Daily Papers

Automated ICD-10 coding from clinical discharge summaries requires models that are both accurate on long-tailed multi-label classification tasks and interpretable to clinicians. Concept Bottleneck Models (CBMs) offer a principled framework for interpretability by routing predictions through human-interpretable concepts, but this transparency often comes at a cost: compressing rich clinical text representations into a narrow concept layer can restrict gradient flow and limit predictive capacity. We present ShifaMind, a concept-grounded architecture built around a Multiplicative Concept Bottleneck (MCB), which changes the form, rather than the width, of the bottleneck. Instead of projecting through a narrow concept layer, ShifaMind uses a learned multiplicative gate over a concept-grounded representation while retaining a scalar concept interface for inspection. On MIMIC-IV top-50 ICD-10 coding, ShifaMind achieves performance competitive with LAAT, the strongest baseline, across F1, AUC, and ranking metrics, while outperforming five additional ICD-coding baselines and providing concept-mediated explanations. Its substantial gains over a capacity-matched Vanilla CBM in both predictive performance and interpretability-oriented metrics highlight the importance of the bottleneck design.

Concept Bottleneck Models (CBMs) promote interpretability by grounding predictions in human-understandable concepts. However, existing CBMs typically fix their task predictor to a single linear or Boolean expression, limiting both predictive accuracy and adaptability to diverse user needs. We propose Mixture of Concept Bottleneck Experts (M-CBEs), a framework that generalizes existing CBMs along two dimensions: the number of experts and the functional form of each expert, exposing an underexplored region of the design space. We investigate this region by instantiating two novel models: Linear M-CBE, which learns a finite set of linear expressions, and Symbolic M-CBE, which leverages symbolic regression to discover expert functions from data under user-specified operator vocabularies. Empirical evaluation demonstrates that varying the mixture size and functional form provides a robust framework for navigating the accuracy-interpretability trade-off, adapting to different user and task needs.

Concept Bottleneck Models (CBMs) enhance the interpretability of neural networks by basing predictions on human-understandable concepts. However, current CBMs typically rely on concept sets extracted from large language models or extensive image corpora, limiting their effectiveness in data-sparse scenarios. We propose Data-efficient CBMs (DCBMs), which reduce the need for large sample sizes during concept generation while preserving interpretability. DCBMs define concepts as image regions detected by segmentation or detection foundation models, allowing each image to generate multiple concepts across different granularities. This removes reliance on textual descriptions and large-scale pre-training, making DCBMs applicable for fine-grained classification and out-of-distribution tasks. Attribution analysis using Grad-CAM demonstrates that DCBMs deliver visual concepts that can be localized in test images. By leveraging dataset-specific concepts instead of predefined ones, DCBMs enhance adaptability to new domains.

Concept Bottleneck Models (CBMs) offer inherent interpretability by initially translating images into human-comprehensible concepts, followed by a linear combination of these concepts for classification. However, the annotation of concepts for visual recognition tasks requires extensive expert knowledge and labor, constraining the broad adoption of CBMs. Recent approaches have leveraged the knowledge of large language models to construct concept bottlenecks, with multimodal models like CLIP subsequently mapping image features into the concept feature space for classification. Despite this, the concepts produced by language models can be verbose and may introduce non-visual attributes, which hurts accuracy and interpretability. In this study, we investigate to avoid these issues by constructing CBMs directly from multimodal models. To this end, we adopt common words as base concept vocabulary and leverage auxiliary unlabeled images to construct a Vision-to-Concept (V2C) tokenizer that can explicitly quantize images into their most relevant visual concepts, thus creating a vision-oriented concept bottleneck tightly coupled with the multimodal model. This leads to our V2C-CBM which is training efficient and interpretable with high accuracy. Our V2C-CBM has matched or outperformed LLM-supervised CBMs on various visual classification benchmarks, validating the efficacy of our approach.

Concept Bottleneck Models (CBMs) map the inputs onto a set of interpretable concepts (``the bottleneck'') and use the concepts to make predictions. A concept bottleneck enhances interpretability since it can be investigated to understand what concepts the model "sees" in an input and which of these concepts are deemed important. However, CBMs are restrictive in practice as they require dense concept annotations in the training data to learn the bottleneck. Moreover, CBMs often do not match the accuracy of an unrestricted neural network, reducing the incentive to deploy them in practice. In this work, we address these limitations of CBMs by introducing Post-hoc Concept Bottleneck models (PCBMs). We show that we can turn any neural network into a PCBM without sacrificing model performance while still retaining the interpretability benefits. When concept annotations are not available on the training data, we show that PCBM can transfer concepts from other datasets or from natural language descriptions of concepts via multimodal models. A key benefit of PCBM is that it enables users to quickly debug and update the model to reduce spurious correlations and improve generalization to new distributions. PCBM allows for global model edits, which can be more efficient than previous works on local interventions that fix a specific prediction. Through a model-editing user study, we show that editing PCBMs via concept-level feedback can provide significant performance gains without using data from the target domain or model retraining.

We propose a novel architecture and method of explainable classification with Concept Bottleneck Models (CBMs). While SOTA approaches to Image Classification task work as a black box, there is a growing demand for models that would provide interpreted results. Such a models often learn to predict the distribution over class labels using additional description of this target instances, called concepts. However, existing Bottleneck methods have a number of limitations: their accuracy is lower than that of a standard model and CBMs require an additional set of concepts to leverage. We provide a framework for creating Concept Bottleneck Model from pre-trained multi-modal encoder and new CLIP-like architectures. By introducing a new type of layers known as Concept Bottleneck Layers, we outline three methods for training them: with ell_1-loss, contrastive loss and loss function based on Gumbel-Softmax distribution (Sparse-CBM), while final FC layer is still trained with Cross-Entropy. We show a significant increase in accuracy using sparse hidden layers in CLIP-based bottleneck models. Which means that sparse representation of concepts activation vector is meaningful in Concept Bottleneck Models. Moreover, with our Concept Matrix Search algorithm we can improve CLIP predictions on complex datasets without any additional training or fine-tuning. The code is available at: https://github.com/Andron00e/SparseCBM.

Concept bottleneck models (CBMs) are a class of interpretable neural network models that predict the target response of a given input based on its high-level concepts. Unlike the standard end-to-end models, CBMs enable domain experts to intervene on the predicted concepts and rectify any mistakes at test time, so that more accurate task predictions can be made at the end. While such intervenability provides a powerful avenue of control, many aspects of the intervention procedure remain rather unexplored. In this work, we develop various ways of selecting intervening concepts to improve the intervention effectiveness and conduct an array of in-depth analyses as to how they evolve under different circumstances. Specifically, we find that an informed intervention strategy can reduce the task error more than ten times compared to the current baseline under the same amount of intervention counts in realistic settings, and yet, this can vary quite significantly when taking into account different intervention granularity. We verify our findings through comprehensive evaluations, not only on the standard real datasets, but also on synthetic datasets that we generate based on a set of different causal graphs. We further discover some major pitfalls of the current practices which, without a proper addressing, raise concerns on reliability and fairness of the intervention procedure.

Existing methods, such as concept bottleneck models (CBMs), have been successful in providing concept-based interpretations for black-box deep learning models. They typically work by predicting concepts given the input and then predicting the final class label given the predicted concepts. However, (1) they often fail to capture the high-order, nonlinear interaction between concepts, e.g., correcting a predicted concept (e.g., "yellow breast") does not help correct highly correlated concepts (e.g., "yellow belly"), leading to suboptimal final accuracy; (2) they cannot naturally quantify the complex conditional dependencies between different concepts and class labels (e.g., for an image with the class label "Kentucky Warbler" and a concept "black bill", what is the probability that the model correctly predicts another concept "black crown"), therefore failing to provide deeper insight into how a black-box model works. In response to these limitations, we propose Energy-based Concept Bottleneck Models (ECBMs). Our ECBMs use a set of neural networks to define the joint energy of candidate (input, concept, class) tuples. With such a unified interface, prediction, concept correction, and conditional dependency quantification are then represented as conditional probabilities, which are generated by composing different energy functions. Our ECBMs address both limitations of existing CBMs, providing higher accuracy and richer concept interpretations. Empirical results show that our approach outperforms the state-of-the-art on real-world datasets.

