Daily Papers

Real-world tables are often heterogeneous, combining numerical features with free-form string columns. Table foundation models (TFMs) excel on numerical tables but require strings to be encoded numerically, while large language models (LLMs) hold semantic knowledge but are not designed for tabular predictions. Most existing bridges use LLMs as plug-in encoders for cell strings, yet how to extract representations effectively for tabular learning remains underexplored. We show that the interface between LLMs and tables matter as much as the LLM itself. Applied cell-wise, larger LLMs do not give better features. With our interface, the same LLMs improve steadily with size. TILE (Table-Interfaced LLM Embeddings) combines four ingredients: row serialization to provide cross-column context, intermediate-layer extraction to avoid layers specialized for next-token prediction, columnar pooling to remove mean pooling's length bias, and by-pass features to route numbers and categories past the LLM. Paired with TFMs, TILE sets a new state of the art for tables with strings. Across 100 datasets, it beats the strongest baseline on 89% of splits, with gains across 7 LLMs and 10 tabular learners, and ranks first on the 108-dataset STRABLE benchmark.

We seek to improve deep neural networks by generalizing the pooling operations that play a central role in current architectures. We pursue a careful exploration of approaches to allow pooling to learn and to adapt to complex and variable patterns. The two primary directions lie in (1) learning a pooling function via (two strategies of) combining of max and average pooling, and (2) learning a pooling function in the form of a tree-structured fusion of pooling filters that are themselves learned. In our experiments every generalized pooling operation we explore improves performance when used in place of average or max pooling. We experimentally demonstrate that the proposed pooling operations provide a boost in invariance properties relative to conventional pooling and set the state of the art on several widely adopted benchmark datasets; they are also easy to implement, and can be applied within various deep neural network architectures. These benefits come with only a light increase in computational overhead during training and a very modest increase in the number of model parameters.

The past two decades have witnessed significant success in applying columnar storage to data warehousing and analytics. However, the rapid growth of machine learning poses new challenges. This paper presents Bullion, a columnar storage system tailored for machine learning workloads. Bullion addresses the complexities of data compliance, optimizes the encoding of long sequence sparse features, efficiently manages wide-table projections, introduces feature quantization in storage, enables quality-aware sequential reads for multimodal training data, and provides a comprehensive cascading encoding framework that unifies diverse encoding schemes through modular, composable interfaces. By aligning with the evolving requirements of ML applications, Bullion facilitates the application of columnar storage and processing to modern application scenarios such as those within advertising, recommendation systems, and Generative AI. Preliminary experimental results and theoretical analysis demonstrate Bullion's improved ability to deliver strong performance in the face of the unique demands of machine learning workloads compared to existing columnar storage solutions. Bullion significantly reduces I/O costs for deletion compliance, achieves substantial storage savings with its optimized encoding scheme for sparse features, and improves metadata parsing speed for wide-table projections. These advancements enable Bullion to become an important component in the future of machine learning infrastructure, enabling organizations to efficiently manage and process the massive volumes of data required for training and inference in modern AI applications.

Spatial pooling has been proven highly effective in capturing long-range contextual information for pixel-wise prediction tasks, such as scene parsing. In this paper, beyond conventional spatial pooling that usually has a regular shape of NxN, we rethink the formulation of spatial pooling by introducing a new pooling strategy, called strip pooling, which considers a long but narrow kernel, i.e., 1xN or Nx1. Based on strip pooling, we further investigate spatial pooling architecture design by 1) introducing a new strip pooling module that enables backbone networks to efficiently model long-range dependencies, 2) presenting a novel building block with diverse spatial pooling as a core, and 3) systematically comparing the performance of the proposed strip pooling and conventional spatial pooling techniques. Both novel pooling-based designs are lightweight and can serve as an efficient plug-and-play module in existing scene parsing networks. Extensive experiments on popular benchmarks (e.g., ADE20K and Cityscapes) demonstrate that our simple approach establishes new state-of-the-art results. Code is made available at https://github.com/Andrew-Qibin/SPNet.

The analysis of tabular data has traditionally been dominated by gradient-boosted decision trees (GBDTs), known for their proficiency with mixed categorical and numerical features. However, recent deep learning innovations are challenging this dominance. We introduce Mambular, an adaptation of the Mamba architecture optimized for tabular data. We extensively benchmark Mambular against state-of-the-art models, including neural networks and tree-based methods, and demonstrate its competitive performance across diverse datasets. Additionally, we explore various adaptations of Mambular to understand its effectiveness for tabular data. We investigate different pooling strategies, feature interaction mechanisms, and bi-directional processing. Our analysis shows that interpreting features as a sequence and passing them through Mamba layers results in surprisingly performant models. The results highlight Mambulars potential as a versatile and powerful architecture for tabular data analysis, expanding the scope of deep learning applications in this domain. The source code is available at https://github.com/basf/mamba-tabular.

Columnar storage is a core component of a modern data analytics system. Although many database management systems (DBMSs) have proprietary storage formats, most provide extensive support to open-source storage formats such as Parquet and ORC to facilitate cross-platform data sharing. But these formats were developed over a decade ago, in the early 2010s, for the Hadoop ecosystem. Since then, both the hardware and workload landscapes have changed. In this paper, we revisit the most widely adopted open-source columnar storage formats (Parquet and ORC) with a deep dive into their internals. We designed a benchmark to stress-test the formats' performance and space efficiency under different workload configurations. From our comprehensive evaluation of Parquet and ORC, we identify design decisions advantageous with modern hardware and real-world data distributions. These include using dictionary encoding by default, favoring decoding speed over compression ratio for integer encoding algorithms, making block compression optional, and embedding finer-grained auxiliary data structures. We also point out the inefficiencies in the format designs when handling common machine learning workloads and using GPUs for decoding. Our analysis identified important considerations that may guide future formats to better fit modern technology trends.

Active learning for imbalanced classification tasks is challenging as the minority classes naturally occur rarely. Gathering a large pool of unlabelled data is thus essential to capture minority instances. Standard pool-based active learning is computationally expensive on large pools and often reaches low accuracy by overfitting the initial decision boundary, thus failing to explore the input space and find minority instances. To address these issues we propose AnchorAL. At each iteration, AnchorAL chooses class-specific instances from the labelled set, or anchors, and retrieves the most similar unlabelled instances from the pool. This resulting subpool is then used for active learning. Using a small, fixed-sized subpool AnchorAL allows scaling any active learning strategy to large pools. By dynamically selecting different anchors at each iteration it promotes class balance and prevents overfitting the initial decision boundary, thus promoting the discovery of new clusters of minority instances. Experiments across different classification tasks, active learning strategies, and model architectures AnchorAL is (i) faster, often reducing runtime from hours to minutes, (ii) trains more performant models, (iii) and returns more balanced datasets than competing methods.

Pooling layers are essential building blocks of convolutional neural networks (CNNs), to reduce computational overhead and increase the receptive fields of proceeding convolutional operations. Their goal is to produce downsampled volumes that closely resemble the input volume while, ideally, also being computationally and memory efficient. Meeting both these requirements remains a challenge. To this end, we propose an adaptive and exponentially weighted pooling method: adaPool. Our method learns a regional-specific fusion of two sets of pooling kernels that are based on the exponent of the Dice-Sorensen coefficient and the exponential maximum, respectively. AdaPool improves the preservation of detail on a range of tasks including image and video classification and object detection. A key property of adaPool is its bidirectional nature. In contrast to common pooling methods, the learned weights can also be used to upsample activation maps. We term this method adaUnPool. We evaluate adaUnPool on image and video super-resolution and frame interpolation. For benchmarking, we introduce Inter4K, a novel high-quality, high frame-rate video dataset. Our experiments demonstrate that adaPool systematically achieves better results across tasks and backbones, while introducing a minor additional computational and memory overhead.

Knowledge graphs are incomplete by nature, with only a limited number of observed facts from the world knowledge being represented as structured relations between entities. To partly address this issue, an important task in statistical relational learning is that of link prediction or knowledge graph completion. Both linear and non-linear models have been proposed to solve the problem. Bilinear models, while expressive, are prone to overfitting and lead to quadratic growth of parameters in number of relations. Simpler models have become more standard, with certain constraints on bilinear map as relation parameters. In this work, we propose a factorized bilinear pooling model, commonly used in multi-modal learning, for better fusion of entities and relations, leading to an efficient and constraint-free model. We prove that our model is fully expressive, providing bounds on the embedding dimensionality and factorization rank. Our model naturally generalizes Tucker decomposition based TuckER model, which has been shown to generalize other models, as efficient low-rank approximation without substantially compromising the performance. Due to low-rank approximation, the model complexity can be controlled by the factorization rank, avoiding the possible cubic growth of TuckER. Empirically, we evaluate on real-world datasets, reaching on par or state-of-the-art performance. At extreme low-ranks, model preserves the performance while staying parameter efficient.

Existing deep convolutional neural networks (CNNs) require a fixed-size (e.g., 224x224) input image. This requirement is "artificial" and may reduce the recognition accuracy for the images or sub-images of an arbitrary size/scale. In this work, we equip the networks with another pooling strategy, "spatial pyramid pooling", to eliminate the above requirement. The new network structure, called SPP-net, can generate a fixed-length representation regardless of image size/scale. Pyramid pooling is also robust to object deformations. With these advantages, SPP-net should in general improve all CNN-based image classification methods. On the ImageNet 2012 dataset, we demonstrate that SPP-net boosts the accuracy of a variety of CNN architectures despite their different designs. On the Pascal VOC 2007 and Caltech101 datasets, SPP-net achieves state-of-the-art classification results using a single full-image representation and no fine-tuning. The power of SPP-net is also significant in object detection. Using SPP-net, we compute the feature maps from the entire image only once, and then pool features in arbitrary regions (sub-images) to generate fixed-length representations for training the detectors. This method avoids repeatedly computing the convolutional features. In processing test images, our method is 24-102x faster than the R-CNN method, while achieving better or comparable accuracy on Pascal VOC 2007. In ImageNet Large Scale Visual Recognition Challenge (ILSVRC) 2014, our methods rank #2 in object detection and #3 in image classification among all 38 teams. This manuscript also introduces the improvement made for this competition.

Multi-vector visual retrievers (e.g., ColPali-style late interaction models) deliver strong accuracy, but scale poorly because each page yields thousands of vectors, making indexing and search increasingly expensive. We present Visual RAG Toolkit, a practical system for scaling visual multi-vector retrieval with training-free, model-aware pooling and multi-stage retrieval. Motivated by Matryoshka Embeddings, our method performs static spatial pooling - including a lightweight sliding-window averaging variant - over patch embeddings to produce compact tile-level and global representations for fast candidate generation, followed by exact MaxSim reranking using full multi-vector embeddings. Our design yields a quadratic reduction in vector-to-vector comparisons by reducing stored vectors per page from thousands to dozens, notably without requiring post-training, adapters, or distillation. Across experiments with interaction-style models such as ColPali and ColSmol-500M, we observe that over the limited ViDoRe v2 benchmark corpus 2-stage retrieval typically preserves NDCG and Recall @ 5/10 with minimal degradation, while substantially improving throughput (approximately 4x QPS); with sensitivity mainly at very large k. The toolkit additionally provides robust preprocessing - high resolution PDF to image conversion, optional margin/empty-region cropping and token hygiene (indexing only visual tokens) - and a reproducible evaluation pipeline, enabling rapid exploration of two-, three-, and cascaded retrieval variants. By emphasizing efficiency at common cutoffs (e.g., k <= 10), the toolkit lowers hardware barriers and makes state-of-the-art visual retrieval more accessible in practice.

Representation Autoencoders (RAEs) generate images from pre-trained visual fea- tures, but their dense token grids make generative modeling expensive. Motivated by local feature correlations, we introduce PoolDINO, a learned affine pooling operator that merges neighboring tokens. Training the pooling operator jointly with the RGB decoder preserves the standard two-stage RAE procedure without a separate feature auto-encoder. On ImageNet-256, 4x token compression retains comparable generation quality under internal guidance, while 16x compression trades some quality for greater efficiency. At a fixed budget of 100 sampling steps, latent-sampling throughput increases by 3.7x and 9.0x, respectively, relative to the unpooled baseline. Classification and dense prediction evaluations show that comparable guided generation quality can coexist with weaker performance on other tasks.

Representation learning is central to many downstream tasks such as search, clustering, classification, and reranking. State-of-the-art sequence encoders typically collapse a variable-length token sequence to a single vector using a pooling operator, most commonly a special [CLS] token or mean pooling over token embeddings. In this paper, we identify systematic weaknesses of these pooling strategies: [CLS] tends to concentrate information toward the initial positions of the sequence and can under-represent distributed evidence, while mean pooling can dilute salient local signals, sometimes leading to worse short-context performance. To address these issues, we introduce Landmark (LMK) pooling, which partitions a sequence into chunks, inserts landmark tokens between chunks, and forms the final representation by mean-pooling the landmark token embeddings. This simple mechanism improves long-context extrapolation without sacrificing local salient features, at the cost of introducing a small number of special tokens. We empirically demonstrate that LMK pooling matches existing methods on short-context retrieval tasks and yields substantial improvements on long-context tasks, making it a practical and scalable alternative to existing pooling methods.

Recent advances in representation learning on graphs, mainly leveraging graph convolutional networks, have brought a substantial improvement on many graph-based benchmark tasks. While novel approaches to learning node embeddings are highly suitable for node classification and link prediction, their application to graph classification (predicting a single label for the entire graph) remains mostly rudimentary, typically using a single global pooling step to aggregate node features or a hand-designed, fixed heuristic for hierarchical coarsening of the graph structure. An important step towards ameliorating this is differentiable graph coarsening---the ability to reduce the size of the graph in an adaptive, data-dependent manner within a graph neural network pipeline, analogous to image downsampling within CNNs. However, the previous prominent approach to pooling has quadratic memory requirements during training and is therefore not scalable to large graphs. Here we combine several recent advances in graph neural network design to demonstrate that competitive hierarchical graph classification results are possible without sacrificing sparsity. Our results are verified on several established graph classification benchmarks, and highlight an important direction for future research in graph-based neural networks.

Deep learning models have achieved state-of-the-art performances on many relation extraction datasets. A common element in these deep learning models involves the pooling mechanisms where a sequence of hidden vectors is aggregated to generate a single representation vector, serving as the features to perform prediction for RE. Unfortunately, the models in the literature tend to employ different strategies to perform pooling for RE, leading to the challenge to determine the best pooling mechanism for this problem, especially in the biomedical domain. In order to answer this question, in this work, we conduct a comprehensive study to evaluate the effectiveness of different pooling mechanisms for the deep learning models in biomedical RE. The experimental results suggest that dependency-based pooling is the best pooling strategy for RE in the biomedical domain, yielding the state-of-the-art performance on two benchmark datasets for this problem.

