset comprising 3,867 instances and 29 features from the Ethiopian Agricultural Transformation Agency and NASA, the paradigm leverages preprocessing methods such as label encoding, outlier removal using IQR, normalization through StandardScaler, and SMOTE for balancing classes. A range of machine learning models such as Logistic Regression, K-Nearest Neighbors, Support Vector Machines, Decision Trees, Random Forest, Gradient Boosting, and a new Relative Error Support Vector Machine are compared, with hyperparameter tuning through Grid Search and cross-validation. The suggested "Final Ensemble" meta-ensemble design outperforms with 98.80% accuracy, precision, recall, and F1-score, compared to individual models such as K-Nearest Neighbors (95.56% accuracy). Explainable AI methods, such as SHAP and permutation importance, offer actionable insights, highlighting critical features such as soil pH, nitrogen, and zinc. The paradigm addresses the gap between intricate ML models and actionable agricultural decision-making, fostering sustainability and trust in AI-powered recommendations

The ability of large language models (LLMs) to perform zero-shot classification makes them viable solutions for data annotation in rapidly evolving domains where quality labeled data is often scarce and costly to obtain. However, the large-scale deployment of LLMs can be prohibitively expensive. This paper introduces an LLM chain ensemble methodology that aligns multiple LLMs in a sequence, routing data subsets to subsequent models based on classification uncertainty. This approach leverages the strengths of individual LLMs within a broader system, allowing each model to handle data points where it exhibits the highest confidence, while forwarding more complex cases to potentially more robust models. Our results show that the chain ensemble method often exceeds the performance of the best individual model in the chain and achieves substantial cost savings, making LLM chain ensembles a practical and efficient solution for large-scale data annotation challenges.

We explore diverse representations of speech audio, and their effect on a performance of late fusion ensemble of E-Branchformer models, applied to Automatic Speech Recognition (ASR) task. Although it is generally known that ensemble methods often improve the performance of the system even for speech recognition, it is very interesting to explore how ensembles of complex state-of-the-art models, such as medium-sized and large E-Branchformers, cope in this setting when their base models are trained on diverse representations of the input speech audio. The results are evaluated on four widely-used benchmark datasets: Librispeech, Aishell, Gigaspeech, TEDLIUMv2 and show that improvements of 1% - 14% can still be achieved over the state-of-the-art models trained using comparable techniques on these datasets. A noteworthy observation is that such ensemble offers improvements even with the use of language models, although the gap is closing.

Deep ensembles (DE) have been successful in improving model performance by learning diverse members via the stochasticity of random initialization. While recent works have attempted to promote further diversity in DE via hyperparameters or regularizing loss functions, these methods primarily still rely on a stochastic approach to explore the hypothesis space. In this work, we present Multi-Symmetry Ensembles (MSE), a framework for constructing diverse ensembles by capturing the multiplicity of hypotheses along symmetry axes, which explore the hypothesis space beyond stochastic perturbations of model weights and hyperparameters. We leverage recent advances in contrastive representation learning to create models that separately capture opposing hypotheses of invariant and equivariant functional classes and present a simple ensembling approach to efficiently combine appropriate hypotheses for a given task. We show that MSE effectively captures the multiplicity of conflicting hypotheses that is often required in large, diverse datasets like ImageNet. As a result of their inherent diversity, MSE improves classification performance, uncertainty quantification, and generalization across a series of transfer tasks.

Tree boosting is a highly effective and widely used machine learning method. In this paper, we describe a scalable end-to-end tree boosting system called XGBoost, which is used widely by data scientists to achieve state-of-the-art results on many machine learning challenges. We propose a novel sparsity-aware algorithm for sparse data and weighted quantile sketch for approximate tree learning. More importantly, we provide insights on cache access patterns, data compression and sharding to build a scalable tree boosting system. By combining these insights, XGBoost scales beyond billions of examples using far fewer resources than existing systems.

Large language models (LLMs) have shown remarkable ability to generate code, yet their outputs often violate syntactic or semantic constraints when guided only through natural language prompts. We introduce TreeCoder, the most general and flexible framework to date for exploring decoding strategies, constraints, and hyperparameters in LLMs, and use it in code generation to enforce correctness and structure during decoding rather than relying on prompt engineering. TreeCoder represents decoding as a tree search over candidate programs, where both decoding strategies and constraint functions - such as style, syntax, execution - are treated as first-class, optimisable components. This design enables systematic exploration and automatic tuning of decoding configurations using standard optimisation techniques. Experiments on the MBPP (Python) and SQL-Spider benchmarks show that TreeCoder consistently improves accuracy across open-source models such as CodeLlama, Mistral and DeepSeek, often outperforming their unconstrained baselines by considerable margins.

We address unsupervised discontinuous constituency parsing, where we observe a high variance in the performance of the only previous model. We propose to build an ensemble of different runs of the existing discontinuous parser by averaging the predicted trees, to stabilize and boost performance. To begin with, we provide comprehensive computational complexity analysis (in terms of P and NP-complete) for tree averaging under different setups of binarity and continuity. We then develop an efficient exact algorithm to tackle the task, which runs in a reasonable time for all samples in our experiments. Results on three datasets show our method outperforms all baselines in all metrics; we also provide in-depth analyses of our approach.

We propose a deep-learning system -- for the SQuAD2.0 task -- that finds, or indicates the lack of, a correct answer to a question in a context paragraph. Our goal is to learn an ensemble of heterogeneous SQuAD2.0 models that, when blended properly, outperforms the best model in the ensemble per se. We created a stacking ensemble that combines top-N predictions from two models, based on ALBERT and RoBERTa, into a multiclass classification task to pick the best answer out of their predictions. We explored various ensemble configurations, input representations, and model architectures. For evaluation, we examined test-set EM and F1 scores; our best-performing ensemble incorporated a CNN-based meta-model and scored 87.117 and 90.306, respectively -- a relative improvement of 0.55% for EM and 0.61% for F1 scores, compared to the baseline performance of the best model in the ensemble, an ALBERT-based model, at 86.644 for EM and 89.760 for F1.

Generalization to out-of-distribution (OOD) data is a critical challenge in machine learning. Ensemble-based methods, like weight space ensembles that interpolate model parameters, have been shown to achieve superior OOD performance. However, the underlying mechanism for their effectiveness remains unclear. In this study, we closely examine WiSE-FT, a popular weight space ensemble method that interpolates between a pre-trained and a fine-tuned model. We observe an unexpected phenomenon, in which WiSE-FT successfully corrects many cases where each individual model makes incorrect predictions, which contributes significantly to its OOD effectiveness. To gain further insights, we conduct theoretical analysis in a multi-class setting with a large number of spurious features. Our analysis predicts the above phenomenon and it further shows that ensemble-based models reduce prediction errors in the OOD settings by utilizing a more diverse set of spurious features. Contrary to the conventional wisdom that focuses on learning invariant features for better OOD performance, our findings suggest that incorporating a large number of diverse spurious features weakens their individual contributions, leading to improved overall OOD generalization performance. Empirically we demonstrate the effectiveness of utilizing diverse spurious features on a MultiColorMNIST dataset, and our experimental results are consistent with the theoretical analysis. Building upon the new theoretical insights into the efficacy of ensemble methods, we further identify an issue of WiSE-FT caused by the overconfidence of fine-tuned models in OOD situations. This overconfidence magnifies the fine-tuned model's incorrect prediction, leading to deteriorated OOD ensemble performance. To remedy this problem, we propose a novel method called BAlaNced averaGing (BANG), which significantly enhances the OOD performance of WiSE-FT.

Skid-steered wheel mobile robots (SSWMRs) are characterized by the unique domination of the tire-terrain skidding for the robot to move. The lack of reliable friction models cascade into unreliable motion models, especially the reduced ordered variants used for state estimation and robot control. Ensemble modeling is an emerging research direction where the overall motion model is broken down into a family of local models to distribute the performance and resource requirement and provide a fast real-time prediction. To this end, a gaussian mixture model based modeling identification of model clusters is adopted and implemented within an interactive multiple model (IMM) based state estimation. The framework is adopted and implemented for angular velocity as the estimated state for a mid scaled skid-steered wheel mobile robot platform.