Concept Bottleneck Models (CBMs) have recently been proposed to address the 'black-box' problem of deep neural networks, by first mapping images to a human-understandable concept space and then linearly combining concepts for classification. Such models typically require first coming up with a set of concepts relevant to the task and then aligning the representations of a feature extractor to map to these concepts. However, even with powerful foundational feature extractors like CLIP, there are no guarantees that the specified concepts are detectable. In this work, we leverage recent advances in mechanistic interpretability and propose a novel CBM approach -- called Discover-then-Name-CBM (DN-CBM) -- that inverts the typical paradigm: instead of pre-selecting concepts based on the downstream classification task, we use sparse autoencoders to first discover concepts learnt by the model, and then name them and train linear probes for classification. Our concept extraction strategy is efficient, since it is agnostic to the downstream task, and uses concepts already known to the model. We perform a comprehensive evaluation across multiple datasets and CLIP architectures and show that our method yields semantically meaningful concepts, assigns appropriate names to them that make them easy to interpret, and yields performant and interpretable CBMs. Code available at https://github.com/neuroexplicit-saar/discover-then-name.

Concept-based explanation methods, such as concept bottleneck models (CBMs), aim to improve the interpretability of machine learning models by linking their decisions to human-understandable concepts, under the critical assumption that such concepts can be accurately attributed to the network's feature space. However, this foundational assumption has not been rigorously validated, mainly because the field lacks standardised metrics and benchmarks to assess the existence and spatial alignment of such concepts. To address this, we propose three metrics: the concept global importance metric, the concept existence metric, and the concept location metric, including a technique for visualising concept activations, i.e., concept activation mapping. We benchmark post-hoc CBMs to illustrate their capabilities and challenges. Through qualitative and quantitative experiments, we demonstrate that, in many cases, even the most important concepts determined by post-hoc CBMs are not present in input images; moreover, when they are present, their saliency maps fail to align with the expected regions by either activating across an entire object or misidentifying relevant concept-specific regions. We analyse the root causes of these limitations, such as the natural correlation of concepts. Our findings underscore the need for more careful application of concept-based explanation techniques especially in settings where spatial interpretability is critical.

Concept Bottleneck Models (CBM) are inherently interpretable models that factor model decisions into human-readable concepts. They allow people to easily understand why a model is failing, a critical feature for high-stakes applications. CBMs require manually specified concepts and often under-perform their black box counterparts, preventing their broad adoption. We address these shortcomings and are first to show how to construct high-performance CBMs without manual specification of similar accuracy to black box models. Our approach, Language Guided Bottlenecks (LaBo), leverages a language model, GPT-3, to define a large space of possible bottlenecks. Given a problem domain, LaBo uses GPT-3 to produce factual sentences about categories to form candidate concepts. LaBo efficiently searches possible bottlenecks through a novel submodular utility that promotes the selection of discriminative and diverse information. Ultimately, GPT-3's sentential concepts can be aligned to images using CLIP, to form a bottleneck layer. Experiments demonstrate that LaBo is a highly effective prior for concepts important to visual recognition. In the evaluation with 11 diverse datasets, LaBo bottlenecks excel at few-shot classification: they are 11.7% more accurate than black box linear probes at 1 shot and comparable with more data. Overall, LaBo demonstrates that inherently interpretable models can be widely applied at similar, or better, performance than black box approaches.

The Information Bottleneck (IB) principle has emerged as a promising approach for enhancing the generalization, robustness, and interpretability of deep neural networks, demonstrating efficacy across image segmentation, document clustering, and semantic communication. Among IB implementations, the IB Lagrangian method, employing Lagrangian multipliers, is widely adopted. While numerous methods for the optimizations of IB Lagrangian based on variational bounds and neural estimators are feasible, their performance is highly dependent on the quality of their design, which is inherently prone to errors. To address this limitation, we introduce Structured IB, a framework for investigating potential structured features. By incorporating auxiliary encoders to extract missing informative features, we generate more informative representations. Our experiments demonstrate superior prediction accuracy and task-relevant information preservation compared to the original IB Lagrangian method, even with reduced network size.

Concept bottleneck models (CBM) aim to produce inherently interpretable models that rely on human-understandable concepts for their predictions. However, existing approaches to design interpretable generative models based on CBMs are not yet efficient and scalable, as they require expensive generative model training from scratch as well as real images with labor-intensive concept supervision. To address these challenges, we present two novel and low-cost methods to build interpretable generative models through post-hoc techniques and we name our approaches: concept-bottleneck autoencoder (CB-AE) and concept controller (CC). Our proposed approaches enable efficient and scalable training without the need of real data and require only minimal to no concept supervision. Additionally, our methods generalize across modern generative model families including generative adversarial networks and diffusion models. We demonstrate the superior interpretability and steerability of our methods on numerous standard datasets like CelebA, CelebA-HQ, and CUB with large improvements (average ~25%) over the prior work, while being 4-15x faster to train. Finally, a large-scale user study is performed to validate the interpretability and steerability of our methods.

Concept Bottleneck Models (CBMs) are regarded as inherently interpretable because they first predict a set of human-defined concepts which are used to predict a task label. For inherent interpretability to be fully realised, and ensure trust in a model's output, it's desirable for concept predictions to use semantically meaningful input features. For instance, in an image, pixels representing a broken bone should contribute to predicting a fracture. However, current literature suggests that concept predictions often rely on irrelevant input features. We hypothesise that this occurs when dataset labels include inaccurate concept annotations, or the relationship between input features and concepts is unclear. In general, the effect of dataset labelling on concept representations remains an understudied area. In this paper, we demonstrate that CBMs can learn to map concepts to semantically meaningful input features, by utilising datasets with a clear link between the input features and the desired concept predictions. This is achieved, for instance, by ensuring multiple concepts do not always co-occur and, therefore provide a clear training signal for the CBM to distinguish the relevant input features for each concept. We validate our hypothesis on both synthetic and real-world image datasets, and demonstrate under the correct conditions, CBMs can learn to attribute semantically meaningful input features to the correct concept predictions.

Concept Bottleneck Models (CBMs) and other concept-based interpretable models show great promise for making AI applications more transparent, which is essential in fields like medicine. Despite their success, we demonstrate that CBMs struggle to reliably identify the correct concepts under distribution shifts. To assess the robustness of CBMs to concept variations, we introduce SUB: a fine-grained image and concept benchmark containing 38,400 synthetic images based on the CUB dataset. To create SUB, we select a CUB subset of 33 bird classes and 45 concepts to generate images which substitute a specific concept, such as wing color or belly pattern. We introduce a novel Tied Diffusion Guidance (TDG) method to precisely control generated images, where noise sharing for two parallel denoising processes ensures that both the correct bird class and the correct attribute are generated. This novel benchmark enables rigorous evaluation of CBMs and similar interpretable models, contributing to the development of more robust methods. Our code is available at https://github.com/ExplainableML/sub and the dataset at http://huggingface.co/datasets/Jessica-bader/SUB.

Numerous deep learning algorithms have been inspired by and understood via the notion of information bottleneck, where unnecessary information is (often implicitly) minimized while task-relevant information is maximized. However, a rigorous argument for justifying why it is desirable to control information bottlenecks has been elusive. In this paper, we provide the first rigorous learning theory for justifying the benefit of information bottleneck in deep learning by mathematically relating information bottleneck to generalization errors. Our theory proves that controlling information bottleneck is one way to control generalization errors in deep learning, although it is not the only or necessary way. We investigate the merit of our new mathematical findings with experiments across a range of architectures and learning settings. In many cases, generalization errors are shown to correlate with the degree of information bottleneck: i.e., the amount of the unnecessary information at hidden layers. This paper provides a theoretical foundation for current and future methods through the lens of information bottleneck. Our new generalization bounds scale with the degree of information bottleneck, unlike the previous bounds that scale with the number of parameters, VC dimension, Rademacher complexity, stability or robustness. Our code is publicly available at: https://github.com/xu-ji/information-bottleneck

While deep networks have achieved broad success in analyzing natural images, when applied to medical scans, they often fail in unexcepted situations. We investigate this challenge and focus on model sensitivity to domain shifts, such as data sampled from different hospitals or data confounded by demographic variables such as sex, race, etc, in the context of chest X-rays and skin lesion images. A key finding we show empirically is that existing visual backbones lack an appropriate prior from the architecture for reliable generalization in these settings. Taking inspiration from medical training, we propose giving deep networks a prior grounded in explicit medical knowledge communicated in natural language. To this end, we introduce Knowledge-enhanced Bottlenecks (KnoBo), a class of concept bottleneck models that incorporates knowledge priors that constrain it to reason with clinically relevant factors found in medical textbooks or PubMed. KnoBo uses retrieval-augmented language models to design an appropriate concept space paired with an automatic training procedure for recognizing the concept. We evaluate different resources of knowledge and recognition architectures on a broad range of domain shifts across 20 datasets. In our comprehensive evaluation with two imaging modalities, KnoBo outperforms fine-tuned models on confounded datasets by 32.4% on average. Finally, evaluations reveal that PubMed is a promising resource for making medical models less sensitive to domain shift, outperforming other resources on both diversity of information and final prediction performance.