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve expressive power of message passing neural networks. The method is then extended to higher dimensional WL, leading to a novel k,l-WL algorithm, a more general framework than k-WL. Theoretically, we analyze the expressivity of k,l-WL with respect to k and l and unifies it with a great number of subgraph GNNs. Complexity reduction methods are also systematically discussed to build powerful and practical k,l-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our k,l-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework.

Block-sparse attention is promising for accelerating long-context LLM pre-filling, yet identifying relevant blocks efficiently remains a bottleneck. Existing methods typically employ coarse-grained attention as a proxy for block importance estimation, but often resort to expensive token-level searching or scoring, resulting in significant selection overhead. In this work, we trace the inaccuracy of standard coarse-grained attention via mean pooling to a theoretical root cause: the interaction between mean pooling and Rotary Positional Embeddings (RoPE). We prove that mean pooling acts as a low-pass filter that induces destructive interference in high-frequency dimensions, effectively creating a "blind spot" for local positional information (e.g., slash patterns). To address this, we introduce Prism, a training-free spectral-aware approach that decomposes block selection into high-frequency and low-frequency branches. By applying energy-based temperature calibration, Prism restores the attenuated positional signals directly from pooled representations, enabling block importance estimation using purely block-level operations, thereby improving efficiency. Extensive evaluations confirm that Prism maintains accuracy parity with full attention while delivering up to 5.1times speedup.

Predictive distributions need to be aggregated when probabilistic forecasts are merged, or when expert opinions expressed in terms of probability distributions are fused. We take a prediction space approach that applies to discrete, mixed discrete-continuous and continuous predictive distributions alike, and study combination formulas for cumulative distribution functions from the perspectives of coherence, probabilistic and conditional calibration, and dispersion. Both linear and non-linear aggregation methods are investigated, including generalized, spread-adjusted and beta-transformed linear pools. The effects and techniques are demonstrated theoretically, in simulation examples, and in case studies on density forecasts for S&P 500 returns and daily maximum temperature at Seattle-Tacoma Airport.

Many dynamical processes unfold on the sphere but the default scientific machine learning architectures are Euclidean. Applying these architectures on a regular lat-lon grid causes problems: Cartesian convolutions become distorted at high latitude; 2D FFTs in Fourier neural operators incorrectly assume double periodicity; Cartesian positional encodings in ViTs distort spherical geodesic distances. Recent work moves towards natively spherical primitives, including spherical convolutions (e.g., DeepSphere or DISCO), Spherical Fourier Neural Operators (SFNOs), and geodesic attention. Here we propose Dandelion, a spherical version of Flower, a warp-based neural PDE solver. Layers of Dandelion predict a tangent-plane displacement and transport features along great circles. We obtain a U-Net-like structure by implementing hierarchical pooling entirely in the spherical-harmonic domain. There are thus no convolutions: spatial mixing is achieved only through spherical coordinate changes, or warps. To compare Dandelion with existing spherical architectures, we release an evolving benchmark suite of challenging, natively-spherical PDE datasets including a modified Galewsky jet, anomalous chained turbulence, Cahn-Hilliard decomposition, spherical Riemann shocks, Held-Suarez dry atmospheric transport and global ocean dynamics. This new benchmark fills the gap in existing spherical datasets which are either too small and stylized, or much too large (ERA5) for model iteration. Dandelion is best or second-best on every dataset, and the gap to non-warp baselines widens with resolution: at 256times 512, Dandelion and Flower2D occupy the top two slots in both single-step prediction and rollout.

Downsampling layers, including pooling and strided convolutions, are crucial components of the convolutional neural network architecture that determine both the granularity/scale of image feature analysis as well as the receptive field size of a given layer. To fully understand this problem, we analyse the performance of models independently trained with each pooling configurations on CIFAR10, using a ResNet20 network, and show that the position of the downsampling layers can highly influence the performance of a network and predefined downsampling configurations are not optimal. Network Architecture Search (NAS) might be used to optimize downsampling configurations as an hyperparameter. However, we find that common one-shot NAS based on a single SuperNet does not work for this problem. We argue that this is because a SuperNet trained for finding the optimal pooling configuration fully shares its parameters among all pooling configurations. This makes its training hard, because learning some configurations can harm the performance of others. Therefore, we propose a balanced mixture of SuperNets that automatically associates pooling configurations to different weight models and helps to reduce the weight-sharing and inter-influence of pooling configurations on the SuperNet parameters. We evaluate our proposed approach on CIFAR10, CIFAR100, as well as Food101 and show that in all cases, our model outperforms other approaches and improves over the default pooling configurations.

Vision Transformer (ViT) extracts the final representation from either class token or an average of all patch tokens, following the architecture of Transformer in Natural Language Processing (NLP) or Convolutional Neural Networks (CNNs) in computer vision. However, studies for the best way of aggregating the patch tokens are still limited to average pooling, while widely-used pooling strategies, such as max and GeM pooling, can be considered. Despite their effectiveness, the existing pooling strategies do not consider the architecture of ViT and the channel-wise difference in the activation maps, aggregating the crucial and trivial channels with the same importance. In this paper, we present Group Generalized Mean (GGeM) pooling as a simple yet powerful pooling strategy for ViT. GGeM divides the channels into groups and computes GeM pooling with a shared pooling parameter per group. As ViT groups the channels via a multi-head attention mechanism, grouping the channels by GGeM leads to lower head-wise dependence while amplifying important channels on the activation maps. Exploiting GGeM shows 0.1%p to 0.7%p performance boosts compared to the baselines and achieves state-of-the-art performance for ViT-Base and ViT-Large models in ImageNet-1K classification task. Moreover, GGeM outperforms the existing pooling strategies on image retrieval and multi-modal representation learning tasks, demonstrating the superiority of GGeM for a variety of tasks. GGeM is a simple algorithm in that only a few lines of code are necessary for implementation.

Multi-vector embedding models have emerged as a powerful paradigm for document retrieval, preserving fine-grained visual and textual details through token-level representations. However, this expressiveness comes at a staggering cost: storing embeddings for every token inflates index sizes by over 1000times compared to single-vector approaches, severely limiting scalability. We introduce ReinPool, a reinforcement learning framework that learns to dynamically filter and pool multi-vector embeddings into compact, retrieval-optimized representations. By training with an inverse retrieval objective and NDCG-based rewards, ReinPool identifies and retains only the most discriminative vectors without requiring manual importance annotations. On the Vidore V2 benchmark across three vision-language embedding models, ReinPool compresses multi-vector representations by 746--1249times into single vectors while recovering 76--81\% of full multi-vector retrieval performance. Compared to static mean pooling baselines, ReinPool achieves 22--33\% absolute NDCG@3 improvement, demonstrating that learned selection significantly outperforms heuristic aggregation.

Obtaining a single-vector representation from a Large Language Model's (LLM) token-level outputs is a critical step for nearly all sentence-level tasks. However, standard pooling methods like mean or max aggregation treat tokens as an independent set, discarding the rich relational structure captured by the model's self-attention layers and making them susceptible to signal dilution. To address this, we introduce GLOT, a lightweight, structure-aware pooling module that reframes pooling as relational learning followed by aggregation. Operating on the outputs of a frozen LLM, GLOT first constructs a latent token-similarity graph, then refines token representations with a graph neural network, and finally aggregates them using a readout layer. Experimentally, our approach is remarkably robust and efficient: on a diagnostic stress test where 90% of tokens are random distractors, GLOT maintains over 97% accuracy while baseline methods collapse. Furthermore, it is competitive with state-of-the-art techniques on benchmarks like GLUE and MTEB with 20x fewer trainable parameters and speeds up the training time by over 100x compared with parameter-efficient fine-tuning methods. Supported by a theoretical analysis of its expressive power, our work shows that learning over token graphs is a powerful paradigm for the efficient adaptation of frozen LLMs. Our code is published at https://github.com/ipsitmantri/GLOT.

The significant advancements of Large Language Models (LLMs) in generative tasks have led to a growing body of work exploring LLM-based embedding models. While these models, employing different pooling and attention strategies, have achieved state-of-the-art performance on public embedding benchmarks, questions still arise about what constitutes an effective design for LLM-based embedding models. However, these models are often trained on different datasets, using different LLM base models or training settings. Moreover, evaluations on public embedding benchmarks often fail to report statistical significance, making it difficult to determine which designs truly contribute to final performance. This complicates the process for practitioners seeking optimal training recipes for LLM-based embedding models. In this study, we conduct a large-scale experiment by training a series of LLM-based embedding models using the same training data and base model but differing in their pooling and attention strategies. The results show that there is no one-size-fits-all solution: while bidirectional attention and an additional trainable pooling layer outperform in text similarity and information retrieval tasks, they do not significantly surpass simpler designs like EOS-last token pooling and default causal attention in clustering and classification tasks. Furthermore, we propose a new pooling strategy, Multi-Layers Trainable Pooling, which transforms the outputs of all hidden layers, rather than just the last layer, using a cross-attention network. This method proves to be statistically superior in text similarity and retrieval tasks compared to existing pooling methods. Overall, this paper sheds light on effective training strategies for LLM-based embedding models.

Large Vision-Language Models (LVLMs) map visual inputs into dense token sequences, imposing a quadratic computational bottleneck for inference. Elastic visual-token compression addresses this by training a single model that can run at multiple visual-token budgets. However, existing approaches struggle under aggressive compression. Spatial-only compression, as in nested pooling, behaves as an imperfect low-pass filter and induces spectral aliasing that obscures fine-grained detail. Query-only compression, as in nested query resampling, replaces explicit grid-aligned tokens with non-local summaries and substantially degrades spatial grounding. To resolve this representational conflict, we introduce PARCEL (Pool-Anchored Resampling with Conditioned Elastic Queries for Efficient Vision-Language Understanding), a visual tokenization architecture that dynamically partitions the labor of feature extraction. PARCEL establishes spatial pool tokens as low-frequency layout anchors and conditions elastic query tokens on these anchors through Pool-Conditioned Query Resampling. This encourages query tokens to focus on complementary visual features rather than redundant spatial mapping. Extensive evaluations across 27 benchmarks show that PARCEL improves the performance-efficiency Pareto frontier, consistently outperforming existing matryoshka baselines across visual-token budgets while preserving the "train once, deploy anywhere" paradigm.

Convolutional networks and vision transformers have different forms of pairwise interactions, pooling across layers and pooling at the end of the network. Does the latter really need to be different? As a by-product of pooling, vision transformers provide spatial attention for free, but this is most often of low quality unless self-supervised, which is not well studied. Is supervision really the problem? In this work, we develop a generic pooling framework and then we formulate a number of existing methods as instantiations. By discussing the properties of each group of methods, we derive SimPool, a simple attention-based pooling mechanism as a replacement of the default one for both convolutional and transformer encoders. We find that, whether supervised or self-supervised, this improves performance on pre-training and downstream tasks and provides attention maps delineating object boundaries in all cases. One could thus call SimPool universal. To our knowledge, we are the first to obtain attention maps in supervised transformers of at least as good quality as self-supervised, without explicit losses or modifying the architecture. Code at: https://github.com/billpsomas/simpool.

Multimodal large language models have become the dominant paradigm for visual understanding, but incur substantial costs by encoding inputs into dense, fixed-size patch tokens. However, visual information is unevenly distributed: some regions require fine-grained detail, while others admit compact representations. Downsampling sacrifices this detail, while existing token pruning and adaptive approaches remain limited in content-adaptive granularity, task generalization, and integration with modern MLLMs and serving infrastructure. Overcoming these limitations calls for foundation models that learn, end to end, where-and at what granularity-to allocate visual representations, a native capability we term elastic visual representation weaving. We introduce VisionWeave, establishing this capability in frontier-level MLLMs through large-scale training. It combines two components: a gated spatial pooler constructs coarse-grained representations alongside native fine-grained representations within a shared MRoPE coordinate, while a granularity router learns their content-adaptive allocation. Through self-distillation alone, we validate this capability on Qwen3.5-4B and scale to Qwen3.8-27B with over 30K A100 GPU-hours. Based on Qwen3.8-27B, VisionWeave adaptively adjusts token savings to visual content, saving 43.0% tokens on average while retaining 98.9% native performance across eight benchmarks, versus only 88% performance preserved for token pruning baselines with a fixed 50% savings target. Extensive evaluations confirm robust efficiency-quality trade-offs across diverse tasks, resolutions and video frames. When deployed on SGLang serving engine, our method achieves a 2.3x throughput gain while reducing mean TTFT by 54.4% and mean TPOT by 60.6%. Together, we believe these results position elastic visual weaving as a promising capability for next-generation multimodal models.

We investigate the design of pooling methods used to summarize the outputs of transformer embedding models, primarily motivated by reinforcement learning and vision applications. This work considers problems where a subset of the input vectors contains requisite information for a downstream task (signal) while the rest are distractors (noise). By framing pooling as vector quantization with the goal of minimizing signal loss, we demonstrate that the standard methods used to aggregate transformer outputs, AvgPool, MaxPool, and ClsToken, are vulnerable to performance collapse as the signal-to-noise ratio (SNR) of inputs fluctuates. We then show that an attention-based adaptive pooling method can approximate the signal-optimal vector quantizer within derived error bounds for any SNR. Our theoretical results are first validated by supervised experiments on a synthetic dataset designed to isolate the SNR problem, then generalized to standard relational reasoning, multi-agent reinforcement learning, and vision benchmarks with noisy observations, where transformers with adaptive pooling display superior robustness across tasks.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula (1-β^{n})/(1-β), where n is the number of samples and βin [0,1) is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.

Most modern convolutional neural networks (CNNs) used for object recognition are built using the same principles: Alternating convolution and max-pooling layers followed by a small number of fully connected layers. We re-evaluate the state of the art for object recognition from small images with convolutional networks, questioning the necessity of different components in the pipeline. We find that max-pooling can simply be replaced by a convolutional layer with increased stride without loss in accuracy on several image recognition benchmarks. Following this finding -- and building on other recent work for finding simple network structures -- we propose a new architecture that consists solely of convolutional layers and yields competitive or state of the art performance on several object recognition datasets (CIFAR-10, CIFAR-100, ImageNet). To analyze the network we introduce a new variant of the "deconvolution approach" for visualizing features learned by CNNs, which can be applied to a broader range of network structures than existing approaches.

Evaluating modern machine learning models has become prohibitively expensive. Benchmarks such as LMMs-Eval and HELM demand thousands of GPU hours per model. Costly evaluation reduces inclusivity, slows the cycle of innovation, and worsens environmental impact. The typical approach follows two steps. First, select an anchor subset of data. Second, train a mapping from the accuracy on this subset to the final test result. The drawback is that anchor selection depends on clustering, which can be complex and sensitive to design choices. We argue that promoting diversity among samples is not essential; what matters is to select samples that maximise diversity in model responses. Our method, Diversifying Sample Condensation (DISCO), selects the top-k samples with the greatest model disagreements. This uses greedy, sample-wise statistics rather than global clustering. The approach is conceptually simpler. From a theoretical view, inter-model disagreement provides an information-theoretically optimal rule for such greedy selection. DISCO shows empirical gains over prior methods, achieving state-of-the-art results in performance prediction across MMLU, Hellaswag, Winogrande, and ARC. Code is available here: https://github.com/arubique/disco-public.