This paper studies ensembling in the era of Large Vision-Language Models (LVLMs). Ensembling is a classical method to combine different models to get increased performance. In the recent work on Encyclopedic-VQA the authors examine a wide variety of models to solve their task: from vanilla LVLMs, to models including the caption as extra context, to models augmented with Lens-based retrieval of Wikipedia pages. Intuitively these models are highly complementary, which should make them ideal for ensembling. Indeed, an oracle experiment shows potential gains from 48.8% accuracy (the best single model) all the way up to 67% (best possible ensemble). So it is a trivial exercise to create an ensemble with substantial real gains. Or is it?

Is bigger always better for time series foundation models? With the question in mind, we explore an alternative to training a single, large monolithic model: building a portfolio of smaller, pretrained forecasting models. By applying ensembling or model selection over these portfolios, we achieve competitive performance on large-scale benchmarks using much fewer parameters. We explore strategies for designing such portfolios and find that collections of specialist models consistently outperform portfolios of independently trained generalists. Remarkably, we demonstrate that post-training a base model is a compute-effective approach for creating sufficiently diverse specialists, and provide evidences that ensembling and model selection are more compute-efficient than test-time fine-tuning.

A technique for improving the prediction accuracy of decision trees is proposed. It consists in evaluating the tree's branches in parallel over multiple paths. The technique enables predictions that are more aligned with the ones generated by the nearest neighborhood variant of the deodata algorithms. The technique also enables the hybridization of the decision tree algorithm with the nearest neighborhood variant.

Ensembles of independently trained neural networks are a state-of-the-art approach to estimate predictive uncertainty in Deep Learning, and can be interpreted as an approximation of the posterior distribution via a mixture of delta functions. The training of ensembles relies on non-convexity of the loss landscape and random initialization of their individual members, making the resulting posterior approximation uncontrolled. This paper proposes a novel and principled method to tackle this limitation, minimizing an f-divergence between the true posterior and a kernel density estimator (KDE) in a function space. We analyze this objective from a combinatorial point of view, and show that it is submodular with respect to mixture components for any f. Subsequently, we consider the problem of greedy ensemble construction. From the marginal gain on the negative f-divergence, which quantifies an improvement in posterior approximation yielded by adding a new component into the KDE, we derive a novel diversity term for ensemble methods. The performance of our approach is demonstrated on computer vision out-of-distribution detection benchmarks in a range of architectures trained on multiple datasets. The source code of our method is made publicly available at https://github.com/Oulu-IMEDS/greedy_ensembles_training.

Deep ensemble methods often improve predictive performance, yet they suffer from three practical limitations: redundancy among base models that inflates computational cost and degrades conditioning, unstable weighting under multicollinearity, and overfitting in meta-learning pipelines. We propose a regularized meta-learning framework that addresses these challenges through a four-stage pipeline combining redundancy-aware projection, statistical meta-feature augmentation, and cross-validated regularized meta-models (Ridge, Lasso, and ElasticNet). Our multi-metric de-duplication strategy removes near-collinear predictors using correlation and MSE thresholds (τ_{corr}=0.95), reducing the effective condition number of the meta-design matrix while preserving predictive diversity. Engineered ensemble statistics and interaction terms recover higher-order structure unavailable to raw prediction columns. A final inverse-RMSE blending stage mitigates regularizer-selection variance. On the Playground Series S6E1 benchmark (100K samples, 72 base models), the proposed framework achieves an out-of-fold RMSE of 8.582, improving over simple averaging (8.894) and conventional Ridge stacking (8.627), while matching greedy hill climbing (8.603) with substantially lower runtime (4 times faster). Conditioning analysis shows a 53.7\% reduction in effective matrix condition number after redundancy projection. Comprehensive ablations demonstrate consistent contributions from de-duplication, statistical meta-features, and meta-ensemble blending. These results position regularized meta-learning as a stable and deployment-efficient stacking strategy for high-dimensional ensemble systems.

Deep neural networks are powerful predictors for a variety of tasks. However, they do not capture uncertainty directly. Using neural network ensembles to quantify uncertainty is competitive with approaches based on Bayesian neural networks while benefiting from better computational scalability. However, building ensembles of neural networks is a challenging task because, in addition to choosing the right neural architecture or hyperparameters for each member of the ensemble, there is an added cost of training each model. We propose AutoDEUQ, an automated approach for generating an ensemble of deep neural networks. Our approach leverages joint neural architecture and hyperparameter search to generate ensembles. We use the law of total variance to decompose the predictive variance of deep ensembles into aleatoric (data) and epistemic (model) uncertainties. We show that AutoDEUQ outperforms probabilistic backpropagation, Monte Carlo dropout, deep ensemble, distribution-free ensembles, and hyper ensemble methods on a number of regression benchmarks.

While learning models are typically studied for inputs in the form of a fixed dimensional feature vector, real world data is rarely found in this form. In order to meet the basic requirement of traditional learning models, structural data generally have to be converted into fix-length vectors in a handcrafted manner, which is tedious and may even incur information loss. A common form of structured data is what we term "semantic tree-structures", corresponding to data where rich semantic information is encoded in a compositional manner, such as those expressed in JavaScript Object Notation (JSON) and eXtensible Markup Language (XML). For tree-structured data, several learning models have been studied to allow for working directly on raw tree-structure data, However such learning models are limited to either a specific tree-topology or a specific tree-structured data format, e.g., synthetic parse trees. In this paper, we propose a novel framework for end-to-end learning on generic semantic tree-structured data of arbitrary topology and heterogeneous data types, such as data expressed in JSON, XML and so on. Motivated by the works in recursive and recurrent neural networks, we develop exemplar neural implementations of our framework for the JSON format. We evaluate our approach on several UCI benchmark datasets, including ablation and data-efficiency studies, and on a toy reinforcement learning task. Experimental results suggest that our framework yields comparable performance to use of standard models with dedicated feature-vectors in general, and even exceeds baseline performance in cases where compositional nature of the data is particularly important. The source code for a JSON-based implementation of our framework along with experiments can be downloaded at https://github.com/EndingCredits/json2vec.

Machine learning is now used in many areas of astrophysics, from detecting exoplanets in Kepler transit signals to removing telescope systematics. Recent work demonstrated the potential of using machine learning algorithms for atmospheric retrieval by implementing a random forest to perform retrievals in seconds that are consistent with the traditional, computationally-expensive nested-sampling retrieval method. We expand upon their approach by presenting a new machine learning model, plan-net, based on an ensemble of Bayesian neural networks that yields more accurate inferences than the random forest for the same data set of synthetic transmission spectra. We demonstrate that an ensemble provides greater accuracy and more robust uncertainties than a single model. In addition to being the first to use Bayesian neural networks for atmospheric retrieval, we also introduce a new loss function for Bayesian neural networks that learns correlations between the model outputs. Importantly, we show that designing machine learning models to explicitly incorporate domain-specific knowledge both improves performance and provides additional insight by inferring the covariance of the retrieved atmospheric parameters. We apply plan-net to the Hubble Space Telescope Wide Field Camera 3 transmission spectrum for WASP-12b and retrieve an isothermal temperature and water abundance consistent with the literature. We highlight that our method is flexible and can be expanded to higher-resolution spectra and a larger number of atmospheric parameters.

We present PrediTree, the first comprehensive open-source dataset designed for training and evaluating tree height prediction models at sub-meter resolution. This dataset combines very high-resolution (0.5m) LiDAR-derived canopy height maps, spatially aligned with multi-temporal and multi-spectral imagery, across diverse forest ecosystems in France, totaling 3,141,568 images. PrediTree addresses a critical gap in forest monitoring capabilities by enabling the training of deep learning methods that can predict tree growth based on multiple past observations. %Initially focused on French forests, PrediTree is designed as an expanding resource with ongoing efforts to incorporate data from other countries. To make use of this PrediTree dataset, we propose an encoder-decoder framework that requires the multi-temporal multi-spectral imagery and the relative time differences in years between the canopy height map timestamp (target) and each image acquisition date for which this framework predicts the canopy height. The conducted experiments demonstrate that a U-Net architecture trained on the PrediTree dataset provides the highest masked mean squared error of 11.78%, outperforming the next-best architecture, ResNet-50, by around 12%, and cutting the error of the same experiments but on fewer bands (red, green, blue only), by around 30%. This dataset is publicly available on URL{HuggingFace}, and both processing and training codebases are available on URL{GitHub}.