Large language models often fail at simple counting tasks, even when the items to count are explicitly present in the prompt. We investigate whether this failure occurs because transformers do not represent counts internally, or because they cannot convert those representations into the correct output tokens. Across three model families, Pythia, Qwen3, and Mistral, ranging from 0.4B to 14B parameters, we find strong evidence for the second explanation. Linear probes recover the correct count from intermediate layers with near-perfect accuracy (R^2>0.99), showing that the information is present. However, the internal directions that encode counts are nearly orthogonal to the output-head rows for digit tokens (|cos|leq0.032). In other words, the model stores the count in a form that the digit logits do not naturally read out. We localize this failure with two interventions. Updating only the digit rows of the output head (36,864 parameters) substantially improves constrained next-token digit prediction (60.7 to 100.0% across four tasks), but it does not fix autoregressive generation. By contrast, a small LoRA intervention on attention Q/V weights (7.67M parameters) improves upstream routing and achieves 83.1% +/- 7.2% in true greedy autoregressive generation. Logit-lens measurements confirm the mechanism: the correct digit's vocabulary rank drops from 55,980 to 1, a 50,000x improvement. Additional norm, logit-lens, and cross-task analyses show that the bottleneck generalizes across character counting, addition, and list length, while remaining absent from broader multi-step reasoning benchmarks, including MMLU, GSM8K, and DROP. These results identify counting failure as a geometric readout bottleneck rather than a failure of internal representation: the model knows the count but the output pathway is geometrically misaligned with the tokens needed to express it.

Interpreting and explaining the behavior of deep neural networks is critical for many tasks. Explainable AI provides a way to address this challenge, mostly by providing per-pixel relevance to the decision. Yet, interpreting such explanations may require expert knowledge. Some recent attempts toward interpretability adopt a concept-based framework, giving a higher-level relationship between some concepts and model decisions. This paper proposes Bottleneck Concept Learner (BotCL), which represents an image solely by the presence/absence of concepts learned through training over the target task without explicit supervision over the concepts. It uses self-supervision and tailored regularizers so that learned concepts can be human-understandable. Using some image classification tasks as our testbed, we demonstrate BotCL's potential to rebuild neural networks for better interpretability. Code is available at https://github.com/wbw520/BotCL and a simple demo is available at https://botcl.liangzhili.com/.

Explainable AI (XAI) is crucial for building transparent and trustworthy machine learning systems, especially in high-stakes domains. Concept Bottleneck Models (CBMs) have emerged as a promising ante-hoc approach that provides interpretable, concept-level explanations by explicitly modeling human-understandable concepts. However, existing CBMs often suffer from poor locality faithfulness, failing to spatially align concepts with meaningful image regions, which limits their interpretability and reliability. In this work, we propose SL-CBM (CBM with Semantic Locality), a novel extension that enforces locality faithfulness by generating spatially coherent saliency maps at both concept and class levels. SL-CBM integrates a 1x1 convolutional layer with a cross-attention mechanism to enhance alignment between concepts, image regions, and final predictions. Unlike prior methods, SL-CBM produces faithful saliency maps inherently tied to the model's internal reasoning, facilitating more effective debugging and intervention. Extensive experiments on image datasets demonstrate that SL-CBM substantially improves locality faithfulness, explanation quality, and intervention efficacy while maintaining competitive classification accuracy. Our ablation studies highlight the importance of contrastive and entropy-based regularization for balancing accuracy, sparsity, and faithfulness. Overall, SL-CBM bridges the gap between concept-based reasoning and spatial explainability, setting a new standard for interpretable and trustworthy concept-based models.

Conceptual models such as Concept Bottleneck Models (CBMs) have driven substantial progress in improving interpretability for image classification by leveraging human-interpretable concepts. However, extending these models from static images to sequences of images, such as video data, introduces a significant challenge due to the temporal dependencies inherent in videos, which are essential for capturing actions and events. In this work, we introduce MoTIF (Moving Temporal Interpretable Framework), an architectural design inspired by a transformer that adapts the concept bottleneck framework for video classification and handles sequences of arbitrary length. Within the video domain, concepts refer to semantic entities such as objects, attributes, or higher-level components (e.g., 'bow', 'mount', 'shoot') that reoccur across time - forming motifs collectively describing and explaining actions. Our design explicitly enables three complementary perspectives: global concept importance across the entire video, local concept relevance within specific windows, and temporal dependencies of a concept over time. Our results demonstrate that the concept-based modeling paradigm can be effectively transferred to video data, enabling a better understanding of concept contributions in temporal contexts while maintaining competitive performance. Code available at github.com/patrick-knab/MoTIF.

Deep learning-based medical image classification techniques are rapidly advancing in medical image analysis, making it crucial to develop accurate and trustworthy models that can be efficiently deployed across diverse clinical scenarios. Concept Bottleneck Models (CBMs), which first predict a set of explainable concepts from images and then perform classification based on these concepts, are increasingly being adopted for explainable medical image classification. However, the inherent explainability of CBMs introduces new challenges when deploying trained models to new environments. Variations in imaging protocols and staining methods may induce concept-level shifts, such as alterations in color distribution and scale. Furthermore, since CBM training requires explicit concept annotations, fine-tuning models solely with image-level labels could compromise concept prediction accuracy and faithfulness - a critical limitation given the high cost of acquiring expert-annotated concept labels in medical domains. To address these challenges, we propose a training-free confusion concept identification strategy. By leveraging minimal new data (e.g., 4 images per class) with only image-level labels, our approach enhances out-of-domain performance without sacrificing source domain accuracy through two key operations: masking misactivated confounding concepts and amplifying under-activated discriminative concepts. The efficacy of our method is validated on both skin and white blood cell images. Our code is available at: https://github.com/riverback/TF-TTI-XMed.

In discriminative settings such as regression and classification there are two random variables at play, the inputs X and the targets Y. Here, we demonstrate that the Variational Information Bottleneck can be viewed as a compromise between fully empirical and fully Bayesian objectives, attempting to minimize the risks due to finite sampling of Y only. We argue that this approach provides some of the benefits of Bayes while requiring only some of the work.

Deep learning has advanced NLP, but interpretability remains limited, especially in healthcare and finance. Concept bottleneck models tie predictions to human concepts in vision, but NLP versions either use binary activations that harm text representations or latent concepts that weaken semantics, and they rarely model dynamic concept interactions such as negation and context. We introduce the Concept Language Model Network (CLMN), a neural-symbolic framework that keeps both performance and interpretability. CLMN represents concepts as continuous, human-readable embeddings and applies fuzzy-logic reasoning to learn adaptive interaction rules that state how concepts affect each other and the final decision. The model augments original text features with concept-aware representations and automatically induces interpretable logic rules. Across multiple datasets and pre-trained language models, CLMN achieves higher accuracy than existing concept-based methods while improving explanation quality. These results show that integrating neural representations with symbolic reasoning in a unified concept space can yield practical, transparent NLP systems.

Large-scale vision-language models such as CLIP have achieved remarkable success in zero-shot image recognition, yet their predictions remain largely opaque to human understanding. In contrast, Concept Bottleneck Models provide interpretable intermediate representations by reasoning through human-defined concepts, but they rely on concept supervision and lack the ability to generalize to unseen classes. We introduce EZPC that bridges these two paradigms by explaining CLIP's zero-shot predictions through human-understandable concepts. Our method projects CLIP's joint image-text embeddings into a concept space learned from language descriptions, enabling faithful and transparent explanations without additional supervision. The model learns this projection via a combination of alignment and reconstruction objectives, ensuring that concept activations preserve CLIP's semantic structure while remaining interpretable. Extensive experiments on five benchmark datasets, CIFAR-100, CUB-200-2011, Places365, ImageNet-100, and ImageNet-1k, demonstrate that our approach maintains CLIP's strong zero-shot classification accuracy while providing meaningful concept-level explanations. By grounding open-vocabulary predictions in explicit semantic concepts, our method offers a principled step toward interpretable and trustworthy vision-language models. Code is available at https://github.com/oonat/ezpc.