The growing interest in artificial intelligence has created workloads that require both sequential and random access. At the same time, NVMe-backed storage solutions have emerged, providing caching capability for large columnar datasets in cloud storage. Current columnar storage libraries fall short of effectively utilizing an NVMe device's capabilities, especially when it comes to random access. Historically, this has been assumed an implicit weakness in columnar storage formats, but this has not been sufficiently explored. In this paper, we examine the effectiveness of popular columnar formats such as Apache Arrow, Apache Parquet, and Lance in both random access and full scan tasks against NVMe storage. We argue that effective encoding of a column's structure, such as the repetition and validity information, is the key to unlocking the disk's performance. We show that Parquet, when configured correctly, can achieve over 60x better random access performance than default settings. We also show that this high random access performance requires making minor trade-offs in scan performance and RAM utilization. We then describe the Lance structural encoding scheme, which alternates between two different structural encodings based on data width, and achieves better random access performance without making trade-offs in scan performance or RAM utilization.

Column type annotation is vital for tasks like data cleaning, integration, and visualization. Recent solutions rely on resource-intensive language models fine-tuned on well-annotated columns from a particular set of tables, i.e., a source data lake. In this paper, we study whether we can adapt an existing pre-trained LM-based model to a new (i.e., target) data lake to minimize the annotations required on the new data lake. However, challenges include the source-target knowledge gap, selecting informative target data, and fine-tuning without losing shared knowledge exist. We propose LakeHopper, a framework that identifies and resolves the knowledge gap through LM interactions, employs a cluster-based data selection scheme for unannotated columns, and uses an incremental fine-tuning mechanism that gradually adapts the source model to the target data lake. Our experimental results validate the effectiveness of LakeHopper on two different data lake transfers under both low-resource and high-resource settings.

The paper ``Tropical Geometry of Deep Neural Networks'' by L. Zhang et al. introduces an equivalence between integer-valued neural networks (IVNN) with ReLU_{t} and tropical rational functions, which come with a map to polytopes. Here, IVNN refers to a network with integer weights but real biases, and ReLU_{t} is defined as ReLU_{t}(x)=max(x,t) for tinRcup{-infty}. For every poset with n points, there exists a corresponding order polytope, i.e., a convex polytope in the unit cube [0,1]^n whose coordinates obey the inequalities of the poset. We study neural networks whose associated polytope is an order polytope. We then explain how posets with four points induce neural networks that can be interpreted as 2times 2 convolutional filters. These poset filters can be added to any neural network, not only IVNN. Similarly to maxout, poset pooling filters update the weights of the neural network during backpropagation with more precision than average pooling, max pooling, or mixed pooling, without the need to train extra parameters. We report experiments that support our statements. We also define the structure of algebra over the operad of posets on poset neural networks and tropical polynomials. This formalism allows us to study the composition of poset neural network arquitectures and the effect on their corresponding Newton polytopes, via the introduction of the generalization of two operations on polytopes: the Minkowski sum and the convex envelope.

Knowledge distillation (KD) is a widely used framework for training compact, task-specific models by leveraging the knowledge of teacher models. However, its application to active learning (AL), which aims to minimize annotation costs through iterative sample selection, remains underexplored. This gap stems from the fact that KD typically assumes access to sufficient labeled data, whereas AL operates in data-scarce scenarios where task-specific teacher models are often unavailable. In this paper, we introduce ActiveKD, a framework that integrates AL with KD by leveraging the zero- and few-shot capabilities of large vision-language models (VLMs). A key aspect of ActiveKD is the structured prediction bias of VLMs -- i.e., their predictions form clusters in the probability space. We regard this structure as an inductive bias of the teacher model, capturing generalizable output patterns beneficial to student learning. To exploit this bias, we propose Probabilistic CoreSet (PCoreSet), a selection strategy that maximizes coverage in the probability space rather than the feature space. PCoreSet strategically selects categorically diverse unlabeled samples, facilitating more efficient transfer of teacher knowledge under limited annotation budgets. Evaluations on 11 datasets show that PCoreSet consistently outperforms existing selection methods within the ActiveKD framework, advancing research at the intersection of AL and KD.

Text-to-SQL maps natural language questions to executable SQL queries. Modern databases often contain large and complex schemas, making schema linking a critical step for accurate SQL generation. Existing methods either rely on full-schema generation, which leaves schema linking implicit within a large search space, or use a separate retriever trained with static gold-column supervision, whose targets may be suboptimal for the current generator policy. To address this issue, we propose Adaptive Co-optimization via Empirical Credit Assignment for Text-to-SQL (ACE-SQL), a reinforcement learning (RL) framework that jointly optimizes schema retrieval and SQL generation under execution feedback. ACE-SQL constructs an online column-set pool from generator rollouts and derives adaptive on-policy retrieval targets from the column set most frequently associated with execution-correct rollouts. This induces bidirectional adaptation, where the retriever adapts toward column sets that the generator can execute correctly, while the generator adapts to the retriever's evolving schema selections under execution feedback. With approximately 3k synthetic Text-to-SQL question-database pairs for RL training, ACE-SQL achieves 65.3% greedy execution accuracy on BIRD Dev while using 0.93k output tokens per query. The repository is available at https://github.com/xbchen1/ACE-SQL.

Which forms of test-time compute improve the predictions of strong pretrained tabular foundation models (TFMs)? We systematically study this along three axes: adaptation, aggregation, and context construction. Our evaluation spans modern TFMs across the TabArena benchmark, supplemented by experiments on wide and large-scale tables from OpenML. For adaptation, we introduce DiagScale, a diagonal query-key similarity update. It trains only 0.003-0.03% of model parameters and achieves gains comparable to full fine-tuning across three independently pretrained backbones. For aggregation, both pool composition and selection strategy matter. TabPFN-3 already averages predictions from different preprocessing variants of the same data, and adding more such predictions yields diminishing returns. With a broader pool of 96 configurations, greedy selection reduces error by 2.4% relative to the default predictor, but uniform averaging increases error. For context construction, attention-guided retrieval improves TabPFN-3's predictions on some large tables and supports source pools beyond the full context memory limit. The context expansion methods we test yield no consistent improvement. Taken together, our results suggest that adaptation and selective aggregation yield consistent benchmark-level gains. The benefits of context construction depend more on the task and data regime. Adaptation and aggregation over the same backbone yield further gains when combined, but require substantially more computation than default inference. These trade-offs motivate choosing strategies according to the available computation budget. Code is available at https://github.com/kanghui-learning/test-time-compute-for-tabular-foundation-models.

Hierarchical graph pooling(HGP) are designed to consider the fact that conventional graph neural networks(GNN) are inherently flat and are also not multiscale. However, most HGP methods suffer not only from lack of considering global topology of the graph and focusing on the feature learning aspect, but also they do not align local and global features since graphs should inherently be analyzed in a multiscale way. LGRPool is proposed in the present paper as a HGP in the framework of expectation maximization in machine learning that aligns local and global aspects of message passing with each other using a regularizer to force the global topological information to be inline with the local message passing at different scales through the representations at different layers of HGP. Experimental results on some graph classification benchmarks show that it slightly outperforms some baselines.

Image descriptors based on activations of Convolutional Neural Networks (CNNs) have become dominant in image retrieval due to their discriminative power, compactness of representation, and search efficiency. Training of CNNs, either from scratch or fine-tuning, requires a large amount of annotated data, where a high quality of annotation is often crucial. In this work, we propose to fine-tune CNNs for image retrieval on a large collection of unordered images in a fully automated manner. Reconstructed 3D models obtained by the state-of-the-art retrieval and structure-from-motion methods guide the selection of the training data. We show that both hard-positive and hard-negative examples, selected by exploiting the geometry and the camera positions available from the 3D models, enhance the performance of particular-object retrieval. CNN descriptor whitening discriminatively learned from the same training data outperforms commonly used PCA whitening. We propose a novel trainable Generalized-Mean (GeM) pooling layer that generalizes max and average pooling and show that it boosts retrieval performance. Applying the proposed method to the VGG network achieves state-of-the-art performance on the standard benchmarks: Oxford Buildings, Paris, and Holidays datasets.

In whole slide images (WSIs) analysis, attention-based multi-instance learning (MIL) models are susceptible to spurious correlations and degrade under domain shift. These methods may assign high attention weights to non-tumor regions, such as staining biases or artifacts, leading to unreliable tumor region localization. In this paper, we revisit max-pooling-based MIL methods from a causal perspective. Under mild assumptions, our theoretical results demonstrate that max-pooling encourages the model to focus on causal factors while ignoring bias-related factors. Furthermore, we discover that existing max-pooling-based methods may overfit the training set through rote memorization of instance features and fail to learn meaningful patterns. To address these issues, we propose FocusMIL, which couples max-pooling with an instance-level variational information bottleneck (VIB) to learn compact, predictive latent representations, and employs a multi-bag mini-batch scheme to stabilize optimization. We conduct comprehensive experiments on three real-world datasets and one semi-synthetic dataset. The results show that, by capturing causal factors, FocusMIL exhibits significant advantages in out-of-distribution scenarios and instance-level tumor region localization tasks.

When rows of an n times d matrix A are given in a stream, we study algorithms for approximating the top eigenvector of the matrix {A}^TA (equivalently, the top right singular vector of A). We consider worst case inputs A but assume that the rows are presented to the streaming algorithm in a uniformly random order. We show that when the gap parameter R = σ_1(A)^2/σ_2(A)^2 = Ω(1), then there is a randomized algorithm that uses O(h cdot d cdot polylog(d)) bits of space and outputs a unit vector v that has a correlation 1 - O(1/R) with the top eigenvector v_1. Here h denotes the number of heavy rows in the matrix, defined as the rows with Euclidean norm at least |{A}|_F/d cdot operatorname{polylog(d)}. We also provide a lower bound showing that any algorithm using O(hd/R) bits of space can obtain at most 1 - Ω(1/R^2) correlation with the top eigenvector. Thus, parameterizing the space complexity in terms of the number of heavy rows is necessary for high accuracy solutions. Our results improve upon the R = Ω(log n cdot log d) requirement in a recent work of Price and Xun (FOCS 2024). We note that the algorithm of Price and Xun works for arbitrary order streams whereas our algorithm requires a stronger assumption that the rows are presented in a uniformly random order. We additionally show that the gap requirements in their analysis can be brought down to R = Ω(log^2 d) for arbitrary order streams and R = Ω(log d) for random order streams. The requirement of R = Ω(log d) for random order streams is nearly tight for their analysis as we obtain a simple instance with R = Ω(log d/loglog d) for which their algorithm, with any fixed learning rate, cannot output a vector approximating the top eigenvector v_1.

Selecting a subset of features (columns) from a tabular dataset is a ubiquitous challenge in real-world applications. Industry experts seek to minimize model training costs, climate scientists require an interpretable subset of factors to understand extreme weather events, and clinicians need to choose among diagnostic tests due to financial and time constraints. When looking at the scientific literature to determine which feature selection method to use, practitioners across domains face an unrepresentative landscape of benchmarking. Despite extensive research, existing feature selection benchmarks provide limited guidance because they rely on outdated models, ad hoc evaluation protocols, or artificially generated data that do not reflect real-world problems. To close the gap between scientific benchmarking and real-world applications, we introduce SelectArena, a modern benchmark for feature selection. We compare 15 widely used feature selection methods on 71 manually curated real-world tabular datasets, covering classification and regression problems, using standardized evaluation protocols and state-of-the-art tabular (foundation) models. Our results reveal clear trade-offs across predictive performance, runtime, stability, and validity. Tree-based methods, CART and RFImportance, along with F-Test are Pareto-optimal when taking into account predictive performance and runtime. F-Test, information-theory-, and distance-based methods lead on stability and validity, with F-Test emerging as a balanced choice across our metrics. Search-based methods are slow, unstable and achieve low performance. SelectArena turns these findings into practical guidance and, as an extensible platform, supports future feature selection research.

Graph pooling compresses graph information into a compact representation. State-of-the-art graph pooling methods follow a hierarchical approach, which reduces the graph size step-by-step. These methods must balance memory efficiency with preserving node information, depending on whether they use node dropping or node clustering. Additionally, fixed pooling ratios or numbers of pooling layers are predefined for all graphs, which prevents personalized pooling structures from being captured for each individual graph. In this work, inspired by bottom-up grammar induction, we propose an efficient graph parsing algorithm to infer the pooling structure, which then drives graph pooling. The resulting Graph Parsing Network (GPN) adaptively learns personalized pooling structure for each individual graph. GPN benefits from the discrete assignments generated by the graph parsing algorithm, allowing good memory efficiency while preserving node information intact. Experimental results on standard benchmarks demonstrate that GPN outperforms state-of-the-art graph pooling methods in graph classification tasks while being able to achieve competitive performance in node classification tasks. We also conduct a graph reconstruction task to show GPN's ability to preserve node information and measure both memory and time efficiency through relevant tests.

Deep learning time-series processing often relies on convolutional neural networks with overlapping windows. This overlap allows the network to produce an output faster than the window length. However, it introduces additional computations. This work explores the potential to optimize computational efficiency during inference by exploiting convolution's shift-invariance properties to skip the calculation of layer activations between successive overlapping windows. Although convolutions are shift-invariant, zero-padding and pooling operations, widely used in such networks, are not efficient and complicate efficient streaming inference. We introduce StreamiNNC, a strategy to deploy Convolutional Neural Networks for online streaming inference. We explore the adverse effects of zero padding and pooling on the accuracy of streaming inference, deriving theoretical error upper bounds for pooling during streaming. We address these limitations by proposing signal padding and pooling alignment and provide guidelines for designing and deploying models for StreamiNNC. We validate our method in simulated data and on three real-world biomedical signal processing applications. StreamiNNC achieves a low deviation between streaming output and normal inference for all three networks (2.03 - 3.55% NRMSE). This work demonstrates that it is possible to linearly speed up the inference of streaming CNNs processing overlapping windows, negating the additional computation typically incurred by overlapping windows.

We revisit the well-studied problem of approximating a matrix product, A^TB, based on small space sketches S(A) and S(B) of A in R^{n times d} and Bin R^{n times m}. We are interested in the setting where the sketches must be computed independently of each other, except for the use of a shared random seed. We prove that, when A and B are sparse, methods based on coordinated random sampling can outperform classical linear sketching approaches, like Johnson-Lindenstrauss Projection or CountSketch. For example, to obtain Frobenius norm error epsilon|A|_F|B|_F, coordinated sampling requires sketches of size O(s/epsilon^2) when A and B have at most s leq d,m non-zeros per row. In contrast, linear sketching leads to sketches of size O(d/epsilon^2) and O(m/epsilon^2) for A and B. We empirically evaluate our approach on two applications: 1) distributed linear regression in databases, a problem motivated by tasks like dataset discovery and augmentation, and 2) approximating attention matrices in transformer-based language models. In both cases, our sampling algorithms yield an order of magnitude improvement over linear sketching.