The remarkable success of Large Language Models (LLMs) has ushered natural language processing (NLP) research into a new era. Despite their diverse capabilities, LLMs trained on different corpora exhibit varying strengths and weaknesses, leading to challenges in maximizing their overall efficiency and versatility. To address these challenges, recent studies have explored collaborative strategies for LLMs. This paper provides a comprehensive overview of this emerging research area, highlighting the motivation behind such collaborations. Specifically, we categorize collaborative strategies into three primary approaches: Merging, Ensemble, and Cooperation. Merging involves integrating multiple LLMs in the parameter space. Ensemble combines the outputs of various LLMs. Cooperation} leverages different LLMs to allow full play to their diverse capabilities for specific tasks. We provide in-depth introductions to these methods from different perspectives and discuss their potential applications. Additionally, we outline future research directions, hoping this work will catalyze further studies on LLM collaborations and paving the way for advanced NLP applications.

The ability of an architecture to realize permutations is quite fundamental. For example, Large Language Models need to be able to correctly copy (and perhaps rearrange) parts of the input prompt into the output. Classical universal approximation theorems guarantee the existence of parameter configurations that solve this task but offer no insights into whether gradient-based algorithms can find them. In this paper, we address this gap by focusing on two-layer fully connected feed-forward neural networks and the task of learning permutations on nonzero binary inputs. We show that in the infinite width Neural Tangent Kernel (NTK) regime, an ensemble of such networks independently trained with gradient descent on only the k standard basis vectors out of 2^k - 1 possible inputs successfully learns any fixed permutation of length k with arbitrarily high probability. By analyzing the exact training dynamics, we prove that the network's output converges to a Gaussian process whose mean captures the ground truth permutation via sign-based features. We then demonstrate how averaging these runs (an "ensemble" method) and applying a simple rounding step yields an arbitrarily accurate prediction on any possible input unseen during training. Notably, the number of models needed to achieve exact learning with high probability (which we refer to as ensemble complexity) exhibits a linearithmic dependence on the input size k for a single test input and a quadratic dependence when considering all test inputs simultaneously.

Ensembling multiple models has always been an effective approach to push the limits of existing performance and is widely used in classification tasks by simply averaging the classification probability vectors from multiple classifiers to achieve better accuracy. However, in the thriving open-source Large Language Model (LLM) community, ensembling methods are rare and typically limited to ensembling the full-text outputs of LLMs, such as selecting the best output using a ranker, which leads to underutilization of token-level probability information. In this paper, we treat the Generation of each token by LLMs as a Classification (GaC) for ensembling. This approach fully exploits the probability information at each generation step and better prevents LLMs from producing early incorrect tokens that lead to snowballing errors. In experiments, we ensemble state-of-the-art LLMs on several benchmarks, including exams, mathematics and reasoning, and observe that our method breaks the existing community performance ceiling. Furthermore, we observed that most of the tokens in the answer are simple and do not affect the correctness of the final answer. Therefore, we also experimented with ensembling only key tokens, and the results showed better performance with lower latency across benchmarks.

Tabular data, a fundamental data format in machine learning, is predominantly utilized in competitions and real-world applications. The performance of tabular models--such as gradient boosted decision trees and neural networks--can vary significantly across datasets due to differences in feature distributions and task characteristics. Achieving top performance on each dataset often requires specialized expert knowledge. To address this variability, practitioners often aggregate the predictions of multiple models. However, conventional aggregation strategies typically rely on static combination rules and lack instance-level adaptability. In this work, we propose an in-context ensemble framework for tabular prediction that leverages large language models (LLMs) to perform dynamic, instance-specific integration of external model predictions. Without access to raw tabular features or semantic information, our method constructs a context around each test instance using its nearest neighbors and the predictions from a pool of external models. Within this enriched context, we introduce Chain of Tabular Thoughts (CoT^2), a prompting strategy that guides LLMs through multi-step, interpretable reasoning, making still further progress toward expert-level decision-making. Experimental results show that our method outperforms well-tuned baselines and standard ensemble techniques across a wide range of tabular datasets.

The Combined Algorithm Selection and Hyperparameters optimization (CASH) problem is one of the fundamental problems in Automated Machine Learning (AutoML). Motivated by the success of ensemble learning, recent AutoML systems build post-hoc ensembles to output the final predictions instead of using the best single learner. However, while most CASH methods focus on searching for a single learner with the best performance, they neglect the diversity among base learners (i.e., they may suggest similar configurations to previously evaluated ones), which is also a crucial consideration when building an ensemble. To tackle this issue and further enhance the ensemble performance, we propose DivBO, a diversity-aware framework to inject explicit search of diversity into the CASH problems. In the framework, we propose to use a diversity surrogate to predict the pair-wise diversity of two unseen configurations. Furthermore, we introduce a temporary pool and a weighted acquisition function to guide the search of both performance and diversity based on Bayesian optimization. Empirical results on 15 public datasets show that DivBO achieves the best average ranks (1.82 and 1.73) on both validation and test errors among 10 compared methods, including post-hoc designs in recent AutoML systems and state-of-the-art baselines for ensemble learning on CASH problems.

Accurate forecasts for day-ahead photovoltaic (PV) power generation are crucial to support a high PV penetration rate in the local electricity grid and to assure stability in the grid. We use state-of-the-art tree-based machine learning methods to produce such forecasts and, unlike previous studies, we hereby account for (i) the effects various meteorological as well as astronomical features have on PV power production, and this (ii) at coarse as well as granular spatial locations. To this end, we use data from Belgium and forecast day-ahead PV power production at an hourly resolution. The insights from our study can assist utilities, decision-makers, and other stakeholders in optimizing grid operations, economic dispatch, and in facilitating the integration of distributed PV power into the electricity grid.

This review presents a comprehensive exploration of hybrid and ensemble deep learning models within Natural Language Processing (NLP), shedding light on their transformative potential across diverse tasks such as Sentiment Analysis, Named Entity Recognition, Machine Translation, Question Answering, Text Classification, Generation, Speech Recognition, Summarization, and Language Modeling. The paper systematically introduces each task, delineates key architectures from Recurrent Neural Networks (RNNs) to Transformer-based models like BERT, and evaluates their performance, challenges, and computational demands. The adaptability of ensemble techniques is emphasized, highlighting their capacity to enhance various NLP applications. Challenges in implementation, including computational overhead, overfitting, and model interpretation complexities, are addressed alongside the trade-off between interpretability and performance. Serving as a concise yet invaluable guide, this review synthesizes insights into tasks, architectures, and challenges, offering a holistic perspective for researchers and practitioners aiming to advance language-driven applications through ensemble deep learning in NLP.

Large language models (LLMs) have shown remarkable capabilities in various natural language understanding tasks. With only a few demonstration examples, these LLMs can quickly adapt to target tasks without expensive gradient updates. Common strategies to boost such 'in-context' learning ability are to ensemble multiple model decoded results and require the model to generate an explanation along with the prediction. However, these models often treat different class predictions equally and neglect the potential discrepancy between the explanations and predictions. To fully unleash the power of explanations, we propose EASE, an Explanation-Aware Soft Ensemble framework to empower in-context learning with LLMs. We design two techniques, explanation-guided ensemble, and soft probability aggregation, to mitigate the effect of unreliable explanations and improve the consistency between explanations and final predictions. Experiments on seven natural language understanding tasks and four varying-size LLMs demonstrate the effectiveness of our proposed framework.

We present the design and implementation of a custom discrete optimization technique for building rule lists over a categorical feature space. Our algorithm produces rule lists with optimal training performance, according to the regularized empirical risk, with a certificate of optimality. By leveraging algorithmic bounds, efficient data structures, and computational reuse, we achieve several orders of magnitude speedup in time and a massive reduction of memory consumption. We demonstrate that our approach produces optimal rule lists on practical problems in seconds. Our results indicate that it is possible to construct optimal sparse rule lists that are approximately as accurate as the COMPAS proprietary risk prediction tool on data from Broward County, Florida, but that are completely interpretable. This framework is a novel alternative to CART and other decision tree methods for interpretable modeling.

Deep Ensembles (DE) are a prominent approach for achieving excellent performance on key metrics such as accuracy, calibration, uncertainty estimation, and out-of-distribution detection. However, hardware limitations of real-world systems constrain to smaller ensembles and lower-capacity networks, significantly deteriorating their performance and properties. We introduce Packed-Ensembles (PE), a strategy to design and train lightweight structured ensembles by carefully modulating the dimension of their encoding space. We leverage grouped convolutions to parallelize the ensemble into a single shared backbone and forward pass to improve training and inference speeds. PE is designed to operate within the memory limits of a standard neural network. Our extensive research indicates that PE accurately preserves the properties of DE, such as diversity, and performs equally well in terms of accuracy, calibration, out-of-distribution detection, and robustness to distribution shift. We make our code available at https://github.com/ENSTA-U2IS/torch-uncertainty.