Dot-product attention mechanism plays a crucial role in modern deep architectures (e.g., Transformer) for sequence modeling, however, na\"ive exact computation of this model incurs quadratic time and memory complexities in sequence length, hindering the training of long-sequence models. Critical bottlenecks are due to the computation of partition functions in the denominator of softmax function as well as the multiplication of the softmax matrix with the matrix of values. Our key observation is that the former can be reduced to a variant of the kernel density estimation (KDE) problem, and an efficient KDE solver can be further utilized to accelerate the latter via subsampling-based fast matrix products. Our proposed KDEformer can approximate the attention in sub-quadratic time with provable spectral norm bounds, while all prior results merely provide entry-wise error bounds. Empirically, we verify that KDEformer outperforms other attention approximations in terms of accuracy, memory, and runtime on various pre-trained models. On BigGAN image generation, we achieve better generative scores than the exact computation with over 4times speedup. For ImageNet classification with T2T-ViT, KDEformer shows over 18times speedup while the accuracy drop is less than 0.5%.

The R-Learner is a powerful, theoretically-grounded framework for estimating heterogeneous treatment effects, prized for its robustness to nuisance model errors. However, its application to network data, where causal heterogeneity is often graph-dependent, presents a critical challenge to its core assumption of a well-specified final-stage model. In this paper, we conduct a large-scale empirical study to systematically dissect the R-Learner framework on graphs. We provide the first rigorous evidence that the primary driver of performance is the inductive bias of the final-stage CATE estimator, an effect that dominates the choice of nuisance models. Our central finding is the quantification of a catastrophic "representation bottleneck": we prove with overwhelming statistical significance (p < 0.001) that R-Learners with a graph-blind final stage fail completely (MSE > 4.0), even when paired with powerful GNN nuisance models. Conversely, our proposed end-to-end Graph R-Learner succeeds and significantly outperforms a strong, non-DML GNN T-Learner baseline. Furthermore, we identify and provide a mechanistic explanation for a subtle, topology-dependent "nuisance bottleneck," linking it to GNN over-squashing via a targeted "Hub-Periphery Trade-off" analysis. Our findings are validated across diverse synthetic and semi-synthetic benchmarks. We release our code as a reproducible benchmark to facilitate future research on this critical "final-stage bottleneck."

We present a variational approximation to the information bottleneck of Tishby et al. (1999). This variational approach allows us to parameterize the information bottleneck model using a neural network and leverage the reparameterization trick for efficient training. We call this method "Deep Variational Information Bottleneck", or Deep VIB. We show that models trained with the VIB objective outperform those that are trained with other forms of regularization, in terms of generalization performance and robustness to adversarial attack.

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

This paper introduces MultiBooth, a novel and efficient technique for multi-concept customization in image generation from text. Despite the significant advancements in customized generation methods, particularly with the success of diffusion models, existing methods often struggle with multi-concept scenarios due to low concept fidelity and high inference cost. MultiBooth addresses these issues by dividing the multi-concept generation process into two phases: a single-concept learning phase and a multi-concept integration phase. During the single-concept learning phase, we employ a multi-modal image encoder and an efficient concept encoding technique to learn a concise and discriminative representation for each concept. In the multi-concept integration phase, we use bounding boxes to define the generation area for each concept within the cross-attention map. This method enables the creation of individual concepts within their specified regions, thereby facilitating the formation of multi-concept images. This strategy not only improves concept fidelity but also reduces additional inference cost. MultiBooth surpasses various baselines in both qualitative and quantitative evaluations, showcasing its superior performance and computational efficiency. Project Page: https://multibooth.github.io/

Black-box deep neural networks excel in text classification, yet their application in high-stakes domains is hindered by their lack of interpretability. To address this, we propose Text Bottleneck Models (TBM), an intrinsically interpretable text classification framework that offers both global and local explanations. Rather than directly predicting the output label, TBM predicts categorical values for a sparse set of salient concepts and uses a linear layer over those concept values to produce the final prediction. These concepts can be automatically discovered and measured by a Large Language Model (LLM) without the need for human curation. Experiments on 12 diverse text understanding datasets demonstrate that TBM can rival the performance of black-box baselines such as few-shot GPT-4 and finetuned DeBERTa while falling short against finetuned GPT-3.5. Comprehensive human evaluation validates that TBM can generate high-quality concepts relevant to the task, and the concept measurement aligns well with human judgments, suggesting that the predictions made by TBMs are interpretable. Overall, our findings suggest that TBM is a promising new framework that enhances interpretability with minimal performance tradeoffs.

Diffusion Transformers (DiT) have become the de-facto model for generating high-quality visual content like videos and images. A huge bottleneck is the attention mechanism where complexity scales quadratically with resolution and video length. One logical way to lessen this burden is sparse attention, where only a subset of tokens or patches are included in the calculation. However, existing techniques fail to preserve visual quality at extremely high sparsity levels and might even incur non-negligible compute overheads. % To address this concern, we propose Re-ttention, which implements very high sparse attention for visual generation models by leveraging the temporal redundancy of Diffusion Models to overcome the probabilistic normalization shift within the attention mechanism. Specifically, Re-ttention reshapes attention scores based on the prior softmax distribution history in order to preserve the visual quality of the full quadratic attention at very high sparsity levels. % Experimental results on T2V/T2I models such as CogVideoX and the PixArt DiTs demonstrate that Re-ttention requires as few as 3.1\% of the tokens during inference, outperforming contemporary methods like FastDiTAttn, Sparse VideoGen and MInference. Further, we measure latency to show that our method can attain over 45\% end-to-end % and over 92\% self-attention latency reduction on an H100 GPU at negligible overhead cost. Code available online here: https://github.com/cccrrrccc/Re-ttention{https://github.com/cccrrrccc/Re-ttention}

The rapid proliferation of Vision-Language Models (VLMs) is widely celebrated as the dawn of unified multimodal knowledge discovery but its foundation operates on a dangerous, unquestioned axiom: that current VLMs faithfully synthesise multimodal data. We argue they do not. Instead, a profound crisis of trustworthiness underlies the dominant Vision Encoder-Projector-LLM paradigm. Rather than extracting grounded knowledge from visual inputs, state-of-the-art models frequently exhibit functional blindness, i.e., exploiting strong language priors to bypass severe visual representation bottlenecks. In this work, we challenge the conventional methodology of multimodal evaluation, which relies on data ablation or new dataset creation and therefore fatally conflates dataset biases with architectural incapacity. We propose a radical, information-theoretic departure: the Modality Translation Protocol, designed to quantifiably unmask the Expense of Seeing. By translating semantic payloads rather than ablating them, we formulate three novel metrics -- the Toll (ToS), Curse (CoS), and Fallacy (FoS) of Seeing -- culminating in the Semantic Sufficiency Criterion (SSC). Furthermore, we posit a provocative Divergence Law of Multimodal Scaling, hypothesising that as the underlying language engines scale to unprecedented reasoning capabilities, the mathematical penalty of the visual knowledge bottleneck paradoxically increases. We challenge the KDD community to abandon the illusory pursuit of "multimodal gain". By elevating the SSC from a passive diagnostic constraint to an active architectural blueprint, we provide the rigorous, trustworthy foundation required to force the next generation of AI systems to truly see the data, achieving true multimodal reasoning.

Deep neural networks have demonstrated remarkable performance in supervised learning tasks but require large amounts of labeled data. Self-supervised learning offers an alternative paradigm, enabling the model to learn from data without explicit labels. Information theory has been instrumental in understanding and optimizing deep neural networks. Specifically, the information bottleneck principle has been applied to optimize the trade-off between compression and relevant information preservation in supervised settings. However, the optimal information objective in self-supervised learning remains unclear. In this paper, we review various approaches to self-supervised learning from an information-theoretic standpoint and present a unified framework that formalizes the self-supervised information-theoretic learning problem. We integrate existing research into a coherent framework, examine recent self-supervised methods, and identify research opportunities and challenges. Moreover, we discuss empirical measurement of information-theoretic quantities and their estimators. This paper offers a comprehensive review of the intersection between information theory, self-supervised learning, and deep neural networks.