We consider the problem of representation learning for graph data. Convolutional neural networks can naturally operate on images, but have significant challenges in dealing with graph data. Given images are special cases of graphs with nodes lie on 2D lattices, graph embedding tasks have a natural correspondence with image pixel-wise prediction tasks such as segmentation. While encoder-decoder architectures like U-Nets have been successfully applied on many image pixel-wise prediction tasks, similar methods are lacking for graph data. This is due to the fact that pooling and up-sampling operations are not natural on graph data. To address these challenges, we propose novel graph pooling (gPool) and unpooling (gUnpool) operations in this work. The gPool layer adaptively selects some nodes to form a smaller graph based on their scalar projection values on a trainable projection vector. We further propose the gUnpool layer as the inverse operation of the gPool layer. The gUnpool layer restores the graph into its original structure using the position information of nodes selected in the corresponding gPool layer. Based on our proposed gPool and gUnpool layers, we develop an encoder-decoder model on graph, known as the graph U-Nets. Our experimental results on node classification and graph classification tasks demonstrate that our methods achieve consistently better performance than previous models.

Large Language Models (LLMs) have demonstrated remarkable capabilities across diverse domains, but their training remains resource- and time-intensive, requiring massive compute power and careful orchestration of training procedures. Model souping-the practice of averaging weights from multiple models of the same architecture-has emerged as a promising pre- and post-training technique that can enhance performance without expensive retraining. In this paper, we introduce Soup Of Category Experts (SoCE), a principled approach for model souping that utilizes benchmark composition to identify optimal model candidates and applies non-uniform weighted averaging to maximize performance. Contrary to previous uniform-averaging approaches, our method leverages the observation that benchmark categories often exhibit low inter-correlations in model performance. SoCE identifies "expert" models for each weakly-correlated category cluster and combines them using optimized weighted averaging rather than uniform weights. We demonstrate that the proposed method improves performance and robustness across multiple domains, including multilingual capabilities, tool calling, and math and achieves state-of-the-art results on the Berkeley Function Calling Leaderboard.

Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution, and sometimes pooling, operations on triangle meshes. These methods, however, either consider the input mesh as a graph, and do not exploit specific geometric properties of meshes for feature aggregation and downsampling, or are specialized for meshes, but rely on a rigid definition of convolution that does not properly capture the local topology of the mesh. We propose a method that combines the advantages of both types of approaches, while addressing their limitations: we extend a primal-dual framework drawn from the graph-neural-network literature to triangle meshes, and define convolutions on two types of graphs constructed from an input mesh. Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them using an attention mechanism. At the same time, we introduce a pooling operation with a precise geometric interpretation, that allows handling variations in the mesh connectivity by clustering mesh faces in a task-driven fashion. We provide theoretical insights of our approach using tools from the mesh-simplification literature. In addition, we validate experimentally our method in the tasks of shape classification and shape segmentation, where we obtain comparable or superior performance to the state of the art.

In ecology, psychometrics, and the analysis of social and financial networks, binary matrices are often analyzed conditional on their observed row and column sums, which restricts the problem to a finite sample space of matrices with the same margins. Two fundamental problems are to count this space and to sample uniformly from it. Sequential importance sampling (SIS) addresses both with independent weighted samples and an unbiased count estimator, but its efficiency depends critically on the proposal distribution. Existing proposals are analytically designed, and their accuracy can vary substantially with the margins. We show that the ideal SIS proposal, under which every weight equals the count and the variance vanishes, is exactly the policy of a generative flow network (GFlowNet) with unit reward on every matrix that has the given margins. We therefore propose MarginFlow, a framework that turns the design of the proposal into a learning problem and amortizes it across margins by exploiting their self-similarity. Every partial matrix is itself an instance with reduced margins, so one set transformer that reads the remaining margins serves every margin. We train MarginFlow on a pool of 1904 margins and evaluate it zero-shot on 1190 held-out margins, synthetic and real, from 3times3 to 870times6. On 1187 of the 1190 margins it matches or beats the best of 31 analytically designed configurations, chosen post hoc for each margin, and its median effective sample fraction is 99.8%. On the 56 margins where that best loses more than one nat of effective sample size, MarginFlow wins every one and raises the median effective sample fraction from 10.3% to 94.1%.

Modern image classifiers widely adopt global average pooling (GAP) followed by a linear classification head. This linearity ensures that the image-level logits equal the average of logits obtained by applying the classification head pointwise to the feature grid prior to GAP. Consequently, standard classifiers may inherently retain spatial class evidence that remains recoverable even when the image-level prediction is incorrect. This structure naturally suggests a multiple-instance learning (MIL) interpretation, where an image is viewed as a bag of spatial instances. Within this formulation, we demonstrate that standard classifiers trained with a single label per image can still learn the intended classification task in multi-object scenes. We further exploit this property to decompose image-level logits into a prediction grid, providing a post-hoc diagnostic to extract spatial class evidence that GAP otherwise obscures. Our systematic evaluation reveals that off-the-shelf models consistently recover the ground-truth class within foreground regions. The MIL interpretation further suggests that common classifier failures reflect known limitations of mean aggregation.

Conformal prediction is often calibrated with a single pooled threshold, but this can hide cross-group heterogeneity in score distributions and distort group-wise coverage. We study this phenomenon through the population score distributions underlying split conformal calibration. First, we derive a conservation law and lower bound showing that pooled calibration incurs irreducible group-wise coverage distortion at a scale set by cross-group quantile heterogeneity. Second, we demonstrate that the two leading fairness definitions for conformal prediction, Equalized Coverage and Equalized Set Size, are fundamentally in tension. Third, we quantify the cost of moving between policies which treat groups separately or pool them. Experiments on synthetic and real data confirm the same bidirectional trade-off after finite-sample calibration. Our results show that, for the policy families studied here, calibration choice does not remove cross-group heterogeneity; it determines whether the resulting distortion appears in the coverage or size dimension, providing a principled lens for analyzing fairness-oriented calibration choices in practice.

Ensuring equitable treatment (fairness) across protected attributes (such as gender or ethnicity) is a critical issue in machine learning. Most existing literature focuses on binary classification, but achieving fairness in regression tasks-such as insurance pricing or hiring score assessments-is equally important. Moreover, anti-discrimination laws also apply to continuous attributes, such as age, for which many existing methods are not applicable. In practice, multiple protected attributes can exist simultaneously; however, methods targeting fairness across several attributes often overlook so-called "fairness gerrymandering", thereby ignoring disparities among intersectional subgroups (e.g., African-American women or Hispanic men). In this paper, we propose a distance covariance regularisation framework that mitigates the association between model predictions and protected attributes, in line with the fairness definition of demographic parity, and that captures both linear and nonlinear dependencies. To enhance applicability in the presence of multiple protected attributes, we extend our framework by incorporating two multivariate dependence measures based on distance covariance: the previously proposed joint distance covariance (JdCov) and our novel concatenated distance covariance (CCdCov), which effectively address fairness gerrymandering in both regression and classification tasks involving protected attributes of various types. We discuss and illustrate how to calibrate regularisation strength, including a method based on Jensen-Shannon divergence, which quantifies dissimilarities in prediction distributions across groups. We apply our framework to the COMPAS recidivism dataset and a large motor insurance claims dataset.

Benchmarks of machine learning models often include many datasets, making evaluation expensive. For efficiency, it is preferable to perform evaluations on small, representative datasets instead. The selection of such subsets typically relies on heuristics and is rarely analyzed for the robustness of the resulting model rankings. We introduce a framework to perform the task of selecting datasets subsets with an evaluation of how different selection strategies preserve the global model rankings. Our framework includes bootstrap aggregation, which provides valid confidence intervals, allowing a principled comparison of selection strategies. We consider clustering, design criteria (A/D-optimality), random baselines, and greedy farthest-first (FAFI). For the latter, we derive upper bounds on selection quality in terms of ranking errors as a function of the number of selected datasets. Empirically, in time series classification (TSC, 112 datasets) and in a supplementary natural language processing benchmark derived from MTEB (57 tasks), several selection strategies improve rank preservation compared with random subsets, including simple FAFI. In contrast, in recommender systems (30 datasets), the improvement of strategies over random selection is small and typically statistically insignificant. For TSC, our best-performing strategy achieves a Spearman correlation of 0.95 with the full benchmark model rankings using only five selected datasets. Additional experiments indicate that the effectiveness of selection approaches depends on both the quality of dataset representations and the scale of the benchmarking regime.

Various visual foundation models have distinct strengths and weaknesses, both of which can be improved through heterogeneous multi-teacher knowledge distillation without labels, termed "agglomerative models." We build upon this body of work by studying the effect of the teachers' activation statistics, particularly the impact of the loss function on the resulting student model quality. We explore a standard toolkit of statistical normalization techniques to better align the different distributions and assess their effects. Further, we examine the impact on downstream teacher-matching metrics, which motivates the use of Hadamard matrices. With these matrices, we demonstrate useful properties, showing how they can be used for isotropic standardization, where each dimension of a multivariate distribution is standardized using the same scale. We call this technique "PHI Standardization" (PHI-S) and empirically demonstrate that it produces the best student model across the suite of methods studied.

One-shot coreset selection aims to select a representative subset of the training data, given a pruning rate, that can later be used to train future models while retaining high accuracy. State-of-the-art coreset selection methods pick the highest importance examples based on an importance metric and are found to perform well at low pruning rates. However, at high pruning rates, they suffer from a catastrophic accuracy drop, performing worse than even random sampling. This paper explores the reasons behind this accuracy drop both theoretically and empirically. We first propose a novel metric to measure the coverage of a dataset on a specific distribution by extending the classical geometric set cover problem to a distribution cover problem. This metric helps explain why coresets selected by SOTA methods at high pruning rates perform poorly compared to random sampling because of worse data coverage. We then propose a novel one-shot coreset selection method, Coverage-centric Coreset Selection (CCS), that jointly considers overall data coverage upon a distribution as well as the importance of each example. We evaluate CCS on five datasets and show that, at high pruning rates (e.g., 90%), it achieves significantly better accuracy than previous SOTA methods (e.g., at least 19.56% higher on CIFAR10) as well as random selection (e.g., 7.04% higher on CIFAR10) and comparable accuracy at low pruning rates. We make our code publicly available at https://github.com/haizhongzheng/Coverage-centric-coreset-selection.

Federated Learning (FL) is a machine learning technique that often suffers from training instability due to the diverse nature of client data. Although utility-based client selection methods like Oort are used to converge by prioritizing high-loss clients, they frequently experience significant drops in accuracy during later stages of training. We propose a theoretical HeteRo-Select framework designed to maintain high performance and ensure long-term training stability. We provide a theoretical analysis showing that when client data is very different (high heterogeneity), choosing a smart subset of client participation can reduce communication more effectively compared to full participation. Our HeteRo-Select method uses a clear, step-by-step scoring system that considers client usefulness, fairness, update speed, and data variety. It also shows convergence guarantees under strong regularization. Our experimental results on the CIFAR-10 dataset under significant label skew (α=0.1) support the theoretical findings. The HeteRo-Select method performs better than existing approaches in terms of peak accuracy, final accuracy, and training stability. Specifically, HeteRo-Select achieves a peak accuracy of 74.75%, a final accuracy of 72.76%, and a minimal stability drop of 1.99%. In contrast, Oort records a lower peak accuracy of 73.98%, a final accuracy of 71.25%, and a larger stability drop of 2.73%. The theoretical foundations and empirical performance in our study make HeteRo-Select a reliable solution for real-world heterogeneous FL problems.

Transformers achieve unrivalled performance in modelling language, but remain inefficient in terms of memory and time complexity. A possible remedy is to reduce the sequence length in the intermediate layers by pooling fixed-length segments of tokens. Nevertheless, natural units of meaning, such as words or phrases, display varying sizes. To address this mismatch, we equip language models with a dynamic-pooling mechanism, which predicts segment boundaries in an autoregressive fashion. We compare several methods to infer boundaries, including end-to-end learning through stochastic re-parameterisation, supervised learning (based on segmentations from subword tokenizers or spikes in conditional entropy), as well as linguistically motivated boundaries. We perform character-level evaluation on texts from multiple datasets and morphologically diverse languages. The results demonstrate that dynamic pooling, which jointly segments and models language, is both faster and more accurate than vanilla Transformers and fixed-length pooling within the same computational budget.

Over the last few years, multi-vector retrieval methods, spearheaded by ColBERT, have become an increasingly popular approach to Neural IR. By storing representations at the token level rather than at the document level, these methods have demonstrated very strong retrieval performance, especially in out-of-domain settings. However, the storage and memory requirements necessary to store the large number of associated vectors remain an important drawback, hindering practical adoption. In this paper, we introduce a simple clustering-based token pooling approach to aggressively reduce the number of vectors that need to be stored. This method can reduce the space & memory footprint of ColBERT indexes by 50% with virtually no retrieval performance degradation. This method also allows for further reductions, reducing the vector count by 66%-to-75% , with degradation remaining below 5% on a vast majority of datasets. Importantly, this approach requires no architectural change nor query-time processing, and can be used as a simple drop-in during indexation with any ColBERT-like model.

The rapid scaling of large language models necessitates more lightweight finetuning methods to reduce the explosive GPU memory overhead when numerous customized models are served simultaneously. Targeting more parameter-efficient low-rank adaptation (LoRA), parameter sharing presents a promising solution. Empirically, our research into high-level sharing principles highlights the indispensable role of differentiation in reversing the detrimental effects of pure sharing. Guided by this finding, we propose Mixture of Shards (MoS), incorporating both inter-layer and intra-layer sharing schemes, and integrating four nearly cost-free differentiation strategies, namely subset selection, pair dissociation, vector sharding, and shard privatization. Briefly, it selects a designated number of shards from global pools with a Mixture-of-Experts (MoE)-like routing mechanism before sequentially concatenating them to low-rank matrices. Hence, it retains all the advantages of LoRA while offering enhanced parameter efficiency, and effectively circumvents the drawbacks of peer parameter-sharing methods. Our empirical experiments demonstrate approximately 8x parameter savings in a standard LoRA setting. The ablation study confirms the significance of each component. Our insights into parameter sharing and MoS method may illuminate future developments of more parameter-efficient finetuning methods.