Recent research suggests that tree search algorithms (e.g. Monte Carlo Tree Search) can dramatically boost LLM performance on complex mathematical reasoning tasks. However, they often require more than 10 times the computational resources of greedy decoding due to wasteful search strategies, making them difficult to be deployed in practical applications. This study introduces a novel guided tree search algorithm with dynamic node selection and node-level exploration budget (maximum number of children) calculation to tackle this issue. By considering the search progress towards the final answer (history) and the guidance from a value network (future) trained without any step-wise annotations, our algorithm iteratively selects the most promising tree node before expanding it within the boundaries of the allocated computational budget. Experiments conducted on the GSM8K and TabMWP datasets demonstrate that our approach not only offers competitive performance but also enjoys significantly lower computational costs compared to baseline methods.

Localizing the root cause of network faults is crucial to network operation and maintenance. However, due to the complicated network architectures and wireless environments, as well as limited labeled data, accurately localizing the true root cause is challenging. In this paper, we propose a novel algorithm named NetRCA to deal with this problem. Firstly, we extract effective derived features from the original raw data by considering temporal, directional, attribution, and interaction characteristics. Secondly, we adopt multivariate time series similarity and label propagation to generate new training data from both labeled and unlabeled data to overcome the lack of labeled samples. Thirdly, we design an ensemble model which combines XGBoost, rule set learning, attribution model, and graph algorithm, to fully utilize all data information and enhance performance. Finally, experiments and analysis are conducted on the real-world dataset from ICASSP 2022 AIOps Challenge to demonstrate the superiority and effectiveness of our approach.

Ensembling Large Language Models (LLMs) has gained attention as a promising approach to surpass the performance of individual models by leveraging their complementary strengths. In particular, aggregating models' next-token probability distributions to select the next token has been shown to be effective in various tasks. However, while successful for short-form answers, its application to long-form generation remains underexplored. In this paper, we show that using existing ensemble methods in long-form generation requires a careful choice of ensembling positions, since the standard practice of ensembling at every token often degrades performance. We identify two key factors for determining these positions: tokenization mismatch across models and consensus in their next-token probability distributions. Based on this, we propose SAFE, (Stable And Fast LLM Ensembling), a framework that selectively ensembles by jointly considering these factors. To further improve stability, we introduce a probability sharpening strategy that consolidates probabilities spread across multiple sub-word tokens representing the same word into a single representative token. Our experiments on diverse benchmarks, including MATH500 and BBH, demonstrate that SAFE outperforms existing methods in both accuracy and efficiency, with gains achieved even when ensembling fewer than 1% of tokens.

We study sampling algorithms for β-ensembles with time complexity less than cubic in the cardinality of the ensemble. Following Dumitriu & Edelman (2002), we see the ensemble as the eigenvalues of a random tridiagonal matrix, namely a random Jacobi matrix. First, we provide a unifying and elementary treatment of the tridiagonal models associated to the three classical Hermite, Laguerre and Jacobi ensembles. For this purpose, we use simple changes of variables between successive reparametrizations of the coefficients defining the tridiagonal matrix. Second, we derive an approximate sampler for the simulation of β-ensembles, and illustrate how fast it can be for polynomial potentials. This method combines a Gibbs sampler on Jacobi matrices and the diagonalization of these matrices. In practice, even for large ensembles, only a few Gibbs passes suffice for the marginal distribution of the eigenvalues to fit the expected theoretical distribution. When the conditionals in the Gibbs sampler can be simulated exactly, the same fast empirical convergence is observed for the fluctuations of the largest eigenvalue. Our experimental results support a conjecture by Krishnapur et al. (2016), that the Gibbs chain on Jacobi matrices of size N mixes in O(log(N)).

Large language models (LLMs) now achieve near-human performance on standard math word problem benchmarks (e.g., GSM8K), yet their true reasoning ability remains disputed. A key concern is that models often produce confident, yet unfounded, answers to unanswerable problems. We introduce TreeCut, a synthetic dataset that systematically generates infinite unanswerable math word problems and their answerable counterparts, by representing each question as a tree and removing chosen necessary conditions. Experiments show TreeCut effectively induce hallucinations in large language models, including GPT-4o and o3-mini, with rates of 64% and 44% in their respective worst-case scenarios under zero-shot setting. Further analysis highlights that deeper or more complex trees, composite item names, and removing necessary condition near the middle of a path all increase the likelihood of hallucinations, underscoring the persistent challenges LLMs face in identifying unanswerable math problems. The dataset generation code and sample data are available at https://github.com/j-bagel/treecut-math.

This study aims to develop and evaluate an ensemble machine learning-based framework for the automatic detection of Wide QRS Complex Tachycardia (WCT) from ECG signals, emphasizing diagnostic accuracy and interpretability using Explainable AI. The proposed system integrates ensemble learning techniques, i.e., an optimized Random Forest known as CardioForest, and models like XGBoost and LightGBM. The models were trained and tested on ECG data from the publicly available MIMIC-IV dataset. The testing was carried out with the assistance of accuracy, balanced accuracy, precision, recall, F1 score, ROC-AUC, and error rate (RMSE, MAE) measures. In addition, SHAP (SHapley Additive exPlanations) was used to ascertain model explainability and clinical relevance. The CardioForest model performed best on all metrics, achieving a test accuracy of 94.95%, a balanced accuracy of 88.31%, and high precision and recall metrics. SHAP analysis confirmed the model's ability to rank the most relevant ECG features, such as QRS duration, in accordance with clinical intuitions, thereby fostering trust and usability in clinical practice. The findings recognize CardioForest as an extremely dependable and interpretable WCT detection model. Being able to offer accurate predictions and transparency through explainability makes it a valuable tool to help cardiologists make timely and well-informed diagnoses, especially for high-stakes and emergency scenarios.

A heuristic extending the Squarified Treemap technique for the representation of hierarchical information as treemaps is presented. The original technique gives high quality treemap views, since items are laid out with rectangles that approximate squares, allowing easy comparison and selection operations. New key steps, with a low computational impact, have been introduced to yield treemaps with even better aspect ratios and higher homogeneity among items.

Error detection (ED), which aims to identify incorrect or inconsistent cell values in tabular data, is important for ensuring data quality. Recent state-of-the-art ED methods leverage the pre-trained knowledge and semantic capability embedded in large language models (LLMs) to directly label whether a cell is erroneous. However, this LLM-as-a-labeler pipeline (1) relies on the black box, implicit decision process, thus failing to provide explainability for the detection results, and (2) is highly sensitive to prompts, yielding inconsistent outputs due to inherent model stochasticity, therefore lacking robustness. To address these limitations, we propose an LLM-as-an-inducer framework that adopts LLM to induce the decision tree for ED (termed TreeED) and further ensembles multiple such trees for consensus detection (termed ForestED), thereby improving explainability and robustness. Specifically, based on prompts derived from data context, decision tree specifications and output requirements, TreeED queries the LLM to induce the decision tree skeleton, whose root-to-leaf decision paths specify the stepwise procedure for evaluating a given sample. Each tree contains three types of nodes: (1) rule nodes that perform simple validation checks (e.g., format or range), (2) Graph Neural Network (GNN) nodes that capture complex patterns (e.g., functional dependencies), and (3) leaf nodes that output the final decision types (error or clean). Furthermore, ForestED employs uncertainty-based sampling to obtain multiple row subsets, constructing a decision tree for each subset using TreeED. It then leverages an Expectation-Maximization-based algorithm that jointly estimates tree reliability and optimizes the consensus ED prediction. Extensive xperiments demonstrate that our methods are accurate, explainable and robust, achieving an average F1-score improvement of 16.1% over the best baseline.

Categorical variables often appear in datasets for classification and regression tasks, and they need to be encoded into numerical values before training. Since many encoders have been developed and can significantly impact performance, choosing the appropriate encoder for a task becomes a time-consuming yet important practical issue. This study broadly classifies machine learning models into three categories: 1) ATI models that implicitly perform affine transformations on inputs, such as multi-layer perceptron neural network; 2) Tree-based models that are based on decision trees, such as random forest; and 3) the rest, such as kNN. Theoretically, we prove that the one-hot encoder is the best choice for ATI models in the sense that it can mimic any other encoders by learning suitable weights from the data. We also explain why the target encoder and its variants are the most suitable encoders for tree-based models. This study conducted comprehensive computational experiments to evaluate 14 encoders, including one-hot and target encoders, along with eight common machine-learning models on 28 datasets. The computational results agree with our theoretical analysis. The findings in this study shed light on how to select the suitable encoder for data scientists in fields such as fraud detection, disease diagnosis, etc.