Humans organize knowledge into compact categories through semantic compression by mapping diverse instances to abstract representations while preserving meaning (e.g., robin and blue jay are both birds; most birds can fly). These concepts reflect a trade-off between expressive fidelity and representational simplicity. Large Language Models (LLMs) demonstrate remarkable linguistic abilities, yet whether their internal representations strike a human-like trade-off between compression and semantic fidelity is unclear. We introduce a novel information-theoretic framework, drawing from Rate-Distortion Theory and the Information Bottleneck principle, to quantitatively compare these strategies. Analyzing token embeddings from a diverse suite of LLMs against seminal human categorization benchmarks, we uncover key divergences. While LLMs form broad conceptual categories that align with human judgment, they struggle to capture the fine-grained semantic distinctions crucial for human understanding. More fundamentally, LLMs demonstrate a strong bias towards aggressive statistical compression, whereas human conceptual systems appear to prioritize adaptive nuance and contextual richness, even if this results in lower compressional efficiency by our measures. These findings illuminate critical differences between current AI and human cognitive architectures, guiding pathways toward LLMs with more human-aligned conceptual representations.

Chain-of-Thought (CoT) prompting improves LLM accuracy on complex tasks but often increases token usage and inference cost. Existing "Budget Forcing" methods reducing cost via fine-tuning with heuristic length penalties, suppress both essential reasoning and redundant filler. We recast efficient reasoning as a lossy compression problem under the Information Bottleneck (IB) principle, and identify a key theoretical gap when applying naive IB to transformers: attention violates the Markov property between prompt, reasoning trace, and response. To resolve this issue, we model CoT generation under the Conditional Information Bottleneck (CIB) principle, where the reasoning trace Z acts as a computational bridge that contains only the information about the response Y that is not directly accessible from the prompt X. This yields a general Reinforcement Learning objective: maximize task reward while compressing completions under a prior over reasoning traces, subsuming common heuristics (e.g., length penalties) as special cases (e.g., uniform priors). In contrast to naive token-counting-based approaches, we introduce a semantic prior that measures token cost by surprisal under a language model prior. Empirically, our CIB objective prunes cognitive bloat while preserving fluency and logic, improving accuracy at moderate compression and enabling aggressive compression with minimal accuracy drop.

Retrieval-augmented generation integrates the capabilities of large language models with relevant information retrieved from an extensive corpus, yet encounters challenges when confronted with real-world noisy data. One recent solution is to train a filter module to find relevant content but only achieve suboptimal noise compression. In this paper, we propose to introduce the information bottleneck theory into retrieval-augmented generation. Our approach involves the filtration of noise by simultaneously maximizing the mutual information between compression and ground output, while minimizing the mutual information between compression and retrieved passage. In addition, we derive the formula of information bottleneck to facilitate its application in novel comprehensive evaluations, the selection of supervised fine-tuning data, and the construction of reinforcement learning rewards. Experimental results demonstrate that our approach achieves significant improvements across various question answering datasets, not only in terms of the correctness of answer generation but also in the conciseness with 2.5% compression rate.

The information bottleneck (IB) approach is popular to improve the generalization, robustness and explainability of deep neural networks. Essentially, it aims to find a minimum sufficient representation t by striking a trade-off between a compression term I(x;t) and a prediction term I(y;t), where I(cdot;cdot) refers to the mutual information (MI). MI is for the IB for the most part expressed in terms of the Kullback-Leibler (KL) divergence, which in the regression case corresponds to prediction based on mean squared error (MSE) loss with Gaussian assumption and compression approximated by variational inference. In this paper, we study the IB principle for the regression problem and develop a new way to parameterize the IB with deep neural networks by exploiting favorable properties of the Cauchy-Schwarz (CS) divergence. By doing so, we move away from MSE-based regression and ease estimation by avoiding variational approximations or distributional assumptions. We investigate the improved generalization ability of our proposed CS-IB and demonstrate strong adversarial robustness guarantees. We demonstrate its superior performance on six real-world regression tasks over other popular deep IB approaches. We additionally observe that the solutions discovered by CS-IB always achieve the best trade-off between prediction accuracy and compression ratio in the information plane. The code is available at https://github.com/SJYuCNEL/Cauchy-Schwarz-Information-Bottleneck.

Augmenting a language model (LM) with k-nearest neighbors (kNN) retrieval on its training data alone can decrease its perplexity, though the underlying reasons for this remains elusive. In this work, we first rule out one previously posited possibility -- the "softmax bottleneck." We further identify the MLP hurdle phenomenon, where the final MLP layer in LMs may impede LM optimization early on. We explore memorization and generalization in language models with two new datasets, where advanced model like GPT-3.5-turbo find generalizing to irrelevant information in the training data challenging. However, incorporating kNN retrieval to vanilla GPT-2 117M can consistently improve performance in this setting.

We introduce Concept Bottleneck Large Language Models (CB-LLMs), a novel framework for building inherently interpretable Large Language Models (LLMs). In contrast to traditional black-box LLMs that rely on limited post-hoc interpretations, CB-LLMs integrate intrinsic interpretability directly into the LLMs -- allowing accurate explanations with scalability and transparency. We build CB-LLMs for two essential NLP tasks: text classification and text generation. In text classification, CB-LLMs is competitive with, and at times outperforms, traditional black-box models while providing explicit and interpretable reasoning. For the more challenging task of text generation, interpretable neurons in CB-LLMs enable precise concept detection, controlled generation, and safer outputs. The embedded interpretability empowers users to transparently identify harmful content, steer model behavior, and unlearn undesired concepts -- significantly enhancing the safety, reliability, and trustworthiness of LLMs, which are critical capabilities notably absent in existing models. Our code is available at https://github.com/Trustworthy-ML-Lab/CB-LLMs.

The Information Bottleneck (IB) principle offers an information-theoretic framework for analyzing the training process of deep neural networks (DNNs). Its essence lies in tracking the dynamics of two mutual information (MI) values: one between the hidden layer and the class label, and the other between the hidden layer and the DNN input. According to the hypothesis put forth by Shwartz-Ziv and Tishby (2017), the training process consists of two distinct phases: fitting and compression. The latter phase is believed to account for the good generalization performance exhibited by DNNs. Due to the challenging nature of estimating MI between high-dimensional random vectors, this hypothesis has only been verified for toy NNs or specific types of NNs, such as quantized NNs and dropout NNs. In this paper, we introduce a comprehensive framework for conducting IB analysis of general NNs. Our approach leverages the stochastic NN method proposed by Goldfeld et al. (2019) and incorporates a compression step to overcome the obstacles associated with high dimensionality. In other words, we estimate the MI between the compressed representations of high-dimensional random vectors. The proposed method is supported by both theoretical and practical justifications. Notably, we demonstrate the accuracy of our estimator through synthetic experiments featuring predefined MI values. Finally, we perform IB analysis on a close-to-real-scale convolutional DNN, which reveals new features of the MI dynamics.

PromptReps showed that an autoregressive language model can be used directly as a retriever by prompting it to generate dense and sparse representations of a query or passage. Extending this to multiple representatives is inefficient for autoregressive models, since tokens must be generated sequentially, and prior multi-token variants did not reliably improve over single-token decoding. We show that the bottleneck is sequential generation, not the multi-token idea itself. DiffRetriever is a representative-token retriever for diffusion language models: it appends K masked positions to the prompt and reads all K in a single bidirectional forward pass. Across in-domain and out-of-domain evaluation, multi-token DiffRetriever substantially improves over single-token on every diffusion backbone we test, while autoregressive multi-token is flat or negative and pays a latency cost that scales with K where diffusion does not. After supervised fine-tuning, DiffRetriever on Dream is the strongest BEIR-7 retriever in our comparison, ahead of PromptReps, the encoder-style DiffEmbed baseline on the same diffusion backbones, and the contrastively fine-tuned single-vector RepLLaMA. A per-query oracle on the frozen base model exceeds contrastive fine-tuning at the same fixed budget, pointing to adaptive budget selection as future work. Code is available at https://github.com/ielab/diffretriever.

In supervised learning, understanding an input's proximity to the training data can help a model decide whether it has sufficient evidence for reaching a reliable prediction. While powerful probabilistic models such as Gaussian Processes naturally have this property, deep neural networks often lack it. In this paper, we introduce Distance Aware Bottleneck (DAB), i.e., a new method for enriching deep neural networks with this property. Building on prior information bottleneck approaches, our method learns a codebook that stores a compressed representation of all inputs seen during training. The distance of a new example from this codebook can serve as an uncertainty estimate for the example. The resulting model is simple to train and provides deterministic uncertainty estimates by a single forward pass. Finally, our method achieves better out-of-distribution (OOD) detection and misclassification prediction than prior methods, including expensive ensemble methods, deep kernel Gaussian Processes, and approaches based on the standard information bottleneck.