Convolutional Neural Networks (CNNs) use pooling to decrease the size of activation maps. This process is crucial to increase the receptive fields and to reduce computational requirements of subsequent convolutions. An important feature of the pooling operation is the minimization of information loss, with respect to the initial activation maps, without a significant impact on the computation and memory overhead. To meet these requirements, we propose SoftPool: a fast and efficient method for exponentially weighted activation downsampling. Through experiments across a range of architectures and pooling methods, we demonstrate that SoftPool can retain more information in the reduced activation maps. This refined downsampling leads to improvements in a CNN's classification accuracy. Experiments with pooling layer substitutions on ImageNet1K show an increase in accuracy over both original architectures and other pooling methods. We also test SoftPool on video datasets for action recognition. Again, through the direct replacement of pooling layers, we observe consistent performance improvements while computational loads and memory requirements remain limited.

As machine learning tasks continue to evolve, the trend has been to gather larger datasets and train increasingly larger models. While this has led to advancements in accuracy, it has also escalated computational costs to unsustainable levels. Addressing this, our work aims to strike a delicate balance between computational efficiency and model accuracy, a persisting challenge in the field. We introduce a novel method that employs core subset selection for reweighting, effectively optimizing both computational time and model performance. By focusing on a strategically selected coreset, our approach offers a robust representation, as it efficiently minimizes the influence of outliers. The re-calibrated weights are then mapped back to and propagated across the entire dataset. Our experimental results substantiate the effectiveness of this approach, underscoring its potential as a scalable and precise solution for model training.

Clustering is an unsupervised learning problem that aims to partition unlabelled data points into groups with similar features. Traditional clustering algorithms provide limited insight into the groups they find as their main focus is accuracy and not the interpretability of the group assignments. This has spurred a recent line of work on explainable machine learning for clustering. In this paper we focus on the cluster description problem where, given a dataset and its partition into clusters, the task is to explain the clusters. We introduce a new approach to explain clusters by constructing polyhedra around each cluster while minimizing either the complexity of the resulting polyhedra or the number of features used in the description. We formulate the cluster description problem as an integer program and present a column generation approach to search over an exponential number of candidate half-spaces that can be used to build the polyhedra. To deal with large datasets, we introduce a novel grouping scheme that first forms smaller groups of data points and then builds the polyhedra around the grouped data, a strategy which out-performs simply sub-sampling data. Compared to state of the art cluster description algorithms, our approach is able to achieve competitive interpretability with improved description accuracy.

Tabular data, structured as rows and columns, is among the most prevalent data types in machine learning classification and regression applications. Models for learning from tabular data have continuously evolved, with Deep Neural Networks (DNNs) recently demonstrating promising results through their capability of representation learning. In this survey, we systematically introduce the field of tabular representation learning, covering the background, challenges, and benchmarks, along with the pros and cons of using DNNs. We organize existing methods into three main categories according to their generalization capabilities: specialized, transferable, and general models. Specialized models focus on tasks where training and evaluation occur within the same data distribution. We introduce a hierarchical taxonomy for specialized models based on the key aspects of tabular data -- features, samples, and objectives -- and delve into detailed strategies for obtaining high-quality feature- and sample-level representations. Transferable models are pre-trained on one or more datasets and subsequently fine-tuned on downstream tasks, leveraging knowledge acquired from homogeneous or heterogeneous sources, or even cross-modalities such as vision and language. General models, also known as tabular foundation models, extend this concept further, allowing direct application to downstream tasks without fine-tuning. We group these general models based on the strategies used to adapt across heterogeneous datasets. Additionally, we explore ensemble methods, which integrate the strengths of multiple tabular models. Finally, we discuss representative extensions of tabular learning, including open-environment tabular machine learning, multimodal learning with tabular data, and tabular understanding. More information can be found in the following repository: https://github.com/LAMDA-Tabular/Tabular-Survey.

Data organized in tabular format is ubiquitous in real-world applications, and users often craft tables with biased feature definitions and flexibly set prediction targets of their interests. Thus, a rapid development of a robust, effective, dataset-versatile, user-friendly tabular prediction approach is highly desired. While Gradient Boosting Decision Trees (GBDTs) and existing deep neural networks (DNNs) have been extensively utilized by professional users, they present several challenges for casual users, particularly: (i) the dilemma of model selection due to their different dataset preferences, and (ii) the need for heavy hyperparameter searching, failing which their performances are deemed inadequate. In this paper, we delve into this question: Can we develop a deep learning model that serves as a "sure bet" solution for a wide range of tabular prediction tasks, while also being user-friendly for casual users? We delve into three key drawbacks of deep tabular models, encompassing: (P1) lack of rotational variance property, (P2) large data demand, and (P3) over-smooth solution. We propose ExcelFormer, addressing these challenges through a semi-permeable attention module that effectively constrains the influence of less informative features to break the DNNs' rotational invariance property (for P1), data augmentation approaches tailored for tabular data (for P2), and attentive feedforward network to boost the model fitting capability (for P3). These designs collectively make ExcelFormer a "sure bet" solution for diverse tabular datasets. Extensive and stratified experiments conducted on real-world datasets demonstrate that our model outperforms previous approaches across diverse tabular data prediction tasks, and this framework can be friendly to casual users, offering ease of use without the heavy hyperparameter tuning.

In neural Information Retrieval (IR), ongoing research is directed towards improving the first retriever in ranking pipelines. Learning dense embeddings to conduct retrieval using efficient approximate nearest neighbors methods has proven to work well. Meanwhile, there has been a growing interest in learning sparse representations for documents and queries, that could inherit from the desirable properties of bag-of-words models such as the exact matching of terms and the efficiency of inverted indexes. Introduced recently, the SPLADE model provides highly sparse representations and competitive results with respect to state-of-the-art dense and sparse approaches. In this paper, we build on SPLADE and propose several significant improvements in terms of effectiveness and/or efficiency. More specifically, we modify the pooling mechanism, benchmark a model solely based on document expansion, and introduce models trained with distillation. We also report results on the BEIR benchmark. Overall, SPLADE is considerably improved with more than 9\% gains on NDCG@10 on TREC DL 2019, leading to state-of-the-art results on the BEIR benchmark.

The word embedding space in neural models is skewed, and correcting this can improve task performance. We point out that most approaches for modeling, correcting, and measuring the symmetry of an embedding space implicitly assume that the word frequencies are uniform; in reality, word frequencies follow a highly non-uniform distribution, known as Zipf's law. Surprisingly, simply performing PCA whitening weighted by the empirical word frequency that follows Zipf's law significantly improves task performance, surpassing established baselines. From a theoretical perspective, both our approach and existing methods can be clearly categorized: word representations are distributed according to an exponential family with either uniform or Zipfian base measures. By adopting the latter approach, we can naturally emphasize informative low-frequency words in terms of their vector norm, which becomes evident from the information-geometric perspective, and in terms of the loss functions for imbalanced classification. Additionally, our theory corroborates that popular natural language processing methods, such as skip-gram negative sampling, WhiteningBERT, and headless language models, work well just because their word embeddings encode the empirical word frequency into the underlying probabilistic model.

Online active learning is a paradigm in machine learning that aims to select the most informative data points to label from a data stream. The problem of minimizing the cost associated with collecting labeled observations has gained a lot of attention in recent years, particularly in real-world applications where data is only available in an unlabeled form. Annotating each observation can be time-consuming and costly, making it difficult to obtain large amounts of labeled data. To overcome this issue, many active learning strategies have been proposed in the last decades, aiming to select the most informative observations for labeling in order to improve the performance of machine learning models. These approaches can be broadly divided into two categories: static pool-based and stream-based active learning. Pool-based active learning involves selecting a subset of observations from a closed pool of unlabeled data, and it has been the focus of many surveys and literature reviews. However, the growing availability of data streams has led to an increase in the number of approaches that focus on online active learning, which involves continuously selecting and labeling observations as they arrive in a stream. This work aims to provide an overview of the most recently proposed approaches for selecting the most informative observations from data streams in real time. We review the various techniques that have been proposed and discuss their strengths and limitations, as well as the challenges and opportunities that exist in this area of research.

The Platonic Representation Hypothesis suggests that independently trained neural networks converge to increasingly similar latent spaces. However, current strategies for mapping these representations are inherently pairwise, scaling quadratically with the number of models and failing to yield a consistent global reference. In this paper, we study the alignment of M ge 3 models. We first adapt Generalized Procrustes Analysis (GPA) to construct a shared orthogonal universe that preserves the internal geometry essential for tasks like model stitching. We then show that strict isometric alignment is suboptimal for retrieval, where agreement-maximizing methods like Canonical Correlation Analysis (CCA) typically prevail. To bridge this gap, we finally propose Geometry-Corrected Procrustes Alignment (GCPA), which establishes a robust GPA-based universe followed by a post-hoc correction for directional mismatch. Extensive experiments demonstrate that GCPA consistently improves any-to-any retrieval while retaining a practical shared reference space.

Real-world data often exhibits long tail distributions with heavy class imbalance, where the majority classes can dominate the training process and alter the decision boundaries of the minority classes. Recently, researchers have investigated the potential of supervised contrastive learning for long-tailed recognition, and demonstrated that it provides a strong performance gain. In this paper, we show that while supervised contrastive learning can help improve performance, past baselines suffer from poor uniformity brought in by imbalanced data distribution. This poor uniformity manifests in samples from the minority class having poor separability in the feature space. To address this problem, we propose targeted supervised contrastive learning (TSC), which improves the uniformity of the feature distribution on the hypersphere. TSC first generates a set of targets uniformly distributed on a hypersphere. It then makes the features of different classes converge to these distinct and uniformly distributed targets during training. This forces all classes, including minority classes, to maintain a uniform distribution in the feature space, improves class boundaries, and provides better generalization even in the presence of long-tail data. Experiments on multiple datasets show that TSC achieves state-of-the-art performance on long-tailed recognition tasks.

Partially class-disjoint data (PCDD), a common yet under-explored data formation where each client contributes a part of classes (instead of all classes) of samples, severely challenges the performance of federated algorithms. Without full classes, the local objective will contradict the global objective, yielding the angle collapse problem for locally missing classes and the space waste problem for locally existing classes. As far as we know, none of the existing methods can intrinsically mitigate PCDD challenges to achieve holistic improvement in the bilateral views (both global view and local view) of federated learning. To address this dilemma, we are inspired by the strong generalization of simplex Equiangular Tight Frame~(ETF) on the imbalanced data, and propose a novel approach called FedGELA where the classifier is globally fixed as a simplex ETF while locally adapted to the personal distributions. Globally, FedGELA provides fair and equal discrimination for all classes and avoids inaccurate updates of the classifier, while locally it utilizes the space of locally missing classes for locally existing classes. We conduct extensive experiments on a range of datasets to demonstrate that our FedGELA achieves promising performance~(averaged improvement of 3.9% to FedAvg and 1.5% to best baselines) and provide both local and global convergence guarantees. Source code is available at:https://github.com/MediaBrain-SJTU/FedGELA.git.

While Deep Learning excels in structured data as encountered in vision and natural language processing, it failed to meet its expectations on tabular data. For tabular data, Support Vector Machines (SVMs), Random Forests, and Gradient Boosting are the best performing techniques with Gradient Boosting in the lead. Recently, we saw a surge of Deep Learning methods that were tailored to tabular data but still underperform compared to Gradient Boosting on small-sized datasets. We suggest "Hopular", a novel Deep Learning architecture for medium- and small-sized datasets, where each layer is equipped with continuous modern Hopfield networks. The modern Hopfield networks use stored data to identify feature-feature, feature-target, and sample-sample dependencies. Hopular's novelty is that every layer can directly access the original input as well as the whole training set via stored data in the Hopfield networks. Therefore, Hopular can step-wise update its current model and the resulting prediction at every layer like standard iterative learning algorithms. In experiments on small-sized tabular datasets with less than 1,000 samples, Hopular surpasses Gradient Boosting, Random Forests, SVMs, and in particular several Deep Learning methods. In experiments on medium-sized tabular data with about 10,000 samples, Hopular outperforms XGBoost, CatBoost, LightGBM and a state-of-the art Deep Learning method designed for tabular data. Thus, Hopular is a strong alternative to these methods on tabular data.

Transformers have shown great potential in computer vision tasks. A common belief is their attention-based token mixer module contributes most to their competence. However, recent works show the attention-based module in Transformers can be replaced by spatial MLPs and the resulted models still perform quite well. Based on this observation, we hypothesize that the general architecture of the Transformers, instead of the specific token mixer module, is more essential to the model's performance. To verify this, we deliberately replace the attention module in Transformers with an embarrassingly simple spatial pooling operator to conduct only basic token mixing. Surprisingly, we observe that the derived model, termed as PoolFormer, achieves competitive performance on multiple computer vision tasks. For example, on ImageNet-1K, PoolFormer achieves 82.1% top-1 accuracy, surpassing well-tuned Vision Transformer/MLP-like baselines DeiT-B/ResMLP-B24 by 0.3%/1.1% accuracy with 35%/52% fewer parameters and 50%/62% fewer MACs. The effectiveness of PoolFormer verifies our hypothesis and urges us to initiate the concept of "MetaFormer", a general architecture abstracted from Transformers without specifying the token mixer. Based on the extensive experiments, we argue that MetaFormer is the key player in achieving superior results for recent Transformer and MLP-like models on vision tasks. This work calls for more future research dedicated to improving MetaFormer instead of focusing on the token mixer modules. Additionally, our proposed PoolFormer could serve as a starting baseline for future MetaFormer architecture design. Code is available at https://github.com/sail-sg/poolformer.

Kolmogorov-Arnold Networks (KANs) place learnable B-spline activations on network edges rather than fixed activations on nodes. The standard Cox-de Boor recursion evaluates these activations through k sequential passes for degree-k splines, consuming over 90% of forward-pass time. InKAN replaces this recursion with the truncated power form, a classical result from approximation theory that expresses each uniform cubic B-spline as five (x)_+^3 terms at shifted knot positions. The resulting expression computes exact B-spline basis values: the same mathematical function as the Cox-de Boor recursion, evaluated without sequential passes. This paper documents three contributions: (1) an implementation structured for torch . compile fusion, eliminating recursion, span lookup, and scatter-gather operations; (2) a bounded-coordinate evaluation that clamps the normalized input to [0, k{+}1], preventing the growth of cancellation error at large off-support coordinates; and (3) an open-source package (pip install inkan). In the tested configurations, InKAN has 2.8--3.5times lower forward-pass latency than the Cox-de Boor recursion. Partition-of-unity errors remain below 10^{-5} for grid sizes up to 200.

3D Gaussian Splatting (3DGS) has become the de facto method of 3D representation in many vision tasks. This calls for the 3D understanding directly in this representation space. To facilitate the research in this direction, we first build a large-scale dataset of 3DGS using the commonly used ShapeNet and ModelNet datasets. Our dataset ShapeSplat consists of 65K objects from 87 unique categories, whose labels are in accordance with the respective datasets. The creation of this dataset utilized the compute equivalent of 2 GPU years on a TITAN XP GPU. We utilize our dataset for unsupervised pretraining and supervised finetuning for classification and segmentation tasks. To this end, we introduce \textit{Gaussian-MAE}, which highlights the unique benefits of representation learning from Gaussian parameters. Through exhaustive experiments, we provide several valuable insights. In particular, we show that (1) the distribution of the optimized GS centroids significantly differs from the uniformly sampled point cloud (used for initialization) counterpart; (2) this change in distribution results in degradation in classification but improvement in segmentation tasks when using only the centroids; (3) to leverage additional Gaussian parameters, we propose Gaussian feature grouping in a normalized feature space, along with splats pooling layer, offering a tailored solution to effectively group and embed similar Gaussians, which leads to notable improvement in finetuning tasks.

