Large output spaces, also referred to as Extreme multilabel classification (XMC), is a setting that arises, e.g., in large-scale tagging and product-to-product recommendation, and is characterized by the number of labels ranging from hundreds of thousands to millions. This means that the linear classification head, usually only a tiny fraction of the overall model, turns into the main driver for compute and memory demand. Current state-of-the-art XMC methods predominantly rely on FP16-FP32 mixed-precision training, which we show can be unstable, and inefficient in terms of memory usage and computational overhead. Meanwhile, existing low-precision methods typically retain higher precision for the classification layer. In this work, we propose ELMO, a pure low-precision training framework for XMC models using BFloat16 and Float8 data types. By leveraging Kahan summation and stochastic rounding, we demonstrate that XMC models can be effectively trained entirely in Float8, without relying on single-precision master weights or tensor scaling. Low-precision training, combined with our proposed memory optimizations—gradient fusion and chunking—enables significant reductions in GPU memory usage. For example, we train a 3-million-label XMC model with only 6.6 GiB of GPU memory, compared to the 39.7GiB required by the optimized SOTA method, Renee without compromising accuracy.

Extreme multilabel classification (XMLC) problems occur in settings such as related product recommendation, large-scale document tagging, or ad prediction, and are characterized by a label space that can span millions of possible labels. There are two implicit tasks that the classifier performs: Evaluating each potential label for its expected worth, and then selecting the best candidates. For the latter task, only the relative order of scores matters, and this is what is captured by the standard evaluation procedure in the XMLC literature. However, in many practical applications, it is important to have a good estimate of the actual probability of a label being relevant, e.g., to decide whether to pay the fee to be allowed to display the corresponding ad. To judge whether an extreme classifier is indeed suited to this task, one can look, for example, to whether it returns calibrated probabilities, which has hitherto not been done in this field. Therefore, this paper aims to establish the current status quo of calibration in XMLC by providing a systematic evaluation, comprising nine models from four different model families across seven benchmark datasets. As naive application of Expected Calibration Error (ECE) leads to meaningless results in long-tailed XMC datasets, we instead introduce the notion of calibration@k (e.g., ECE@k), which focusses on the top-k probability mass, offering a more appropriate measure for evaluating probability calibration in XMLC scenarios. While we find that different models can exhibit widely varying reliability plots, we also show that post-training calibration via a computationally efficient isotonic regression method enhances model calibration without sacrificing prediction accuracy. Thus, the practitioner can choose the model family based on accuracy considerations, and leave calibration to isotonic regression.

Large Language Models (LLMs) have demonstrated the ability to tackle increasingly complex tasks through advanced reasoning, long-form content generation, and tool use. Solving these tasks often involves long inference-time computations. In human problem solving, a common strategy to expedite work is collaboration: by dividing the problem into sub-tasks, exploring different strategies concurrently, etc. Recent research has shown that LLMs can also operate in parallel by implementing explicit cooperation frameworks, such as voting mechanisms or the explicit creation of independent sub-tasks that can be executed in parallel. However, each of these frameworks may not be suitable for all types of tasks, which can hinder their applicability. In this work, we propose a different design approach: we run LLM "workers" in parallel , allowing them to synchronize via a concurrently-updated attention cache and prompt these workers to decide how best to collaborate. Our approach allows the instances to come up with their own collaboration strategy for the problem at hand, all the while "seeing" each other's partial progress in the concurrent cache. We implement this approach via Hogwild! Inference: a parallel LLM inference engine where multiple instances of the same LLM run in parallel with the same attention cache, with "instant" access to each other's generated tokens. Hogwild! inference takes advantage of Rotary Position Embeddings (RoPE) to avoid recomputation while improving parallel hardware utilization. We find that modern reasoning-capable LLMs can perform inference with shared Key-Value cache out of the box, without additional fine-tuning.

We consider the optimization of complex performance metrics in multi-label classification under the population utility framework. We mainly focus on metrics linearly decomposable into a sum of binary classification utilities applied separately to each label with an additional requirement of exactly $k$ labels predicted for each instance. These "macro-at-$k$" metrics possess desired properties for extreme classification problems with long tail labels. Unfortunately, the at-$k$ constraint couples the otherwise independent binary classification tasks, leading to a much more challenging optimization problem than standard macro-averages. We provide a statistical framework to study this problem, prove the existence and the form of the optimal classifier, and propose a statistically consistent and practical learning algorithm based on the Frank-Wolfe method. Interestingly, our main results concern even more general metrics being non-linear functions of label-wise confusion matrices. Empirical results provide evidence for the competitive performance of the proposed approach.

We consider sequential maximization of performance metrics that are general functions of a confusion matrix of a classifier (such as precision, F-measure, or G-mean). Such metrics are, in general, non-decomposable over individual instances, making their optimization very challenging. While they have been extensively studied under different frameworks in the batch setting, their analysis in the online learning regime is very limited, with only a few distinguished exceptions. In this paper, we introduce and analyze a general online algorithm that can be used in a straightforward way with a variety of complex performance metrics in binary, multi-class, and multi-label classification problems. The algorithm’s update and prediction rules are appealingly simple and computationally efficient without the need to store any past data. We show the algorithm attains $\mathcal{O}(\frac{\ln n}{n})$ regret for concave and smooth metrics and verify the efficiency of the proposed algorithm in empirical studies.