Random forests is a common non-parametric regression technique which performs well for mixed-type data and irrelevant covariates, while being robust to monotonic variable transformations. Existing random forest implementations target regression or classification. We introduce the RFCDE package for fitting random forest models optimized for nonparametric conditional density estimation, including joint densities for multiple responses. This enables analysis of conditional probability distributions which is useful for propagating uncertainty and of joint distributions that describe relationships between multiple responses and covariates. RFCDE is released under the MIT open-source license and can be accessed at https://github.com/tpospisi/rfcde . Both R and Python versions, which call a common C++ library, are available.

Deep learning has achieved impressive performance in many domains, such as computer vision and natural language processing, but its advantage over classical shallow methods on tabular datasets remains questionable. It is especially challenging to surpass the performance of tree-like ensembles, such as XGBoost or Random Forests, on small-sized datasets (less than 1k samples). To tackle this challenge, we introduce HyperTab, a hypernetwork-based approach to solving small sample problems on tabular datasets. By combining the advantages of Random Forests and neural networks, HyperTab generates an ensemble of neural networks, where each target model is specialized to process a specific lower-dimensional view of the data. Since each view plays the role of data augmentation, we virtually increase the number of training samples while keeping the number of trainable parameters unchanged, which prevents model overfitting. We evaluated HyperTab on more than 40 tabular datasets of a varying number of samples and domains of origin, and compared its performance with shallow and deep learning models representing the current state-of-the-art. We show that HyperTab consistently outranks other methods on small data (with a statistically significant difference) and scores comparable to them on larger datasets. We make a python package with the code available to download at https://pypi.org/project/hypertab/

Recent advances in foundation models have shown great promise in domains such as natural language processing and computer vision, and similar efforts are now emerging in the Earth Observation community. These models aim to generalize across tasks with limited supervision, reducing the need for training separate models for each task. However, current strategies, which largely focus on scaling model size and dataset volume, require prohibitive computational and data resources, limiting accessibility to only a few large institutions. Moreover, this paradigm of ever-larger models stands in stark contrast with the principles of sustainable and environmentally responsible AI, as it leads to immense carbon footprints and resource inefficiency. In this work, we present a novel and efficient alternative: an Ensemble-of-Specialists framework for building Remote Sensing Foundation Models (RSFMs). Our method decomposes the training process into lightweight, task-specific ConvNeXtV2 specialists that can be frozen and reused. This modular approach offers strong advantages in efficiency, interpretability, and extensibility. Moreover, it naturally supports federated training, pruning, and continuous specialist integration, making it particularly well-suited for collaborative and resource-constrained settings. Our framework sets a new direction for building scalable and efficient RSFMs. All codes and pretrained models are available at https://github.com/pierreadorni/EoS-FM.

We propose a direct estimation method for R\'{e}nyi and f-divergence measures based on a new graph theoretical interpretation. Suppose that we are given two sample sets X and Y, respectively with N and M samples, where eta:=M/N is a constant value. Considering the k-nearest neighbor (k-NN) graph of Y in the joint data set (X,Y), we show that the average powered ratio of the number of X points to the number of Y points among all k-NN points is proportional to R\'{e}nyi divergence of X and Y densities. A similar method can also be used to estimate f-divergence measures. We derive bias and variance rates, and show that for the class of gamma-H\"{o}lder smooth functions, the estimator achieves the MSE rate of O(N^{-2gamma/(gamma+d)}). Furthermore, by using a weighted ensemble estimation technique, for density functions with continuous and bounded derivatives of up to the order d, and some extra conditions at the support set boundary, we derive an ensemble estimator that achieves the parametric MSE rate of O(1/N). Our estimators are more computationally tractable than other competing estimators, which makes them appealing in many practical applications.

Recurrent neural networks have been very successful at predicting sequences of words in tasks such as language modeling. However, all such models are based on the conventional classification framework, where the model is trained against one-hot targets, and each word is represented both as an input and as an output in isolation. This causes inefficiencies in learning both in terms of utilizing all of the information and in terms of the number of parameters needed to train. We introduce a novel theoretical framework that facilitates better learning in language modeling, and show that our framework leads to tying together the input embedding and the output projection matrices, greatly reducing the number of trainable variables. Our framework leads to state of the art performance on the Penn Treebank with a variety of network models.

Given the generational gap in available hardware between lay practitioners and the most endowed institutions, LLMs are becoming increasingly inaccessible as they grow in size. Whilst many approaches have been proposed to compress LLMs to make their resource consumption manageable, these methods themselves tend to be resource intensive, putting them out of the reach of the very user groups they target. In this work, we explore the problem of structured pruning of LLMs using only forward passes. We seek to empower practitioners to prune models so large that their available hardware has just enough memory to run inference. We develop Bonsai, a gradient-free, perturbative pruning method capable of delivering small, fast, and accurate pruned models. We observe that Bonsai outputs pruned models that (i) outperform those generated by more expensive gradient-based structured pruning methods, and (ii) are twice as fast (with comparable accuracy) as those generated by semi-structured pruning methods requiring comparable resources as Bonsai. We also leverage Bonsai to produce a new sub-2B model using a single A6000 that yields state-of-the-art performance on 4/6 tasks on the Huggingface Open LLM leaderboard.

A natural strategy for continual learning is to weigh a Bayesian ensemble of fixed functions. This suggests that if a (single) neural network could be interpreted as an ensemble, one could design effective algorithms that learn without forgetting. To realize this possibility, we observe that a neural network classifier with N parameters can be interpreted as a weighted ensemble of N classifiers, and that in the lazy regime limit these classifiers are fixed throughout learning. We call these classifiers the neural tangent experts and show they output valid probability distributions over the labels. We then derive the likelihood and posterior probability of each expert given past data. Surprisingly, the posterior updates for these experts are equivalent to a scaled and projected form of stochastic gradient descent (SGD) over the network weights. Away from the lazy regime, networks can be seen as ensembles of adaptive experts which improve over time. These results offer a new interpretation of neural networks as Bayesian ensembles of experts, providing a principled framework for understanding and mitigating catastrophic forgetting in continual learning settings.

Classic results establish that encouraging predictive diversity improves performance in ensembles of low-capacity models, e.g. through bagging or boosting. Here we demonstrate that these intuitions do not apply to high-capacity neural network ensembles (deep ensembles), and in fact the opposite is often true. In a large scale study of nearly 600 neural network classification ensembles, we examine a variety of interventions that trade off component model performance for predictive diversity. While such interventions can improve the performance of small neural network ensembles (in line with standard intuitions), they harm the performance of the large neural network ensembles most often used in practice. Surprisingly, we also find that discouraging predictive diversity is often benign in large-network ensembles, fully inverting standard intuitions. Even when diversity-promoting interventions do not sacrifice component model performance (e.g. using heterogeneous architectures and training paradigms), we observe an opportunity cost associated with pursuing increased predictive diversity. Examining over 1000 ensembles, we observe that the performance benefits of diverse architectures/training procedures are easily dwarfed by the benefits of simply using higher-capacity models, despite the fact that such higher capacity models often yield significantly less predictive diversity. Overall, our findings demonstrate that standard intuitions around predictive diversity, originally developed for low-capacity ensembles, do not directly apply to modern high-capacity deep ensembles. This work clarifies fundamental challenges to the goal of improving deep ensembles by making them more diverse, while suggesting an alternative path: simply forming ensembles from ever more powerful (and less diverse) component models.

Given thousands of equally accurate machine learning (ML) models, how can users choose among them? A recent ML technique enables domain experts and data scientists to generate a complete Rashomon set for sparse decision trees--a huge set of almost-optimal interpretable ML models. To help ML practitioners identify models with desirable properties from this Rashomon set, we develop TimberTrek, the first interactive visualization system that summarizes thousands of sparse decision trees at scale. Two usage scenarios highlight how TimberTrek can empower users to easily explore, compare, and curate models that align with their domain knowledge and values. Our open-source tool runs directly in users' computational notebooks and web browsers, lowering the barrier to creating more responsible ML models. TimberTrek is available at the following public demo link: https://poloclub.github.io/timbertrek.