This paper presents algorithms for hierarchical, agglomerative clustering which perform most efficiently in the general-purpose setup that is given in modern standard software. Requirements are: (1) the input data is given by pairwise dissimilarities between data points, but extensions to vector data are also discussed (2) the output is a "stepwise dendrogram", a data structure which is shared by all implementations in current standard software. We present algorithms (old and new) which perform clustering in this setting efficiently, both in an asymptotic worst-case analysis and from a practical point of view. The main contributions of this paper are: (1) We present a new algorithm which is suitable for any distance update scheme and performs significantly better than the existing algorithms. (2) We prove the correctness of two algorithms by Rohlf and Murtagh, which is necessary in each case for different reasons. (3) We give well-founded recommendations for the best current algorithms for the various agglomerative clustering schemes.

We study the complexity of sampling from a distribution over all index subsets of the set {1,...,n} with the probability of a subset S proportional to the determinant of the submatrix L_S of some ntimes n p.s.d. matrix L, where L_S corresponds to the entries of L indexed by S. Known as a determinantal point process, this distribution is used in machine learning to induce diversity in subset selection. In practice, we often wish to sample multiple subsets S with small expected size k = E[|S|] ll n from a very large matrix L, so it is important to minimize the preprocessing cost of the procedure (performed once) as well as the sampling cost (performed repeatedly). For this purpose, we propose a new algorithm which, given access to L, samples exactly from a determinantal point process while satisfying the following two properties: (1) its preprocessing cost is n cdot poly(k), i.e., sublinear in the size of L, and (2) its sampling cost is poly(k), i.e., independent of the size of L. Prior to our results, state-of-the-art exact samplers required O(n^3) preprocessing time and sampling time linear in n or dependent on the spectral properties of L. We also give a reduction which allows using our algorithm for exact sampling from cardinality constrained determinantal point processes with ncdotpoly(k) time preprocessing.

We present a faster algorithm to generate a warm start for sampling an arbitrary logconcave density specified by an evaluation oracle, leading to the first sub-cubic sampling algorithms for inputs in (near-)isotropic position. A long line of prior work incurred a warm-start penalty of at least linear in the dimension, hitting a cubic barrier, even for the special case of uniform sampling from convex bodies. Our improvement relies on two key ingredients of independent interest. (1) We show how to sample given a warm start in weaker notions of distance, in particular q-R\'enyi divergence for q=mathcal{O}(1), whereas previous analyses required stringent infty-R\'enyi divergence (with the exception of Hit-and-Run, whose known mixing time is higher). This marks the first improvement in the required warmness since Lov\'asz and Simonovits (1991). (2) We refine and generalize the log-Sobolev inequality of Lee and Vempala (2018), originally established for isotropic logconcave distributions in terms of the diameter of the support, to logconcave distributions in terms of a geometric average of the support diameter and the largest eigenvalue of the covariance matrix.

Reordering multiple-choice options can change a model's answer, an effect studied as selection bias (a preference for certain option letters) and as order sensitivity (changes in answers across option orderings). We connect these perspectives through the pooled selection-rate standard deviation (pooled SD), which measures how unevenly option letters are selected across questions and orderings. When every option of each question appears equally often at each position, the pooled SD is exactly the product of two label-free factors: the flip rate and the positional skew. The flip rate is the fraction of questions whose chosen option changes across orderings; the positional skew is the standard deviation of option-letter selection rates among those questions. Across 41 checkpoints and 12 benchmarks, the flip rate tracks accuracy and output uncertainty, while the positional skew tracks the estimated option-symbol prior. Prior correction for selection bias mainly reduces the positional skew. Aggregating each ordering with its reversal, a mitigation for order sensitivity, mainly reduces the flip rate. Both reduce the range of accuracy across correct-answer letters by similar amounts, but aggregation leaves fewer model-rank reversals. Applying prior correction before aggregation reduces both factors and further narrows this accuracy range. However, aggregation lowers the flip rate partly by settling questions on the same wrong option. We therefore recommend reporting both factors to distinguish mitigation effects, alongside accuracy to distinguish stability from correctness.

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

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN, a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness of our task-driven pooling on various learning tasks applied to 3D meshes.

Despite the recent success in many applications, the high computational requirements of vision transformers limit their use in resource-constrained settings. While many existing methods improve the quadratic complexity of attention, in most vision transformers, self-attention is not the major computation bottleneck, e.g., more than 80% of the computation is spent on fully-connected layers. To improve the computational complexity of all layers, we propose a novel token downsampling method, called Token Pooling, efficiently exploiting redundancies in the images and intermediate token representations. We show that, under mild assumptions, softmax-attention acts as a high-dimensional low-pass (smoothing) filter. Thus, its output contains redundancy that can be pruned to achieve a better trade-off between the computational cost and accuracy. Our new technique accurately approximates a set of tokens by minimizing the reconstruction error caused by downsampling. We solve this optimization problem via cost-efficient clustering. We rigorously analyze and compare to prior downsampling methods. Our experiments show that Token Pooling significantly improves the cost-accuracy trade-off over the state-of-the-art downsampling. Token Pooling is a simple and effective operator that can benefit many architectures. Applied to DeiT, it achieves the same ImageNet top-1 accuracy using 42% fewer computations.

This paper considers a novel application of deep AUC maximization (DAM) for multi-instance learning (MIL), in which a single class label is assigned to a bag of instances (e.g., multiple 2D slices of a CT scan for a patient). We address a neglected yet non-negligible computational challenge of MIL in the context of DAM, i.e., bag size is too large to be loaded into {GPU} memory for backpropagation, which is required by the standard pooling methods of MIL. To tackle this challenge, we propose variance-reduced stochastic pooling methods in the spirit of stochastic optimization by formulating the loss function over the pooled prediction as a multi-level compositional function. By synthesizing techniques from stochastic compositional optimization and non-convex min-max optimization, we propose a unified and provable muli-instance DAM (MIDAM) algorithm with stochastic smoothed-max pooling or stochastic attention-based pooling, which only samples a few instances for each bag to compute a stochastic gradient estimator and to update the model parameter. We establish a similar convergence rate of the proposed MIDAM algorithm as the state-of-the-art DAM algorithms. Our extensive experiments on conventional MIL datasets and medical datasets demonstrate the superiority of our MIDAM algorithm.

Speculative decoding accelerates language-model inference by drafting future tokens the target model verifies in parallel. A diffusion-style drafter such as DFlash drafts an entire block in one forward pass. It is trained on the per-position marginals rather than on the joint distribution over the block, so the tokens it emits are individually plausible yet jointly incoherent. We introduce LiLiCorr, a Lightweight Likelihood-based model that Correlates the per-position marginals such a drafter produces. It keeps the top-K tokens at each position and processes them jointly, emitting an in and an out vector for each. Two candidates at consecutive positions match when the earlier out vector aligns, in cosine similarity, with the later in vector. Training scores the correct pairings highest and pushes competing ones down, so coherent blocks outscore incoherent ones. The joint distribution over the block, exponential in its length, is never materialized. One lightweight network pass produces all the vectors, the pairwise scores follow as batched matrix operations, leaving only a cheap greedy walk sequential. We co-train the DFlash drafter with LiLiCorr, so it proposes candidates that correlate into longer accepted sequences. Over the vanilla DFlash drafter it builds on, LiLiCorr accepts more and serves faster at all 72 settings we test: nine benchmarks at two target sizes under greedy and temperature-one decoding, plus a throughput sweep over six concurrencies, two input lengths and three output-entropy tiers. It raises acceptance length by 7 to 19%, while its single-pass scoring head costs only about 3% of the per-block latency. Against three concurrently developed methods that also restore coherence at draft time, all equally optimized on a common stack, LiLiCorr holds the highest throughput in 63 of those settings, ties within a measured noise floor in 6, and trails in only 3.

We study the problem of detecting the correlation between two Gaussian databases XinR^{ntimes d} and Y^{ntimes d}, each composed of n users with d features. This problem is relevant in the analysis of social media, computational biology, etc. We formulate this as a hypothesis testing problem: under the null hypothesis, these two databases are statistically independent. Under the alternative, however, there exists an unknown permutation sigma over the set of n users (or, row permutation), such that X is rho-correlated with Y^sigma, a permuted version of Y. We determine sharp thresholds at which optimal testing exhibits a phase transition, depending on the asymptotic regime of n and d. Specifically, we prove that if rho^2dto0, as dtoinfty, then weak detection (performing slightly better than random guessing) is statistically impossible, irrespectively of the value of n. This compliments the performance of a simple test that thresholds the sum all entries of X^TY. Furthermore, when d is fixed, we prove that strong detection (vanishing error probability) is impossible for any rho<rho^star, where rho^star is an explicit function of d, while weak detection is again impossible as long as rho^2dto0. These results close significant gaps in current recent related studies.

A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the fundamental question of ``what are the most effective algorithms for OOD generalization'' remains open even under the standard setting of covariate shift. This paper addresses this fundamental question by proving that, surprisingly, classical Maximum Likelihood Estimation (MLE) purely using source data (without any modification) achieves the minimax optimality for covariate shift under the well-specified setting. That is, no algorithm performs better than MLE in this setting (up to a constant factor), justifying MLE is all you need. Our result holds for a very rich class of parametric models, and does not require any boundedness condition on the density ratio. We illustrate the wide applicability of our framework by instantiating it to three concrete examples -- linear regression, logistic regression, and phase retrieval. This paper further complement the study by proving that, under the misspecified setting, MLE is no longer the optimal choice, whereas Maximum Weighted Likelihood Estimator (MWLE) emerges as minimax optimal in certain scenarios.

A common architectural choice for deep metric learning is a convolutional neural network followed by global average pooling (GAP). Albeit simple, GAP is a highly effective way to aggregate information. One possible explanation for the effectiveness of GAP is considering each feature vector as representing a different semantic entity and GAP as a convex combination of them. Following this perspective, we generalize GAP and propose a learnable generalized sum pooling method (GSP). GSP improves GAP with two distinct abilities: i) the ability to choose a subset of semantic entities, effectively learning to ignore nuisance information, and ii) learning the weights corresponding to the importance of each entity. Formally, we propose an entropy-smoothed optimal transport problem and show that it is a strict generalization of GAP, i.e., a specific realization of the problem gives back GAP. We show that this optimization problem enjoys analytical gradients enabling us to use it as a direct learnable replacement for GAP. We further propose a zero-shot loss to ease the learning of GSP. We show the effectiveness of our method with extensive evaluations on 4 popular metric learning benchmarks. Code is available at: GSP-DML Framework

Using the weights of trained Neural Network (NN) models as data modality has recently gained traction as a research field - dubbed Weight Space Learning (WSL). Multiple recent works propose WSL methods to analyze models, evaluate methods, or synthesize weights. Weight space learning methods require populations of trained models as datasets for development and evaluation. However, existing collections of models - called `model zoos' - are unstructured or follow a rudimentary definition of diversity. In parallel, work rooted in statistical physics has identified phases and phase transitions in NN models. Models are homogeneous within the same phase but qualitatively differ from one phase to another. We combine the idea of `model zoos' with phase information to create a controlled notion of diversity in populations. We introduce 12 large-scale zoos that systematically cover known phases and vary over model architecture, size, and datasets. These datasets cover different modalities, such as computer vision, natural language processing, and scientific ML. For every model, we compute loss landscape metrics and validate full coverage of the phases. With this dataset, we provide the community with a resource with a wide range of potential applications for WSL and beyond. Evidence suggests the loss landscape phase plays a role in applications such as model training, analysis, or sparsification. We demonstrate this in an exploratory study of the downstream methods like transfer learning or model weights averaging.

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.

Pool-based active learning (AL) aims to optimize the annotation process (i.e., labeling) as the acquisition of annotations is often time-consuming and therefore expensive. For this purpose, an AL strategy queries annotations intelligently from annotators to train a high-performance classification model at a low annotation cost. Traditional AL strategies operate in an idealized framework. They assume a single, omniscient annotator who never gets tired and charges uniformly regardless of query difficulty. However, in real-world applications, we often face human annotators, e.g., crowd or in-house workers, who make annotation mistakes and can be reluctant to respond if tired or faced with complex queries. Recently, a wide range of novel AL strategies has been proposed to address these issues. They differ in at least one of the following three central aspects from traditional AL: (1) They explicitly consider (multiple) human annotators whose performances can be affected by various factors, such as missing expertise. (2) They generalize the interaction with human annotators by considering different query and annotation types, such as asking an annotator for feedback on an inferred classification rule. (3) They take more complex cost schemes regarding annotations and misclassifications into account. This survey provides an overview of these AL strategies and refers to them as real-world AL. Therefore, we introduce a general real-world AL strategy as part of a learning cycle and use its elements, e.g., the query and annotator selection algorithm, to categorize about 60 real-world AL strategies. Finally, we outline possible directions for future research in the field of AL.

Conformal prediction (CP) for regression can be challenging, especially when the output distribution is heteroscedastic, multimodal, or skewed. Some of the issues can be addressed by estimating a distribution over the output, but in reality, such approaches can be sensitive to estimation error and yield unstable intervals.~Here, we circumvent the challenges by converting regression to a classification problem and then use CP for classification to obtain CP sets for regression.~To preserve the ordering of the continuous-output space, we design a new loss function and make necessary modifications to the CP classification techniques.~Empirical results on many benchmarks shows that this simple approach gives surprisingly good results on many practical problems.

Language models pretrained on large collections of tabular data have demonstrated their effectiveness in several downstream tasks. However, many of these models do not take into account the row/column permutation invariances, hierarchical structure, etc. that exist in tabular data. To alleviate these limitations, we propose HYTREL, a tabular language model, that captures the permutation invariances and three more structural properties of tabular data by using hypergraphs - where the table cells make up the nodes and the cells occurring jointly together in each row, column, and the entire table are used to form three different types of hyperedges. We show that HYTREL is maximally invariant under certain conditions for tabular data, i.e., two tables obtain the same representations via HYTREL iff the two tables are identical up to permutations. Our empirical results demonstrate that HYTREL consistently outperforms other competitive baselines on four downstream tasks with minimal pretraining, illustrating the advantages of incorporating the inductive biases associated with tabular data into the representations. Finally, our qualitative analyses showcase that HYTREL can assimilate the table structures to generate robust representations for the cells, rows, columns, and the entire table.