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In recent years, Dynamic Sparse Training (DST) has emerged as an alternative to post-training pruning for generating efficient models. In principle, DST allows for a much more memory efficient training process, as it maintains sparsity throughout the entire training run. However, current DST implementations fail to capitalize on this. Because sparse matrix multiplication is much less efficient than dense matrix multiplication on GPUs, most implementations simulate sparsity by masking weights. In this paper, we leverage recent advances in semi-structured sparse training to apply DST in the domain of classification with large output spaces, where memory-efficiency is paramount. With a label space of possibly millions of candidates, the classification layer alone will consume several gigabytes of memory. Switching from a dense to a fixed fan-in sparse layer updated with sparse evolutionary training (SET); however, severely hampers training convergence, especially at the largest label spaces. We find that the gradients fed back from the classifier into the text encoder make it much more difficult to learn good input representations, despite using a dense encoder. By employing an intermediate layer or adding an auxiliary training objective, we recover most of the generalisation performance of the dense model. Overall, we demonstrate the applicability of DST in a challenging domain, characterized by a highly skewed label distribution, that lies outside of DST's typical benchmark datasets, and enable end-to-end training with millions of labels on commodity hardware.

Extreme multi-label classification (XMLC) is the task of selecting a small subset of relevant labels from a very large set of possible labels. As such, it is characterized by long-tail labels, i.e., most labels have very few positive instances. With standard performance measures such as precision@k, a classifier can ignore tail labels and still report good performance. However, it is often argued that correct predictions in the tail are more "interesting" or "rewarding," but the community has not yet settled on a metric capturing this intuitive concept. The existing propensity-scored metrics fall short on this goal by confounding the problems of long-tail and missing labels. In this paper, we analyze generalized metrics budgeted "at k" as an alternative solution. To tackle the challenging problem of optimizing these metrics, we formulate it in the expected test utility (ETU) framework, which aims to optimize the expected performance on a given test set. We derive optimal prediction rules and construct their computationally efficient approximations with provable regret guarantees and being robust against model misspecification. Our algorithm, based on block coordinate descent, scales effortlessly to XMLC problems and obtains promising results in terms of long-tail performance.

The propensity model introduced by Jain et al has become a standard approach for dealing with missing and long-tail labels in extreme multi-label classification (XMLC). In this paper, we critically revise this approach showing that despite its theoretical soundness, its application in contemporary XMLC works is debatable. We exhaustively discuss the flaws of the propensity-based approach, and present several recipes, some of them related to solutions used in search engines and recommender systems, that we believe constitute promising alternatives to be followed in XMLC.

Extreme Multi-label Text Classification (XMC) involves learning a classifier that can assign an input with a subset of most relevant labels from millions of label choices. Recent approaches, such as XR-Transformer and LightXML, leverage a transformer instance to achieve state-of-the-art performance. However, in this process, these approaches need to make various trade-offs between performance and computational requirements. A major shortcoming, as compared to the Bi-LSTM based AttentionXML, is that they fail to keep separate feature representations for each resolution in a label tree. We thus propose CascadeXML, an end-to-end multi-resolution learning pipeline, which can harness the multi-layered architecture of a transformer model for attending to different label resolutions with separate feature representations. CascadeXML significantly outperforms all existing approaches with non-trivial gains obtained on benchmark datasets consisting of up to three million labels. Code for CascadeXML will be made publicly available at https://github.com/xmc-aalto/cascadexml.

Abstract In this paper, we show that a simple, data dependent way of setting the initial vector can be used to substantially speed up the training of linear one-versus-all classifiers in extreme multi-label classification (XMC). We discuss the problem of choosing the initial weights from the perspective of three goals. We want to start in a region of weight space (a) with low loss value, (b) that is favourable for second-order optimization, and (c) where the conjugate-gradient (CG) calculations can be performed quickly. For margin losses, such an initialization is achieved by selecting the initial vector such that it separates the mean of all positive (relevant for a label) instances from the mean of all negatives – two quantities that can be calculated quickly for the highly imbalanced binary problems occurring in XMC. We demonstrate a training speedup of up to $$5\times$$ 5 × on Amazon-670K dataset with 670,000 labels. This comes in part from the reduced number of iterations that need to be performed due to starting closer to the solution, and in part from an implicit negative-mining effect that allows to ignore easy negatives in the CG step. Because of the convex nature of the optimization problem, the speedup is achieved without any degradation in classification accuracy. The implementation can be found at https://github.com/xmc-aalto/dismecpp .

Extreme Classification (XC) refers to supervised learning where each training/test instance is labeled with small subset of relevant labels that are chosen from a large set of possible target labels. The framework of XC has been widely employed in web applications such as automatic labeling of web-encyclopedia, prediction of related searches, and recommendation systems.