Sparse autoencoders (SAEs) promise a unified approach for mechanistic interpretability, concept discovery, and model steering in LLMs and LVLMs. However, realizing this potential requires that the learned features be both interpretable and steerable. To that end, we introduce two new computationally inexpensive interpretability and steerability metrics and conduct a systematic analysis on LVLMs. Our analysis uncovers two observations; (i) a majority of SAE neurons exhibit either low interpretability or low steerability or both, rendering them ineffective for downstream use; and (ii) due to the unsupervised nature of SAEs, user-desired concepts are often absent in the learned dictionary, thus limiting their practical utility. To address these limitations, we propose Concept Bottleneck Sparse Autoencoders (CB-SAE) - a novel post-hoc framework that prunes low-utility neurons and augments the latent space with a lightweight concept bottleneck aligned to a user-defined concept set. The resulting CB-SAE improves interpretability by +32.1% and steerability by +14.5% across LVLMs and image generation tasks. We will make our code and model weights available.

Recent work has shown that training loss scales as a power law with both model size and the number of tokens, and that achieving compute-optimal models requires scaling model size and token count together. However, these scaling laws assume an infinite supply of data and apply primarily in compute-bound settings. As modern large language models increasingly rely on massive internet-scale datasets, the assumption that they are compute-bound is becoming less valid. This shift highlights the need for architectures that prioritize token efficiency. In this work, we investigate the use of the 2-simplicial Transformer, an architecture that generalizes standard dot-product attention to trilinear functions through an efficient Triton kernel implementation. We demonstrate that the 2-simplicial Transformer achieves better token efficiency than standard Transformers: for a fixed token budget, similarly sized models outperform their dot-product counterparts on tasks involving mathematics, coding, reasoning, and logic. We quantify these gains by demonstrating that 2-simplicial attention changes the exponent in the scaling laws for knowledge and reasoning tasks compared to dot product attention.

The last layer of neural language models (LMs) projects output features of dimension D to logits in dimension V, the size of the vocabulary, where usually D ll V. This mismatch is known to raise risks of limited expressivity in neural LMs, creating a so-called softmax bottleneck. We show the softmax bottleneck is not only an expressivity bottleneck but also an optimization bottleneck. Backpropagating V-dimensional gradients through a rank-D linear layer induces unavoidable compression, which alters the training feedback provided to the vast majority of the parameters. We present a theoretical analysis of this phenomenon and measure empirically that 95-99% of the gradient norm is suppressed by the output layer, resulting in vastly suboptimal update directions. We conduct controlled pretraining experiments showing that the gradient bottleneck makes trivial patterns unlearnable, and drastically affects the training dynamics of LLMs. We argue that this inherent flaw contributes to training inefficiencies at scale independently of the model architecture, and raises the need for new LM head designs.

Large Language Models (LLMs) apply uniform computation to all tokens, despite language exhibiting highly non-uniform information density. This token-uniform regime wastes capacity on locally predictable spans while under-allocating computation to semantically critical transitions. We propose Dynamic Large Concept Models (DLCM), a hierarchical language modeling framework that learns semantic boundaries from latent representations and shifts computation from tokens to a compressed concept space where reasoning is more efficient. DLCM discovers variable-length concepts end-to-end without relying on predefined linguistic units. Hierarchical compression fundamentally changes scaling behavior. We introduce the first compression-aware scaling law, which disentangles token-level capacity, concept-level reasoning capacity, and compression ratio, enabling principled compute allocation under fixed FLOPs. To stably train this heterogeneous architecture, we further develop a decoupled μP parametrization that supports zero-shot hyperparameter transfer across widths and compression regimes. At a practical setting (R=4, corresponding to an average of four tokens per concept), DLCM reallocates roughly one-third of inference compute into a higher-capacity reasoning backbone, achieving a +2.69\% average improvement across 12 zero-shot benchmarks under matched inference FLOPs.

We document empirical capability ceilings in decoder-only autoregressive language models across knowledge-intensive tasks. Systematic evaluation of OPT and Pythia model families (70M-30B parameters, spanning 240 times scaling) reveals that knowledge retrieval tasks show negligible accuracy improvement despite smooth loss reduction. On MMLU mathematics benchmarks, accuracy remains flat at 19-20% (below 25% random chance) across all scales while cross-entropy loss decreases by 31%. In contrast, procedural tasks like arithmetic show conventional scaling where both metrics improve together. Attention intervention experiments reveal high sensitivity to perturbation: swapping attention patterns between models causes catastrophic performance collapse (complete accuracy loss) rather than graceful degradation. These measurements have immediate engineering implications: for knowledge-intensive applications using OPT and Pythia architectures, parameter scaling beyond 1-2B offers minimal accuracy gains despite continued loss improvement. Our findings quantify capability-specific scaling failures in these model families to inform resource allocation decisions. Whether these patterns reflect fundamental constraints of decoder-only architectures or implementation-specific limitations remains an open question requiring investigation across diverse architectural approaches.

We rethink test-time scaling laws from a practical efficiency perspective, revealing that the effectiveness of smaller models is significantly overestimated. Prior work, grounded in compute-optimality, overlooks critical memory access bottlenecks introduced by inference-time strategies (e.g., Best-of-N, long CoTs). Our holistic analysis, spanning models from 0.6B to 32B parameters, reveals a new Kinetics Scaling Law that better guides resource allocation by incorporating both computation and memory access costs. Kinetics Scaling Law suggests that test-time compute is more effective when used on models above a threshold than smaller ones. A key reason is that in TTS, attention, rather than parameter count, emerges as the dominant cost factor. Motivated by this, we propose a new scaling paradigm centered on sparse attention, which lowers per-token cost and enables longer generations and more parallel samples within the same resource budget. Empirically, we show that sparse attention models consistently outperform dense counterparts, achieving over 60 points gains in low-cost regimes and over 5 points gains in high-cost regimes for problem-solving accuracy on AIME, encompassing evaluations on state-of-the-art MoEs. These results suggest that sparse attention is essential for realizing the full potential of test-time scaling because, unlike training, where parameter scaling saturates, test-time accuracy continues to improve through increased generation. The code is available at https://github.com/Infini-AI-Lab/Kinetics.

Pretrained transformers achieve the state of the art across tasks in natural language processing, motivating researchers to investigate their inner mechanisms. One common direction is to understand what features are important for prediction. In this paper, we apply information bottlenecks to analyze the attribution of each feature for prediction on a black-box model. We use BERT as the example and evaluate our approach both quantitatively and qualitatively. We show the effectiveness of our method in terms of attribution and the ability to provide insight into how information flows through layers. We demonstrate that our technique outperforms two competitive methods in degradation tests on four datasets. Code is available at https://github.com/bazingagin/IBA.

Test-time compute scaling has emerged as a powerful paradigm for enhancing mathematical reasoning in large language models (LLMs) by allocating additional computational resources during inference. However, current methods employ uniform resource distribution across all reasoning sub-problems, creating fundamental bottlenecks where challenging sub-problems receive insufficient attention while routine operations consume disproportionate resources. This uniform allocation creates performance bottlenecks where additional computational resources yield diminishing returns. Inspired by dual-process theory, we propose SCALE (Selective Resource Allocation), a framework that selectively allocates computational resources based on sub-problem difficulty. SCALE operates through four stages: (1) problem decomposition into sequential reasoning sub-problems, (2) difficulty assessment of each sub-problem to distinguish between routine operations and computationally challenging sub-problems, (3) selective processing mode assignment between System 1 for simple sub-problems and System 2 for complex ones, and (4) sequential execution with context propagation. By concentrating resources on challenging sub-problems while processing routine operations efficiently, SCALE achieves substantial performance improvements with superior resource utilization. Extensive experiments demonstrate that SCALE significantly outperforms uniform scaling baselines, achieving accuracy improvements of up to 13.75 percentage points (57.50% to 71.25% on AIME25) while reducing computational costs by 33%-53%, representing a major advance in test-time scaling that addresses fundamental limitations of current approaches.