Understanding how structured internal structure emerges during neural network training is central to the study of deep learning. We investigate this phenomenon through the group composition task, where a two-layer neural network is trained to predict g_1 star g_2 for elements of a finite group G. By lifting the projected gradient flow to the Fourier domain, we demonstrate that the training dynamics are governed by a Riemannian gradient ascent on a representation-theoretic energy functional. We prove that, under random initialization, this flow drives each neuron to converge almost surely toward a single irreducible representation, while the cross-layer Fourier coefficients achieve a rotational rank-one alignment. This framework provides a representation-theoretic account of feature learning and characterizes a novel low-rank compression phenomenon for matrix-valued group representations. Moreover, for Abelian groups, we provide a complete population-level description: random initialization promotes uniform diversification across nontrivial representations and induces Haar-uniform phases, jointly approximating the indicator via a majority-vote mechanism. We further prove that both phase alignment and representation competition emerge with exponential convergence rates.

In representation learning, uniformity refers to the uniform feature distribution in the latent space (i.e., unit hypersphere). Previous work has shown that improving uniformity contributes to the learning of under-represented classes. However, most of the previous work focused on classification; the representation space of imbalanced regression remains unexplored. Classification-based methods are not suitable for regression tasks because they cluster features into distinct groups without considering the continuous and ordered nature essential for regression. In a geometric aspect, we uniquely focus on ensuring uniformity in the latent space for imbalanced regression through two key losses: enveloping and homogeneity. The enveloping loss encourages the induced trace to uniformly occupy the surface of a hypersphere, while the homogeneity loss ensures smoothness, with representations evenly spaced at consistent intervals. Our method integrates these geometric principles into the data representations via a Surrogate-driven Representation Learning (SRL) framework. Experiments with real-world regression and operator learning tasks highlight the importance of uniformity in imbalanced regression and validate the efficacy of our geometry-based loss functions.

Dataset distillation aims to synthesize a smaller, representative dataset that preserves the essential properties of the original data, enabling efficient model training with reduced computational resources. Prior work has primarily focused on improving the alignment or matching process between original and synthetic data, or on enhancing the efficiency of distilling large datasets. In this work, we introduce {bf C}ommittee {bf V}oting for {bf D}ataset {bf D}istillation (CV-DD), a novel and orthogonal approach that leverages the collective wisdom of multiple models or experts to create high-quality distilled datasets. We start by showing how to establish a strong baseline that already achieves state-of-the-art accuracy through leveraging recent advancements and thoughtful adjustments in model design and optimization processes. By integrating distributions and predictions from a committee of models while generating high-quality soft labels, our method captures a wider spectrum of data features, reduces model-specific biases and the adverse effects of distribution shifts, leading to significant improvements in generalization. This voting-based strategy not only promotes diversity and robustness within the distilled dataset but also significantly reduces overfitting, resulting in improved performance on post-eval tasks. Extensive experiments across various datasets and IPCs (images per class) demonstrate that Committee Voting leads to more reliable and adaptable distilled data compared to single/multi-model distillation methods, demonstrating its potential for efficient and accurate dataset distillation. Code is available at: https://github.com/Jiacheng8/CV-DD.

Federated Long-Tailed Learning (Fed-LT), a paradigm wherein data collected from decentralized local clients manifests a globally prevalent long-tailed distribution, has garnered considerable attention in recent times. In the context of Fed-LT, existing works have predominantly centered on addressing the data imbalance issue to enhance the efficacy of the generic global model while neglecting the performance at the local level. In contrast, conventional Personalized Federated Learning (pFL) techniques are primarily devised to optimize personalized local models under the presumption of a balanced global data distribution. This paper introduces an approach termed Federated Local and Generic Model Training in Fed-LT (FedLoGe), which enhances both local and generic model performance through the integration of representation learning and classifier alignment within a neural collapse framework. Our investigation reveals the feasibility of employing a shared backbone as a foundational framework for capturing overarching global trends, while concurrently employing individualized classifiers to encapsulate distinct refinements stemming from each client's local features. Building upon this discovery, we establish the Static Sparse Equiangular Tight Frame Classifier (SSE-C), inspired by neural collapse principles that naturally prune extraneous noisy features and foster the acquisition of potent data representations. Furthermore, leveraging insights from imbalance neural collapse's classifier norm patterns, we develop Global and Local Adaptive Feature Realignment (GLA-FR) via an auxiliary global classifier and personalized Euclidean norm transfer to align global features with client preferences. Extensive experimental results on CIFAR-10/100-LT, ImageNet, and iNaturalist demonstrate the advantage of our method over state-of-the-art pFL and Fed-LT approaches.

In this work, we propose Attentive Pooling (AP), a two-way attention mechanism for discriminative model training. In the context of pair-wise ranking or classification with neural networks, AP enables the pooling layer to be aware of the current input pair, in a way that information from the two input items can directly influence the computation of each other's representations. Along with such representations of the paired inputs, AP jointly learns a similarity measure over projected segments (e.g. trigrams) of the pair, and subsequently, derives the corresponding attention vector for each input to guide the pooling. Our two-way attention mechanism is a general framework independent of the underlying representation learning, and it has been applied to both convolutional neural networks (CNNs) and recurrent neural networks (RNNs) in our studies. The empirical results, from three very different benchmark tasks of question answering/answer selection, demonstrate that our proposed models outperform a variety of strong baselines and achieve state-of-the-art performance in all the benchmarks.

Advances in generative modeling have recently been adapted to tabular data containing discrete and continuous features. However, generating mixed-type features that combine discrete states with an otherwise continuous distribution in a single feature remains challenging. We advance the state-of-the-art in diffusion models for tabular data with a cascaded approach. We first generate a low-resolution version of a tabular data row, that is, the collection of the purely categorical features and a coarse categorical representation of numerical features. Next, this information is leveraged in the high-resolution flow matching model via a novel guided conditional probability path and data-dependent coupling. The low-resolution representation of numerical features explicitly accounts for discrete outcomes, such as missing or inflated values, and therewith enables a more faithful generation of mixed-type features. We formally prove that this cascade tightens the transport cost bound. The results indicate that our model generates significantly more realistic samples and captures distributional details more accurately, for example, the detection score increases by 40%.

A striking geometric disparity has long persisted in the practice of deep learning. While modern neural network architectures naturally exhibit rich symmetry and equivariance properties, popular optimizers such as Adam and its variants operate inherently coordinate-wise, rendering them unable to respect the equivariance structures of the parameter space. We address this disparity by introducing a symmetry-compatible principle for optimizer design: the gradient update rule should be equivariant under the symmetry group acting on the corresponding weight block. Following this principle, we first provide a unified perspective on bi-orthogonally equivariant updates for general matrix layers, as employed by stochastic spectral descent, Muon, Scion, and polar gradient methods. More importantly, by moving from orthogonal groups to permutation and shared-shift symmetries, we derive symmetry-compatible optimizers for parameter blocks whose symmetries differ from those of general matrix layers: embedding and LM head matrices, SwiGLU MLP projections, and MoE router matrices. These constructions include one-sided spectral, row-norm, hybrid row-norm/spectral, row-aware, column-aware, centered row-norm, and left-spectral updates. They yield an end-to-end layerwise optimizer stack in which each major matrix-valued parameter class is assigned an update whose equivariance matches its symmetry group. We corroborate this principle through pre-training experiments on dense and sparse MoE language models, including Qwen3-0.6B-style, Gemma 3 1B-style, OLMoE-1B-7B-style, and downsized gpt-oss architectures. Across these experiments, symmetry-compatible updates consistently improve final validation loss, and in several cases training stability, over corresponding AdamW updates.

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

This paper proposes a novel column generation framework for combinatorial software testing. In particular, it combines Mathematical Programming and Constraint Programming in a hybrid decomposition to generate covering arrays. The approach allows generating parameterized test cases with coverage guarantees between parameter interactions of a given application. Compared to exhaustive testing, combinatorial test case generation reduces the number of tests to run significantly. Our column generation algorithm is generic and can accommodate mixed coverage arrays over heterogeneous alphabets. The algorithm is realized in practice as a cloud service and recognized as one of the five winners of the company-wide cloud application challenge at Oracle. The service is currently helping software developers from a range of different product teams in their testing efforts while exposing declarative constraint models and hybrid optimization techniques to a broader audience.

The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic gradient descent -- exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. 2021. We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we identify intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory.

Realistic text-to-SQL workflows often require joining multiple tables. As a result, accurately retrieving the relevant set of tables becomes a key bottleneck for end-to-end performance. We study an open-book setting where queries must be answered over large, heterogeneous table collections pooled from many sources, without clean scoping signals such as database identifiers. Here, dense retrieval (DR) achieves high recall but returns many distractors, while join-aware alternatives often rely on extra assumptions and/or incur high inference overhead. We propose CORE-T, a scalable, training-free framework that enriches tables with LLM-generated purpose metadata and pre-computes a lightweight table-compatibility cache. At inference time, DR returns top-K candidates; a single LLM call selects a coherent, joinable subset, and a two-step additive adjustment stage restores strongly compatible tables. Across Bird, Spider, MMQA, and Beaver, CORE-T improves over DR by up to 22.7 points in table-selection F1 while returning up to 40% fewer tables, and by up to 24.4 points in multi-table execution accuracy, and uses 1.64-4.20x fewer total selection tokens than LLM-intensive baselines.

Analytic Continual Learning (ACL) offers a computationally efficient alternative to gradient-based approaches. Recent ACL methods are based on Recursive Least Squares (RLS) and have achieved the state-of-the-art results compared to other alternatives. However, they falter significantly in Class-Incremental Learning scenarios characterized by Long-Tailed distributions. While the ill-conditioning of the autocorrelation (Gram) matrix is a known limitation of RLS, we demonstrate that class imbalance exacerbates this issue into a distinct spectral pathology: "tail" classes suffer from severe spectral collapse, rendering their subspaces numerically indistinguishable from noise. Standard Ridge Regression (L_2) fails to address this effectively as it applies isotropic regularization - a uniform penalty that is insufficient to stabilize the tail without over-shrinking the head. To address this, we propose Geometry-Spectral Rectification (GSR), a theoretically grounded framework that treats long-tailed learning as a spectral regularization problem. Unlike standard isotropic regularization (Ridge) which uniformly penalizes all eigenvalues, GSR acts as an anisotropic spectral filter, selectively inflating the collapsed eigenvalues of tail classes. We construct a structured, data-dependent spectral perturbation matrix Δ that selectively inflates collapsed tail eigen-directions of the Gram matrix. Theoretical analysis proves that GSR guarantees an improved stable rank for the Gram matrix, ensuring numerical stability. Extensive experiments show that GSR establishes a new state-of-the-art for analytic CIL, offering a superior trade-off between computational efficiency and robust generalization in long-tailed settings.

Large-scale code generation models such as Codex and CodeT5 have achieved impressive performance. However, libraries are upgraded or deprecated very frequently and re-training large-scale language models is computationally expensive. Therefore, Continual Learning (CL) is an important aspect that remains underexplored in the code domain. In this paper, we introduce a benchmark called CodeTask-CL that covers a wide range of tasks, including code generation, translation, summarization, and refinement, with different input and output programming languages. Next, on our CodeTask-CL benchmark, we compare popular CL techniques from NLP and Vision domains. We find that effective methods like Prompt Pooling (PP) suffer from catastrophic forgetting due to the unstable training of the prompt selection mechanism caused by stark distribution shifts in coding tasks. We address this issue with our proposed method, Prompt Pooling with Teacher Forcing (PP-TF), that stabilizes training by enforcing constraints on the prompt selection mechanism and leads to a 21.54% improvement over Prompt Pooling. Along with the benchmark, we establish a training pipeline that can be used for CL on code models, which we believe can motivate further development of CL methods for code models. Our code is available at https://github.com/amazon-science/codetaskcl-pptf

Mixture of experts (MoE) models achieve state-of-the-art results in language modeling but suffer from inefficient hardware utilization due to imbalanced token routing and communication overhead. While prior work has focused on optimizing MoE training and decoder architectures, inference for encoder-based MoE models in a multi-GPU with expert parallelism setting remains underexplored. We introduce MoEShard, an inference system that achieves perfect load balancing through tensor sharding of MoE experts. Unlike existing approaches that rely on heuristic capacity factors or drop tokens, MoEShard evenly distributes computation across GPUs and ensures full token retention, maximizing utilization regardless of routing skewness. We achieve this through a strategic row- and column-wise decomposition of expert matrices. This reduces idle time and avoids bottlenecks caused by imbalanced expert assignments. Furthermore, MoEShard minimizes kernel launches by fusing decomposed expert computations, significantly improving throughput. We evaluate MoEShard against DeepSpeed on encoder-based architectures, demonstrating speedups of up to 6.4times in time to first token (TTFT). Our results show that tensor sharding, when properly applied to experts, is a viable and effective strategy for efficient MoE inference.

Given a matrix Ain R^{ntimes d} and a vector bin R^n, we consider the regression problem with ell_infty guarantees: finding a vector x'in R^d such that |x'-x^*|_infty leq epsilon{d}cdot |Ax^*-b|_2cdot |A^dagger| where x^*=argmin_{xin R^d}|Ax-b|_2. One popular approach for solving such ell_2 regression problem is via sketching: picking a structured random matrix Sin R^{mtimes n} with mll n and SA can be quickly computed, solve the ``sketched'' regression problem argmin_{xin R^d} |SAx-Sb|_2. In this paper, we show that in order to obtain such ell_infty guarantee for ell_2 regression, one has to use sketching matrices that are dense. To the best of our knowledge, this is the first user case in which dense sketching matrices are necessary. On the algorithmic side, we prove that there exists a distribution of dense sketching matrices with m=epsilon^{-2}dlog^3(n/delta) such that solving the sketched regression problem gives the ell_infty guarantee, with probability at least 1-delta. Moreover, the matrix SA can be computed in time O(ndlog n). Our row count is nearly-optimal up to logarithmic factors, and significantly improves the result in [Price, Song and Woodruff, ICALP'17], in which a super-linear in d rows, m=Omega(epsilon^{-2}d^{1+gamma}) for gamma=Theta(frac{loglog n{log d}}) is required. We also develop a novel analytical framework for ell_infty guarantee regression that utilizes the Oblivious Coordinate-wise Embedding (OCE) property introduced in [Song and Yu, ICML'21]. Our analysis is arguably much simpler and more general than [Price, Song and Woodruff, ICALP'17], and it extends to dense sketches for tensor product of vectors.

We study the fine-grained uniform convergence behavior of halfspaces beyond worst-case VC bounds. For inhomogeneous halfspaces in R^d with dge 2, we show that standard first-order VC bounds are essentially tight: even consistent hypotheses can incur population error Θ(dln(n/d)/n), and in the agnostic setting the deviation scales as τln(1/τ) at true error τ. In contrast, homogeneous halfspaces in R^2 exhibit a markedly different behavior. In the realizable case, every hypothesis consistent with the sample has error O(1/n). In the agnostic case, we prove a bandwise, log-free deviation bound on each dyadic risk band via a critical-wedge localization argument. Unioning over bands incurs only a lnln n overhead, and we establish a matching lower bound showing this overhead is unavoidable. Together, these results give a fine-grained and nearly complete picture of uniform convergence for halfspaces, revealing sharp dimensional and structural thresholds.