Motivation The genotype assignment problem consists of predicting, from the genotype of an individual, which of a known set of populations it originated from. The problem arises in a variety of contexts, including wildlife forensics, invasive species detection and biodiversity monitoring. Existing approaches perform well under ideal conditions but are sensitive to a variety of common violations of the assumptions they rely on. Results In this article, we introduce Mycorrhiza, a machine learning approach for the genotype assignment problem. Our algorithm makes use of phylogenetic networks to engineer features that encode the evolutionary relationships among samples. Those features are then used as input to a Random Forests classifier. The classification accuracy was assessed on multiple published empirical SNP, microsatellite or consensus sequence datasets with wide ranges of size, geographical distribution and population structure and on simulated datasets. It compared favorably against widely used assessment tests or mixture analysis methods such as STRUCTURE and Admixture, and against another machine-learning based approach using principal component analysis for dimensionality reduction. Mycorrhiza yields particularly significant gains on datasets with a large average fixation index (FST) or deviation from the Hardy-Weinberg equilibrium. Moreover, the phylogenetic network approach estimates mixture proportions with good accuracy.

We introduce a hierarchical filtering procedure for generative models of sequences on trees, enabling control over the range of positional correlations in the data. Leveraging this controlled setting, we provide evidence that vanilla encoder-only transformer architectures can implement the optimal Belief Propagation algorithm on both root classification and masked language modeling tasks. Correlations at larger distances corresponding to increasing layers of the hierarchy are sequentially included as the network is trained. We analyze how the transformer layers succeed by focusing on attention maps from models trained with varying degrees of filtering. These attention maps show clear evidence for iterative hierarchical reconstruction of correlations, and we can relate these observations to a plausible implementation of the exact inference algorithm for the network sizes considered.

We present our winning system for Task~B (generation with reference passages) in SemEval-2026 Task~8: MTRAGEval. Our method is a heterogeneous ensemble of seven LLMs with two prompting variants, where a GPT-4o-mini judge selects the best candidate per instance. We ranked 1st out of 26 teams, achieving a conditioned harmonic mean of 0.7827 and outperforming the strongest baseline (gpt-oss-120b, 0.6390). Ablations show that diversity in model families, scales, and prompting strategies is essential, with the ensemble consistently beating any single model. We also introduce Meno-Lite-0.1, a 7B domain-adapted model with a strong cost--performance trade-off, and analyse MTRAGEval, highlighting annotation limitations and directions for improvement. Our code is publicly available: https://github.com/RaguTeam/ragu_mtrag_semeval

Ensemble learning of LLMs has emerged as a promising alternative to enhance performance, but existing approaches typically treat models as black boxes, combining the inputs or final outputs while overlooking the rich internal representations and interactions across models.In this work, we introduce LLMBoost, a novel ensemble fine-tuning framework that breaks this barrier by explicitly leveraging intermediate states of LLMs. Inspired by the boosting paradigm, LLMBoost incorporates three key innovations. First, a cross-model attention mechanism enables successor models to access and fuse hidden states from predecessors, facilitating hierarchical error correction and knowledge transfer. Second, a chain training paradigm progressively fine-tunes connected models with an error-suppression objective, ensuring that each model rectifies the mispredictions of its predecessor with minimal additional computation. Third, a near-parallel inference paradigm design pipelines hidden states across models layer by layer, achieving inference efficiency approaching single-model decoding. We further establish the theoretical foundations of LLMBoost, proving that sequential integration guarantees monotonic improvements under bounded correction assumptions. Extensive experiments on commonsense reasoning and arithmetic reasoning tasks demonstrate that LLMBoost consistently boosts accuracy while reducing inference latency.

Knowledge graph (KG) embedding is a fundamental task in natural language processing, and various methods have been proposed to explore semantic patterns in distinctive ways. In this paper, we propose to learn an ensemble by leveraging existing methods in a relation-aware manner. However, exploring these semantics using relation-aware ensemble leads to a much larger search space than general ensemble methods. To address this issue, we propose a divide-search-combine algorithm RelEns-DSC that searches the relation-wise ensemble weights independently. This algorithm has the same computation cost as general ensemble methods but with much better performance. Experimental results on benchmark datasets demonstrate the effectiveness of the proposed method in efficiently searching relation-aware ensemble weights and achieving state-of-the-art embedding performance. The code is public at https://github.com/LARS-research/RelEns.

We present DEI: Diversity in Evolutionary Inference, a distributed Quality-Diversity (QD) search framework that assigns heterogeneous large language models (LLMs) as mutation operators across peer nodes communicating with non-blocking collective operations. Unlike homogeneous parallel search, which replicates a single model's inductive biases across all workers, DEI treats each LLM's distinct creative prior as a complementary source of behavioral novelty. Extending the Digital Red Queen framework with DEI, nodes share local optimal solutions at the end of each round to seed the next round's population. This creates cross-model adversarial pressure that drives robustness beyond intra-model self-play. Evaluated on the Core War domain, a competitive programming benchmark in which Redcode warrior programs battle inside a simulated machine, a four-node heterogeneous ensemble (GPT-5.4-mini, Claude Sonnet 4.6, GPT-5.2, and Claude Haiku 4.5) achieves 124 percent higher merged-archive QD-Score (45.90 vs. 20.46) and 28 percent higher coverage (80.6 percent vs. 63.0 percent of cells) than a single-node baseline at equal total LLM-call budget. The heterogeneous ensemble also outperforms an equally-budgeted homogeneous ensemble on QD-Score, coverage, and held-out solution generality across all four model families. These results provide the first empirical evidence that model diversity, not merely parallelism, is the key driver of gain in distributed LLM-based QD search.

Decision trees are a crucial class of models offering robust predictive performance and inherent interpretability across various domains, including healthcare, finance, and logistics. However, current tree induction methods often face limitations such as suboptimal solutions from greedy methods or prohibitive computational costs and limited applicability of exact optimization approaches. To address these challenges, we propose an evolutionary optimization method for decision tree induction based on genetic programming (GP). Our key innovation is the integration of semantic priors and domain-specific knowledge about the search space into the optimization algorithm. To this end, we introduce LLEGO, a framework that incorporates semantic priors into genetic search operators through the use of Large Language Models (LLMs), thereby enhancing search efficiency and targeting regions of the search space that yield decision trees with superior generalization performance. This is operationalized through novel genetic operators that work with structured natural language prompts, effectively utilizing LLMs as conditional generative models and sources of semantic knowledge. Specifically, we introduce fitness-guided crossover to exploit high-performing regions, and diversity-guided mutation for efficient global exploration of the search space. These operators are controlled by corresponding hyperparameters that enable a more nuanced balance between exploration and exploitation across the search space. Empirically, we demonstrate across various benchmarks that LLEGO evolves superior-performing trees compared to existing tree induction methods, and exhibits significantly more efficient search performance compared to conventional GP approaches.

Decision trees and diffusion models are ostensibly disparate model classes, one discrete and hierarchical, the other continuous and dynamic. This work unifies the two by establishing a crisp mathematical correspondence between hierarchical decision trees and diffusion processes in appropriate limiting regimes. Our unification reveals a shared optimization principle: Global Trajectory Score Matching (GTSM), for which gradient boosting (in an idealized version) is asymptotically optimal. We underscore the conceptual value of our work through two key practical instantiations: \treeflow, which achieves competitive generation quality on tabular data with higher fidelity and a 2\times computational speedup, and \dsmtree, a novel distillation method that transfers hierarchical decision logic into neural networks, matching teacher performance within 2\% on many benchmarks.

Continual learning with an increasing number of classes is a challenging task. The difficulty rises when each example is presented exactly once, which requires the model to learn online. Recent methods with classic parameter optimization procedures have been shown to struggle in such setups or have limitations like non-differentiable components or memory buffers. For this reason, we present the fully differentiable ensemble method that allows us to efficiently train an ensemble of neural networks in the end-to-end regime. The proposed technique achieves SOTA results without a memory buffer and clearly outperforms the reference methods. The conducted experiments have also shown a significant increase in the performance for small ensembles, which demonstrates the capability of obtaining relatively high classification accuracy with a reduced number of classifiers.