Interpretable models are designed to make decisions in a human-interpretable manner. Representatively, Concept Bottleneck Models (CBM) follow a two-step process of concept prediction and class prediction based on the predicted concepts. CBM provides explanations with high-level concepts derived from concept predictions; thus, reliable concept predictions are important for trustworthiness. In this study, we address the ambiguity issue that can harm reliability. While the existence of a concept can often be ambiguous in the data, CBM predicts concepts deterministically without considering this ambiguity. To provide a reliable interpretation against this ambiguity, we propose Probabilistic Concept Bottleneck Models (ProbCBM). By leveraging probabilistic concept embeddings, ProbCBM models uncertainty in concept prediction and provides explanations based on the concept and its corresponding uncertainty. This uncertainty enhances the reliability of the explanations. Furthermore, as class uncertainty is derived from concept uncertainty in ProbCBM, we can explain class uncertainty by means of concept uncertainty. Code is publicly available at https://github.com/ejkim47/prob-cbm.

Chain-of-Thought (CoT) prompting helps Large Language Models (LLMs) tackle complex reasoning by eliciting explicit step-by-step rationales. However, CoT's verbosity increases latency and memory usage and may propagate early errors across long chains. We propose the Reasoning Capsule (R-Capsule), a framework that aims to combine the efficiency of latent reasoning with the transparency of explicit CoT. The core idea is to compress the high-level plan into a small set of learned latent tokens (a Reasoning Capsule) while keeping execution steps lightweight or explicit. This hybrid approach is inspired by the Information Bottleneck (IB) principle, where we encourage the capsule to be approximately minimal yet sufficient for the task. Minimality is encouraged via a low-capacity bottleneck, which helps improve efficiency. Sufficiency is encouraged via a dual objective: a primary task loss for answer accuracy and an auxiliary plan-reconstruction loss that encourages the capsule to faithfully represent the original textual plan. The reconstruction objective helps ground the latent space, thereby improving interpretability and reducing the use of uninformative shortcuts. Our framework strikes a balance between efficiency, accuracy, and interpretability, thereby reducing the visible token footprint of reasoning while maintaining or improving accuracy on complex benchmarks. Our codes are available at: https://anonymous.4open.science/r/Reasoning-Capsule-7BE0

Transformer LLMs have been shown to exhibit strong reasoning ability that scales with inference-time compute, most prominently through token-space "thinking" chains of thought. A growing line of work pushes extra computation into the model's latent space, which we term Auxiliary Latent-Space Computation (ALSC). Existing ALSC methods largely fall into three buckets: (i) token-mediated latent rollouts, (ii) residual/activation steering, and (iii) memory (KV) compression. An underexplored alternative is memory consolidation/reconsolidation, two processes in the brain that are responsible for stabilising newly formed memory traces, and, upon recall, transiently rendering established traces plastic such they can integrate new contextual information before restabilising. In Transformer LLMs, this can be seen as analogous to performing in-place rewrites of new KV segments, and rewrites of recalled past segments. In this work, we give a theoretical justification as to why memory (re)consolidation via KV cache rewrites is beneficial for improved reasoning. We do this through the lens of Information Bottleneck (IB) theory, which posits that model generalisation emerges from an optimal balance between input information compression and retention of predictive information in latent representations. We then introduce the Bottlenecked Transformer, which augments a backbone LLM with a Cache Processor, an auxiliary Transformer that performs periodic, non-causal, in-place KV rewrites at newline-delimited reasoning step boundaries. The Processor consolidates recently written KV entries and reconsolidates a small, top-k attention-selected set of prior entries. We evaluate our Bottlenecked Transformer architecture on math reasoning benchmarks. Our model sees consistent performance gains over vanilla Transformers and pause-token augmented baselines, with gains of up to +6.6pp for selected tasks/backbones.

A variety of Auto-Regressive Video Diffusion Models (ARVDM) have achieved remarkable successes in generating realistic long-form videos. However, theoretical analyses of these models remain scant. In this work, we develop theoretical underpinnings for these models and use our insights to improve the performance of existing models. We first develop Meta-ARVDM, a unified framework of ARVDMs that subsumes most existing methods. Using Meta-ARVDM, we analyze the KL-divergence between the videos generated by Meta-ARVDM and the true videos. Our analysis uncovers two important phenomena inherent to ARVDM -- error accumulation and memory bottleneck. By deriving an information-theoretic impossibility result, we show that the memory bottleneck phenomenon cannot be avoided. To mitigate the memory bottleneck, we design various network structures to explicitly use more past frames. We also achieve a significantly improved trade-off between the mitigation of the memory bottleneck and the inference efficiency by compressing the frames. Experimental results on DMLab and Minecraft validate the efficacy of our methods. Our experiments also demonstrate a Pareto-frontier between the error accumulation and memory bottleneck across different methods.

Recent years have seen significant advancements in foundation models through generative pre-training, yet algorithmic innovation in this space has largely stagnated around autoregressive models for discrete signals and diffusion models for continuous signals. This stagnation creates a bottleneck that prevents us from fully unlocking the potential of rich multi-modal data, which in turn limits the progress on multimodal intelligence. We argue that an inference-first perspective, which prioritizes scaling efficiency during inference time across sequence length and refinement steps, can inspire novel generative pre-training algorithms. Using Inductive Moment Matching (IMM) as a concrete example, we demonstrate how addressing limitations in diffusion models' inference process through targeted modifications yields a stable, single-stage algorithm that achieves superior sample quality with over an order of magnitude greater inference efficiency.

Discrete diffusion language models (dLLMs) generate text by iteratively denoising a masked sequence. However, standard dLLMs condition each denoising step solely on the current hard-masked sequence, while intermediate continuous representations are discarded after sampling and remasking. We term this bottleneck the Information Island issue: continuous information remains isolated within individual denoising steps and fails to propagate across the trajectory. This bottleneck is especially harmful for reasoning, which requires intermediate reasoning state to be preserved and updated across many denoising steps. To address this limitation, we introduce MetaState, a lightweight recurrent augmentation that equips a frozen dLLM backbone with persistent, fixed-size working memory. MetaState comprises three modules with a shared time conditioner: a cross-attention Mixer that reads backbone activations into memory slots, a GRU-style Updater that integrates information across steps, and a cross-attention Injector that writes the updated memory back into the backbone. We train these modules with a dedicated K-step unrolling pipeline to learn multi-step dynamics. MetaState adds only {sim}0.6% trainable parameters while keeping the backbone frozen, and consistently improves reasoning performance over frozen baselines on mathematical reasoning and code generation benchmarks, with an average gain of 4.5% across all evaluations.

We present a simple method that achieves unexpectedly superior performance for Complex Reasoning involved Visual Question Answering. Our solution collects statistical features from high-frequency words of all the questions asked about an image and use them as accurate knowledge for answering further questions of the same image. We are fully aware that this setting is not ubiquitously applicable, and in a more common setting one should assume the questions are asked separately and they cannot be gathered to obtain a knowledge base. Nonetheless, we use this method as an evidence to demonstrate our observation that the bottleneck effect is more severe on the feature extraction part than it is on the knowledge reasoning part. We show significant gaps when using the same reasoning model with 1) ground-truth features; 2) statistical features; 3) detected features from completely learned detectors, and analyze what these gaps mean to researches on visual reasoning topics. Our model with the statistical features achieves the 2nd place in the GQA Challenge 2019.

Despite its simplicity and efficacy, the high token expenditure of self-consistency can limit its practical utility. Here we investigate if self-consistency can be made more token-efficient for long chain-of-thought reasoning tasks, while preserving its parallelism, through early hypothesis pruning. Concretely, we generate all solutions in parallel, but periodically prune intermediate hypotheses that are deemed unnecessary based on two lightweight indicators: (a) the model's own confidence in individual hypotheses, and (b) lexical coverage of all current hypotheses by candidate subsets that are under consideration for continued retention. We design a fast weighted set cover algorithm that utilizes the two indicators; our evaluation of five LLMs on three math benchmarks shows that this method can improve token efficiency for all models, by 10-35% in many cases.

The Mixture of Experts (MoE) is an effective architecture for scaling large language models by leveraging sparse expert activation, optimizing the trade-off between performance and efficiency. However, under expert parallelism, MoE suffers from inference inefficiencies due to imbalanced token-to-expert assignment, where some experts are overloaded while others remain underutilized. This imbalance leads to poor resource utilization and increased latency, as the most burdened expert dictates the overall delay, a phenomenon we define as the \textit{Straggler Effect}. To mitigate this, we propose Capacity-Aware Inference, including two key techniques: (1) \textit{Capacity-Aware Token Drop}, which discards overloaded tokens to regulate the maximum latency of MoE, and (2) \textit{Capacity-Aware Token Reroute}, which reallocates overflowed tokens to underutilized experts, balancing the token distribution. These techniques collectively optimize both high-load and low-load expert utilization, leading to a more efficient MoE inference pipeline. Extensive experiments demonstrate the effectiveness of our methods, showing significant improvements in inference efficiency, e.g., 0.2\% average performance increase and a 1.94times inference speedup on Mixtral-8times7B-Instruct.