Neural scaling laws approximate a language model's loss as a power-law function of parameter count N and token count D. Following Chinchilla-style compute-optimal training, many studies fit scaling laws from runs performed under a fixed tokens-per-parameter (TPP) ratio k and set D = kN. We show that this collinear design, combined with the empirically common near-equality of the exponents governing N and D, induces an inherent ill-conditioning in the Gauss-Newton least-squares problem: the condition number of the design grows as the inverse square of the gap between the N and D-exponents. The scale coefficients become practically unidentifiable, with confidence intervals inflating by an order of magnitude or more, yielding a ``sloppy'' model whose extrapolations degrade sharply off the training ray. We prove this for four scaling-law formalisms and derive a closed-form TPP-diversity threshold that is necessary and sufficient for well-conditioned estimation. Empirically, non-collinear designs outperform collinear ones on held-out splits with a 97.3\% win rate across four laws, five corpora, multiple floating point precision modes. We further show the degeneracy is rooted in Jacobian geometry and is not an artifact of the loss function: any smooth estimation objective whose curvature involves the Jacobian inherits the same ill-conditioning.

This paper proposes a novel method for deep learning based on the analytical convolution of multidimensional Gaussian mixtures. In contrast to tensors, these do not suffer from the curse of dimensionality and allow for a compact representation, as data is only stored where details exist. Convolution kernels and data are Gaussian mixtures with unconstrained weights, positions, and covariance matrices. Similar to discrete convolutional networks, each convolution step produces several feature channels, represented by independent Gaussian mixtures. Since traditional transfer functions like ReLUs do not produce Gaussian mixtures, we propose using a fitting of these functions instead. This fitting step also acts as a pooling layer if the number of Gaussian components is reduced appropriately. We demonstrate that networks based on this architecture reach competitive accuracy on Gaussian mixtures fitted to the MNIST and ModelNet data sets.

Hyper-Connections (HC) replace the single residual stream of a Transformer with n parallel ones, mixing them at every layer with a learned n times n residual matrix. Leaving that matrix unconstrained places no limit on the factor by which the mixing step rescales the residual streams, and that factor compounds across layers, which destabilizes training. Manifold-constrained Hyper-Connections (mHC) address this by restricting the matrix to the doubly stochastic matrices. That caps the factor at one, so the mixing can no longer amplify any direction, but nothing bounds it from below. We prove that inside this set the mixing step can reduce the norm of the residual streams only by shrinking the differences between the streams, while their mean is left unchanged; and since the reduction accumulates over layers, the streams grow more alike and their diversity is spent with depth. We therefore propose Orthogonal Hyper-Connections (oHC), restricting the residual matrix to the rotation group SO(n), so that the mixing step can neither amplify nor attenuate the residual streams in any direction, which keeps training stable and no longer forces the differences between the streams to contract. Specifically, at the four streams used by recent HC models we parameterize the group in closed form by a pair of unit quaternions, which adds no parameters, replaces the iterative projection with a fixed pattern of signed additions, and can be constructed faster than mHC. We evaluate oHC across a comprehensive set of downstream tasks, where it outperforms the single-stream residual baseline, mHC and iHC, which fixes the residual matrix to the identity.

We study the problem of approximating stationary points of Lipschitz and smooth functions under (varepsilon,delta)-differential privacy (DP) in both the finite-sum and stochastic settings. A point w is called an alpha-stationary point of a function F:R^drightarrowR if |nabla F(w)|leq alpha. We provide a new efficient algorithm that finds an Obig(big[sqrt{d}{nvarepsilon}big]^{2/3}big)-stationary point in the finite-sum setting, where n is the number of samples. This improves on the previous best rate of Obig(big[sqrt{d}{nvarepsilon}big]^{1/2}big). We also give a new construction that improves over the existing rates in the stochastic optimization setting, where the goal is to find approximate stationary points of the population risk. Our construction finds a Obig(1{n^{1/3}} + big[sqrt{d}{nvarepsilon}big]^{1/2}big)-stationary point of the population risk in time linear in n. Furthermore, under the additional assumption of convexity, we completely characterize the sample complexity of finding stationary points of the population risk (up to polylog factors) and show that the optimal rate on population stationarity is tilde Thetabig(1{n}+sqrt{d}{nvarepsilon}big). Finally, we show that our methods can be used to provide dimension-independent rates of Obig(1{n}+minbig(big[sqrt{rank}{nvarepsilon}big]^{2/3},1{(nvarepsilon)^{2/5}}big)big) on population stationarity for Generalized Linear Models (GLM), where rank is the rank of the design matrix, which improves upon the previous best known rate.

Modern Text-to-SQL systems generate multiple candidate SQL queries and rank them to judge a final prediction. However, existing methods face two limitations. First, they often score functionally equivalent SQL queries inconsistently despite identical execution results. Second, ranking cannot recover when the correct SQL is absent from the candidate pool. We propose R^3-SQL, a Text-to-SQL framework that addresses both issues through unified reward for ranking and resampling. R^3-SQL first groups candidates by execution result and ranks groups for consistency. To score each group, it combines a pairwise preference across groups with a pointwise utility from the best group rank and size, capturing relative preference, consistency, and candidate quality. To improve candidate recall, R^3-SQL introduces agentic resampling, which judges the generated candidate pool and selectively resamples when the correct SQL is likely absent. R^3-SQL achieves 75.03 execution accuracy on BIRD-dev, a new state of the art among methods using models with disclosed sizes, with consistent gains across five benchmarks.

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear system Atheta = b for which A and b can only be accessed through random estimates {({bf A}_n, {bf b}_n): n in N^*}. Our analysis is based on new results regarding moments and high probability bounds for products of matrices which are shown to be tight. We derive high probability bounds on the performance of LSA under weaker conditions on the sequence {({bf A}_n, {bf b}_n): n in N^*} than previous works. However, in contrast, we establish polynomial concentration bounds with order depending on the stepsize. We show that our conclusions cannot be improved without additional assumptions on the sequence of random matrices {{bf A}_n: n in N^*}, and in particular that no Gaussian or exponential high probability bounds can hold. Finally, we pay a particular attention to establishing bounds with sharp order with respect to the number of iterations and the stepsize and whose leading terms contain the covariance matrices appearing in the central limit theorems.

Consolidating specialized foundation models into a unified generalist is a central goal of post-training. Two approaches are in common use: model merging, which is fast but treated as a heuristic, and multi-teacher on-policy distillation, which matches distributions but demands heavy rollout compute and suffers from cross-task gradient conflict. We show that the two are one objective seen at different orders. Within a shared basin of homologous specialists, the multi-teacher on-policy distillation objective is, to second order, exactly the Fisher-merging objective. Its minimizer is therefore the Fisher merge, a classic model-merging method given by a closed-form combination of the specialists, so merging is optimal, to second order, as a closed-form stage of distillation. Building on this identification, we propose Residual-Governed Branch-and-Merge(RGBM), a two-phase consolidation procedure. Concretely, a full-parameter Fisher merge is intractable on foundation models, so Phase~1 restricts the merge to the task-vector subspace. Extending tangent-space analyses of merging, we show that the same coefficients that mix task vectors also mix implicit rewards, which lets a residual program on unlabelled prompts solve for them. The program minimizes the worst per-domain residual and reports its energy-normalized values as the domain residual spectrum. Phase~2 lets this spectrum govern what may be added: RGBM passivates domains with low normalized residuals, trains isolated branches only for domains above the spectral gap, and writes back the admitted updates with calibrated shrinkage. On two open-source consolidation suites, the Phase~1 merge alone matches or outperforms fully trained multi-teacher distillation, and RGBM improves on it further with zero extra joint-training steps, whereas every un-gated write-back, including continued joint distillation from the merge, falls below it.

Supervised learning datasets may contain multiple cues that explain the training set equally well, i.e., learning any of them would lead to the correct predictions on the training data. However, many of them can be spurious, i.e., lose their predictive power under a distribution shift and consequently fail to generalize to out-of-distribution (OOD) data. Recently developed "diversification" methods (Lee et al., 2023; Pagliardini et al., 2023) approach this problem by finding multiple diverse hypotheses that rely on different features. This paper aims to study this class of methods and identify the key components contributing to their OOD generalization abilities. We show that (1) diversification methods are highly sensitive to the distribution of the unlabeled data used for diversification and can underperform significantly when away from a method-specific sweet spot. (2) Diversification alone is insufficient for OOD generalization. The choice of the used learning algorithm, e.g., the model's architecture and pretraining, is crucial. In standard experiments (classification on Waterbirds and Office-Home datasets), using the second-best choice leads to an up to 20\% absolute drop in accuracy. (3) The optimal choice of learning algorithm depends on the unlabeled data and vice versa i.e. they are co-dependent. (4) Finally, we show that, in practice, the above pitfalls cannot be alleviated by increasing the number of diverse hypotheses, the major feature of diversification methods. These findings provide a clearer understanding of the critical design factors influencing the OOD generalization abilities of diversification methods. They can guide practitioners in how to use the existing methods best and guide researchers in developing new, better ones.

Throughout the different phases of a drug development program, randomized trials are used to establish the tolerability, safety, and efficacy of a candidate drug. At each stage one aims to optimize the design of future studies by extrapolation from the available evidence at the time. This includes collected trial data and relevant external data. However, relevant external data are typically available as averages only, for example from trials on alternative treatments reported in the literature. Here we report on such an example from a drug development for wet age-related macular degeneration. This disease is the leading cause of severe vision loss in the elderly. While current treatment options are efficacious, they are also a substantial burden for the patient. Hence, new treatments are under development which need to be compared against existing treatments. The general statistical problem this leads to is meta-analysis, which addresses the question of how we can combine datasets collected under different conditions. Bayesian methods have long been used to achieve partial pooling. Here we consider the challenge when the model of interest is complex (hierarchical and nonlinear) and one dataset is given as raw data while the second dataset is given as averages only. In such a situation, common meta-analytic methods can only be applied when the model is sufficiently simple for analytic approaches. When the model is too complex, for example nonlinear, an analytic approach is not possible. We provide a Bayesian solution by using simulation to approximately reconstruct the likelihood of the external summary and allowing the parameters in the model to vary under the different conditions. We first evaluate our approach using fake-data simulations and then report results for the drug development program that motivated this research.

Classical alpha mining achieves strong risk-adjusted returns by combining many low-correlated predictive signals, yet deep learning stock-ranking methods typically produce a single alpha per stock, rely on increasingly complex architectures with diminishing gains, and obtain diversity only through separate models or implicit routing, without explicitly controlling inter-alpha correlation. We introduce MAPLE (Multi-Alpha Position-aware Listwise Ensembling), a backbone-agnostic framework that recovers this diversity principle within a single training pass. MAPLE combines a unified, capacity-scaled prediction head with an extreme-rank weighted listwise ranking loss and a diversity regularizer that explicitly penalizes pairwise correlation across alphas. Across four equity markets spanning the US, China, and Japan, MAPLE achieves the best average Sharpe and Calmar ratios among nine baselines, using up to 55x fewer parameters and 2.5x less training time, and generalizes across five backbone architectures with Sharpe and Calmar Ratio gains of 10-23% and 17-43%, respectively. Behavioral analysis further shows why each component works: the unified head already reduces inter-alpha correlation before any diversity loss is applied, and the extreme-rank loss lets diversity regularization improve rather than erode per-alpha ranking quality as capacity scaling sustains this balance at scale. These results show that principled loss design and capacity allocation, rather than architectural complexity, drive diverse and effective multi-alpha generation.

We address the problem of 3D rotation equivariance in convolutional neural networks. 3D rotations have been a challenging nuisance in 3D classification tasks requiring higher capacity and extended data augmentation in order to tackle it. We model 3D data with multi-valued spherical functions and we propose a novel spherical convolutional network that implements exact convolutions on the sphere by realizing them in the spherical harmonic domain. Resulting filters have local symmetry and are localized by enforcing smooth spectra. We apply a novel pooling on the spectral domain and our operations are independent of the underlying spherical resolution throughout the network. We show that networks with much lower capacity and without requiring data augmentation can exhibit performance comparable to the state of the art in standard retrieval and classification benchmarks.

Federated Learning (FL) is a widespread and well-adopted paradigm of decentralised learning that allows training one model from multiple sources without the need to transfer data between participating clients directly. Since its inception in 2015, it has been divided into numerous subfields that deal with application-specific issues, such as data heterogeneity or resource allocation. One such sub-field, Clustered Federated Learning (CFL), deals with the problem of clustering the population of clients into separate cohorts to deliver personalised models. Although a few remarkable works have been published in this domain, the problem remains largely unexplored, as its basic assumptions and settings differ slightly from those of standard FL. In this work, we present One-Shot Clustered Federated Learning (OCFL), a clustering-agnostic algorithm that can automatically detect the earliest suitable moment for clustering. Our algorithm is based on computing the cosine distance between the gradients of the clients and a temperature measure that detects when the federated model starts to converge. We empirically evaluate our methodology by testing various one-shot clustering algorithms for over forty different tasks on five benchmark datasets. Our experiments showcase the good performance of our approach when used to perform CFL in an automated manner without the need to adjust hyperparameters. We also revisit the practical feasibility of CFL algorithms based on the gradients of the clients, providing firm evidence of the high efficiency of density-based clustering methods when used to differentiate between the loss surfaces of neural networks trained on different distributions. Moreover, by inspecting the feasibility of local explanations generated with the help of GradCAM, we can provide more insights into the relationship between personalisation and the explainability of local predictions.

Tabular data drive most real-world machine learning applications, yet building general-purpose models for them remains difficult. Mixed numeric and categorical fields, weak feature structure, and limited labeled data make scaling and generalization challenging. To this end, we introduce Orion-Bix, a tabular foundation model that combines biaxial attention with meta-learned in-context reasoning for few-shot tabular learning. Its encoder alternates standard, grouped, hierarchical, and relational attention, fusing their outputs through multi-CLS summarization to capture both local and global dependencies efficiently. A label-aware ICL head adapts on the fly and scales to large label spaces via hierarchical decision routing. Meta-trained on synthetically generated, structurally diverse tables with causal priors, Orion-Bix learns transferable inductive biases across heterogeneous data. Delivered as a scikit-learn compatible foundation model, it outperforms gradient-boosting baselines and remains competitive with state-of-the-art tabular foundation models on public benchmarks, showing that biaxial attention with episodic meta-training enables robust, few-shot-ready tabular learning. The model is publicly available at https://github.com/Lexsi-Labs/Orion-BiX .