In this manuscript, we show that any neural network with any activation function can be represented as a decision tree. The representation is equivalence and not an approximation, thus keeping the accuracy of the neural network exactly as is. We believe that this work provides better understanding of neural networks and paves the way to tackle their black-box nature. We share equivalent trees of some neural networks and show that besides providing interpretability, tree representation can also achieve some computational advantages for small networks. The analysis holds both for fully connected and convolutional networks, which may or may not also include skip connections and/or normalizations.

It is of great significance to estimate the performance of a given model architecture without training in the application of Neural Architecture Search (NAS) as it may take a lot of time to evaluate the performance of an architecture. In this paper, a novel NAS framework called GP-NAS-ensemble is proposed to predict the performance of a neural network architecture with a small training dataset. We make several improvements on the GP-NAS model to make it share the advantage of ensemble learning methods. Our method ranks second in the CVPR2022 second lightweight NAS challenge performance prediction track.

Competitions play an invaluable role in the field of forecasting, as exemplified through the recent M4 competition. The competition received attention from both academics and practitioners and sparked discussions around the representativeness of the data for business forecasting. Several competitions featuring real-life business forecasting tasks on the Kaggle platform has, however, been largely ignored by the academic community. We believe the learnings from these competitions have much to offer to the forecasting community and provide a review of the results from six Kaggle competitions. We find that most of the Kaggle datasets are characterized by higher intermittence and entropy than the M-competitions and that global ensemble models tend to outperform local single models. Furthermore, we find the strong performance of gradient boosted decision trees, increasing success of neural networks for forecasting, and a variety of techniques for adapting machine learning models to the forecasting task.

In-context learning is commonly interpreted as a form of conditional inference, in which the prompt specifies a context and the model's output is treated as an estimate of the corresponding conditional distribution. If this interpretation holds, then LLM estimates should satisfy basic probabilistic identities. In particular, the law of total probability asserts that prior-weighted conditional distributions aggregate into population-level marginals over any valid partition of the population. In this work, we investigate to what extent LLM estimates adhere to this self-consistency principle. We use binary trees as an evaluation scaffold to recursively partition a population into increasingly fine-grained subpopulations. We then prompt LLMs with verbalized subpopulation descriptions in context, aggregate the resulting estimates back into population-level estimates, and compare them across partitions of varying granularity. Applying this protocol across problem domains and state-of-the-art frontier models, we show widespread violations of basic consistency properties. An in-depth study of persona prompting reveals a pattern we call the macro fallacy: estimates reconstructed from more fine-grained subpopulation responses are often better aligned with human reference data than direct population-level estimates. This effect persists across variations in tree structure and estimation task, and can be partially recovered through implicit prompting. Together, these findings suggest that models possess relevant subpopulation knowledge but do not reliably propagate it into aggregate estimates. This gap establishes statistical self-consistency as an unsaturated, reference-free criterion for evaluating LLMs.

We present EARCP (Ensemble Auto-Régulé par Cohérence et Performance), a novel ensemble architecture that dynamically weights heterogeneous expert models based on both their individual performance and inter-model coherence. Unlike traditional ensemble methods that rely on static or offline-learned combinations, EARCP continuously adapts model weights through a principled online learning mechanism that balances exploitation of high-performing models with exploration guided by consensus signals. The architecture combines theoretical foundations from multiplicative weight update algorithms with a novel coherence-based regularization term, providing both theoretical guarantees through regret bounds and practical robustness in non-stationary environments. We formalize the EARCP framework, prove sublinear regret bounds of O(sqrt(T log M)) under standard assumptions, and demonstrate its effectiveness through empirical evaluation on sequential prediction tasks including time series forecasting, activity recognition, and financial prediction. The architecture is designed as a general-purpose framework applicable to any domain requiring ensemble learning with temporal dependencies. An open-source implementation is available at https://github.com/Volgat/earcp and via PyPI (pip install earcp).

In this paper, we present an Adaptive Ensemble Learning framework that aims to boost the performance of deep neural networks by intelligently fusing features through ensemble learning techniques. The proposed framework integrates ensemble learning strategies with deep learning architectures to create a more robust and adaptable model capable of handling complex tasks across various domains. By leveraging intelligent feature fusion methods, the Adaptive Ensemble Learning framework generates more discriminative and effective feature representations, leading to improved model performance and generalization capabilities. We conducted extensive experiments and evaluations on several benchmark datasets, including image classification, object detection, natural language processing, and graph-based learning tasks. The results demonstrate that the proposed framework consistently outperforms baseline models and traditional feature fusion techniques, highlighting its effectiveness in enhancing deep learning models' performance. Furthermore, we provide insights into the impact of intelligent feature fusion on model performance and discuss the potential applications of the Adaptive Ensemble Learning framework in real-world scenarios. The paper also explores the design and implementation of adaptive ensemble models, ensemble training strategies, and meta-learning techniques, which contribute to the framework's versatility and adaptability. In conclusion, the Adaptive Ensemble Learning framework represents a significant advancement in the field of feature fusion and ensemble learning for deep neural networks, with the potential to transform a wide range of applications across multiple domains.

Numerous crucial tasks in real-world decision-making rely on machine learning algorithms with calibrated uncertainty estimates. However, modern methods often yield overconfident and uncalibrated predictions. Various approaches involve training an ensemble of separate models to quantify the uncertainty related to the model itself, known as epistemic uncertainty. In an explicit implementation, the ensemble approach has high computational cost and high memory requirements. This particular challenge is evident in state-of-the-art neural networks such as transformers, where even a single network is already demanding in terms of compute and memory. Consequently, efforts are made to emulate the ensemble model without actually instantiating separate ensemble members, referred to as implicit ensembling. We introduce LoRA-Ensemble, a parameter-efficient deep ensemble method for self-attention networks, which is based on Low-Rank Adaptation (LoRA). Initially developed for efficient LLM fine-tuning, we extend LoRA to an implicit ensembling approach. By employing a single pre-trained self-attention network with weights shared across all members, we train member-specific low-rank matrices for the attention projections. Our method exhibits superior calibration compared to explicit ensembles and achieves similar or better accuracy across various prediction tasks and datasets.

Speculative decoding accelerates inference in large language models (LLMs) by generating draft tokens for target model verification. Current approaches for obtaining draft tokens rely on lightweight draft models or additional model structures to generate draft tokens and retrieve context from databases. Due to the draft model's small size and limited training data, model-based speculative decoding frequently becomes less effective in out-of-domain scenarios. Additionally, the time cost of the drafting phase results in a low upper limit on acceptance length during the verification step, limiting overall efficiency. This paper proposes RASD (Retrieval-Augmented Speculative Decoding), which adopts retrieval methods to enhance model-based speculative decoding. We introduce tree pruning and tree fusion to achieve this. Specifically, we develop a pruning method based on the draft model's probability distribution to construct the optimal retrieval tree. Second, we employ the longest prefix matching algorithm to merge the tree generated by the draft model with the retrieval tree, resulting in a unified tree for verification. Experimental results demonstrate that RASD achieves state-of-the-art inference acceleration across tasks such as DocQA, Summary, Code, and In-Domain QA. Moreover, RASD exhibits strong scalability, seamlessly integrating with various speculative decoding approaches, including both generation-based and retrieval-based methods.

Finetuned LLMs often exhibit poor uncertainty quantification, manifesting as overconfidence, poor calibration, and unreliable prediction results on test data or out-of-distribution samples. One approach commonly used in vision for alleviating this issue is a deep ensemble, which constructs an ensemble by training the same model multiple times using different random initializations. However, there is a huge challenge to ensembling LLMs: the most effective LLMs are very, very large. Keeping a single LLM in memory is already challenging enough: keeping an ensemble of e.g. 5 LLMs in memory is impossible in many settings. To address these issues, we propose an ensemble approach using Low-Rank Adapters (LoRA), a parameter-efficient fine-tuning technique. Critically, these low-rank adapters represent a very small number of parameters, orders of magnitude less than the underlying pre-trained model. Thus, it is possible to construct large ensembles of LoRA adapters with almost the same computational overhead as using the original model. We find that LoRA ensembles, applied on its own or on top of pre-existing regularization techniques, gives consistent improvements in predictive accuracy and uncertainty quantification.

In single-cell research, tracing and analyzing high-throughput single-cell differentiation trajectories is crucial for understanding biological processes. Key to this is the robust modeling of hierarchical structures that govern cellular development. Traditional methods face limitations in computational cost, performance, and stability. VAE-based approaches have made strides but still require branch-specific network modules, limiting their scalability and stability, while often suffering from posterior collapse. To overcome these challenges, we introduce HDTree, a generative modeling framework designed for robust lineage inference. HDTree captures tree relationships within a hierarchical latent space using a unified hierarchical codebook and employs a quantized diffusion process to model continuous cell state transitions. By aligning the generative process with the Waddington landscape, this method not only improves stability and scalability but also enhances the biological plausibility of inferred lineages. HDTree's effectiveness is demonstrated through comparisons on both general-purpose and single-cell datasets, where it outperforms existing methods in lineage inference accuracy, reconstruction quality, and hierarchical consistency. These contributions enable accurate and efficient modeling of cellular differentiation paths, offering reliable insights for biological discovery.\footnote{Code is available at https://github.com/zangzelin/code\_HDTree\_icml.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

The advent of Scientific Machine Learning has heralded a transformative era in scientific discovery, driving progress across diverse domains. Central to this progress is uncovering scientific laws from experimental data through symbolic regression. However, existing approaches are dominated by heuristic algorithms or data-hungry black-box methods, which often demand low-noise settings and lack principled uncertainty quantification. Motivated by interpretable Statistical Artificial Intelligence, we develop a hierarchical Bayesian framework for symbolic regression that represents scientific laws as ensembles of tree-structured symbolic expressions endowed with a regularized tree prior. This coherent probabilistic formulation enables full posterior inference via an efficient Markov chain Monte Carlo algorithm, yielding a balance between predictive accuracy and structural parsimony. To guide symbolic model selection, we develop a marginal posterior-based criterion adhering to the Occam's window principle and further quantify structural fidelity to ground truth through a tailored expression-distance metric. On the theoretical front, we establish near-minimax rate of Bayesian posterior concentration, providing the first rigorous guarantee in context of symbolic regression. Empirical evaluation demonstrates robust performance of our proposed methodology against state-of-the-art competing modules on a simulated example, a suite of canonical Feynman equations, and single-atom catalysis dataset.

Over the last three decades, ensemble forecasts have become an integral part of forecasting the weather. They provide users with more complete information than single forecasts as they permit to estimate the probability of weather events by representing the sources of uncertainties and accounting for the day-to-day variability of error growth in the atmosphere. This paper presents a novel approach to obtain a weather forecast model for ensemble forecasting with machine-learning. AIFS-CRPS is a variant of the Artificial Intelligence Forecasting System (AIFS) developed at ECMWF. Its loss function is based on a proper score, the Continuous Ranked Probability Score (CRPS). For the loss, the almost fair CRPS is introduced because it approximately removes the bias in the score due to finite ensemble size yet avoids a degeneracy of the fair CRPS. The trained model is stochastic and can generate as many exchangeable members as desired and computationally feasible in inference. For medium-range forecasts AIFS-CRPS outperforms the physics-based Integrated Forecasting System (IFS) ensemble for the majority of variables and lead times. For subseasonal forecasts, AIFS-CRPS outperforms the IFS ensemble before calibration and is competitive with the IFS ensemble when forecasts are evaluated as anomalies to remove the influence of model biases.

We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast tree-field integrators (FTFIs) are presented, including (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) Topological Transformers (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as three extra learnable parameters per Transformer layer, leading to 1.0-1.5%+ accuracy gains. Importantly, most of FTFIs are exact methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide 5.7-13x speedups. We also provide an extensive theoretical analysis of our methods.

As computer vision continues to advance and finds widespread applications across various domains, the need for interpretability in deep learning models becomes paramount. Existing methods often resort to post-hoc techniques or prototypes to explain the decision-making process, which can be indirect and lack intrinsic illustration. In this research, we introduce ViTree, a novel approach for fine-grained visual categorization that combines the popular vision transformer as a feature extraction backbone with neural decision trees. By traversing the tree paths, ViTree effectively selects patches from transformer-processed features to highlight informative local regions, thereby refining representations in a step-wise manner. Unlike previous tree-based models that rely on soft distributions or ensembles of paths, ViTree selects a single tree path, offering a clearer and simpler decision-making process. This patch and path selectivity enhances model interpretability of ViTree, enabling better insights into the model's inner workings. Remarkably, extensive experimentation validates that this streamlined approach surpasses various strong competitors and achieves state-of-the-art performance while maintaining exceptional interpretability which is proved by multi-perspective methods. Code can be found at https://github.com/SJTU-DeepVisionLab/ViTree.

Probabilistic weather forecasting requires not only accurate trajectories, but calibrated distributions over plausible atmospheric futures. Recent data-driven systems have achieved remarkable deterministic skill, and diffusion-based ensemble forecasters have substantially improved sample realism and uncertainty quantification. However, their inference cost scales with forecast horizon, ensemble size, and the number of denoising steps required for each transition, making large operational ensembles expensive. To address this, we present Tyche, a one-step conditional flow model for efficient probabilistic weather forecasting. Tyche models the conditional forecast distribution with a destination-aware average-velocity flow that maps Gaussian noise directly to future weather states in a single function evaluation (1-NFE). To make this one-step transport learnable in high-dimensional geophysical fields, we derive a JVP-regularized rectification objective that enforces temporal self-consistency across source and destination flow timesteps without explicitly forming Jacobians. The transport field is parameterized by an isotropic Swin-style transformer that preserves fine-scale spatial structure while remaining scalable on global grids. To improve ensemble reliability under autoregressive forecasting, we further introduce a rollout-based finetuning stage with curriculum CRPS calibration supervision. Experiments on ERA5 at 1.5^circ and 6-hour resolution show that our Tyche, using merely a single NFE, matches or exceeds the forecast skill and calibration of state-of-the-art multi-step generative baselines and the operational ECMWF IFS ensemble.

Monitoring deforestation-driven carbon emissions requires both spatially explicit and temporally continuous estimates of aboveground biomass density (AGBD) with calibrated uncertainty. NASA's Global Ecosystem Dynamics Investigation (GEDI) provides reliable LIDAR-derived AGBD, but its orbital sampling causes irregular spatiotemporal coverage, and occasional operational interruptions, including a 13-month hibernation from March 2023 to April 2024, leave extended gaps in the observational record. Prior work has used machine learning approaches to fill GEDI's spatial gaps using satellite-derived features, but temporal interpolation of biomass through unobserved periods, particularly across active disturbance events, remains largely unaddressed. Moreover, standard ensemble methods for biomass mapping have been shown to produce systematically miscalibrated prediction intervals. To address these gaps, we extend the Attentive Neural Process (ANP) framework, previously applied to spatial biomass interpolation, to jointly sparse spatiotemporal settings using geospatial foundation model embeddings. We treat space and time symmetrically, empirically validating a form of space-for-time substitution in which observations from nearby locations at other times inform predictions at held-out periods. Our results demonstrate that the ANP produces well-calibrated uncertainty estimates across disturbance regimes, supporting its use in Measurement, Reporting, and Verification (MRV) applications that require reliable uncertainty quantification for forest carbon accounting.

The K-core of a graph is the unique maximum subgraph within which each vertex connects to K or more other vertices. The optimal K-core attack problem asks to delete the minimum number of vertices from the K-core to induce its complete collapse. A hierarchical cycle-tree packing model is introduced here for this challenging combinatorial optimization problem. We convert the temporally long-range correlated K-core pruning dynamics into locally tree-like static patterns and analyze this model through the replica-symmetric cavity method of statistical physics. A set of coarse-grained belief propagation equations are derived to predict single vertex marginal probabilities efficiently. The associated hierarchical cycle-tree guided attack ({\tt hCTGA}) algorithm is able to construct nearly optimal attack solutions for regular random graphs and Erd\"os-R\'enyi random graphs. Our cycle-tree packing model may also be helpful for constructing optimal initial conditions for other irreversible dynamical processes on sparse random graphs.

This paper introduces PhyloLM, a method adapting phylogenetic algorithms to Large Language Models (LLMs) to explore whether and how they relate to each other and to predict their performance characteristics. Our method calculates a phylogenetic distance metrics based on the similarity of LLMs' output. The resulting metric is then used to construct dendrograms, which satisfactorily capture known relationships across a set of 111 open-source and 45 closed models. Furthermore, our phylogenetic distance predicts performance in standard benchmarks, thus demonstrating its functional validity and paving the way for a time and cost-effective estimation of LLM capabilities. To sum up, by translating population genetic concepts to machine learning, we propose and validate a tool to evaluate LLM development, relationships and capabilities, even in the absence of transparent training information.