Chain-of-Thought (CoT) prompting improves reasoning but often produces long and redundant traces that substantially increase inference cost. We present SyncThink, a training-free and plug-and-play decoding method that reduces CoT overhead without modifying model weights. We find that answer tokens attend weakly to early reasoning and instead focus on the special token "/think", indicating an information bottleneck. Building on this observation, SyncThink monitors the model's own reasoning-transition signal and terminates reasoning. Experiments on GSM8K, MMLU, GPQA, and BBH across three DeepSeek-R1 distilled models show that SyncThink achieves 62.00 percent average Top-1 accuracy using 656 generated tokens and 28.68 s latency, compared to 61.22 percent, 2141 tokens, and 92.01 s for full CoT decoding. On long-horizon tasks such as GPQA, SyncThink can further yield up to +8.1 absolute accuracy by preventing over-thinking.

Language models are increasingly adopting smaller architectures optimized for consumer devices. In this setting, inference efficiency is the primary constraint. Meanwhile, vocabulary sizes continue to grow rapidly, making the classification head a critical bottleneck that accounts for up to 60\% of model parameters, and 50\% of inference compute. We introduce FlashHead, the first efficient drop-in replacement for the dense classification head that is training-free and hardware-friendly. FlashHead builds on principles from information retrieval, reframing that computation at the output head as a retrieval problem rather than a dense classification over the full vocabulary. FlashHead introduces four key innovations: (1) a balanced clustering scheme that structures vocabulary partitions into compact hardware-efficient tensors, (2) extending multiprobe retrieval to language model heads, enabling thousands of clusters to be scored in parallel, (3) a novel inference-time sampling mechanism that extends retrieval beyond top tokens, enabling probabilistic sampling across the full vocabulary, and (4) selective quantization, enabling effective low-bit computation in the head. Experiments on Llama-3.2, Gemma-3, and Qwen-3 show that FlashHead delivers model-level inference speedups of up to 1.75x which maintaining output accuracy compared to the original head. By overcoming the classification head bottleneck, FlashHead establishes a new benchmark for efficient inference and removes a key barrier to developing smaller, capable models for consumer hardware.

Recent advances in Large Language Models (LLMs) have been driven by test-time compute scaling - a strategy that improves reasoning by generating longer, sequential thought processes. While effective, this approach encounters a significant bottleneck as computation increases, where further computation offers only marginal performance gains. We argue this ceiling is not an inherent limit of the model's capability but a flaw in the scaling strategy itself, a phenomenon we term "Tunnel Vision", where a model's imperfect initial steps lock it into a suboptimal reasoning path. To overcome this, we introduce a new scaling paradigm: native thought parallelism. We present ParaThinker, an end-to-end framework that trains an LLM to generate multiple, diverse reasoning paths in parallel and synthesize them into a superior final answer. By exploring different lines of thoughts simultaneously, ParaThinker effectively sidesteps the Tunnel Vision issue and unlocks the model's latent reasoning potential. Our approach demonstrates that scaling compute in parallel (width) is a more effective and efficient way to superior reasoning than simply scaling sequentially (depth). On challenging reasoning benchmarks, ParaThinker achieves substantial accuracy improvements over sequential LLMs (12.3% for 1.5B and 7.5% for 7B models on average with 8 parallel paths), while adding only negligible latency overhead (7.1%). This enables smaller models to surpass much larger counterparts and establishes parallel thinking as a critical, efficient dimension for scaling future LLMs.

Deep neural networks tend to exhibit a bias toward low-rank solutions during training, implicitly learning low-dimensional feature representations. This paper investigates how deep multilayer perceptrons (MLPs) encode these feature manifolds and connects this behavior to the Information Bottleneck (IB) theory. We introduce the concept of local rank as a measure of feature manifold dimensionality and demonstrate, both theoretically and empirically, that this rank decreases during the final phase of training. We argue that networks that reduce the rank of their learned representations also compress mutual information between inputs and intermediate layers. This work bridges the gap between feature manifold rank and information compression, offering new insights into the interplay between information bottlenecks and representation learning.

Recent studies have shown that making a model spend more time thinking through longer Chain of Thoughts (CoTs) enables it to gain significant improvements in complex reasoning tasks. While current researches continue to explore the benefits of increasing test-time compute by extending the CoT lengths of Large Language Models (LLMs), we are concerned about a potential issue hidden behind the current pursuit of test-time scaling: Would excessively scaling the CoT length actually bring adverse effects to a model's reasoning performance? Our explorations on mathematical reasoning tasks reveal an unexpected finding that scaling with longer CoTs can indeed impair the reasoning performance of LLMs in certain domains. Moreover, we discover that there exists an optimal scaled length distribution that differs across different domains. Based on these insights, we propose a Thinking-Optimal Scaling strategy. Our method first uses a small set of seed data with varying response length distributions to teach the model to adopt different reasoning efforts for deep thinking. Then, the model selects its shortest correct response under different reasoning efforts on additional problems for self-improvement. Our self-improved models built upon Qwen2.5-32B-Instruct outperform other distillation-based 32B o1-like models across various math benchmarks, and achieve performance on par with QwQ-32B-Preview.

Deep neural networks perform well on classification tasks where data streams are i.i.d. and labeled data is abundant. Challenges emerge with non-stationary training data streams such as continual learning. One powerful approach that has addressed this challenge involves pre-training of large encoders on volumes of readily available data, followed by task-specific tuning. Given a new task, however, updating the weights of these encoders is challenging as a large number of weights needs to be fine-tuned, and as a result, they forget information about the previous tasks. In the present work, we propose a model architecture to address this issue, building upon a discrete bottleneck containing pairs of separate and learnable key-value codes. Our paradigm will be to encode; process the representation via a discrete bottleneck; and decode. Here, the input is fed to the pre-trained encoder, the output of the encoder is used to select the nearest keys, and the corresponding values are fed to the decoder to solve the current task. The model can only fetch and re-use a sparse number of these key-value pairs during inference, enabling localized and context-dependent model updates. We theoretically investigate the ability of the discrete key-value bottleneck to minimize the effect of learning under distribution shifts and show that it reduces the complexity of the hypothesis class. We empirically verify the proposed method under challenging class-incremental learning scenarios and show that the proposed model - without any task boundaries - reduces catastrophic forgetting across a wide variety of pre-trained models, outperforming relevant baselines on this task.

Interpreting the internal activations of neural networks can produce more faithful explanations of their behavior, but is difficult due to the complex structure of activation space. Existing approaches to scalable interpretability use hand-designed agents that make and test hypotheses about how internal activations relate to external behavior. We propose to instead turn this task into an end-to-end training objective, by training interpretability assistants to accurately predict model behavior from activations through a communication bottleneck. Specifically, an encoder compresses activations to a sparse list of concepts, and a decoder reads this list and answers a natural language question about the model. We show how to pretrain this assistant on large unstructured data, then finetune it to answer questions. The resulting architecture, which we call a Predictive Concept Decoder, enjoys favorable scaling properties: the auto-interp score of the bottleneck concepts improves with data, as does the performance on downstream applications. Specifically, PCDs can detect jailbreaks, secret hints, and implanted latent concepts, and are able to accurately surface latent user attributes.

Chain-of-thought prompting has emerged as a powerful technique for enabling large language models (LLMs) to solve complex reasoning tasks. However, these reasoning chains can be verbose, raising concerns about efficiency. In response, recent works have sought to decrease response lengths through simple prompting strategies (e.g. 'be concise'). In this work, we conduct the first systematic study of the relationship between reasoning length and model performance across a diverse range of compression instructions (e.g. 'use 10 words or less' or 'remove all punctuation'). In doing so, we discover a universal tradeoff between reasoning length and accuracy that persists across even very distinct reasoning chains. We demonstrate that this tradeoff emerges from a sharp threshold behavior at the question level: each task has an intrinsic 'token complexity' - a minimal number of tokens required for successful problem-solving. We show how token complexity enables us to compute information-theoretic limits on the accuracy-compression tradeoff, and find that prompt-based compression strategies operate far from these theoretical limits. This suggests there may be significant room for improvement and our framework provides a benchmark to help researchers evaluate progress in reasoning efficiency. Our work also highlights the importance of adaptive compression -- giving shorter responses for easier questions -- and we show that token complexity is a useful tool for measuring this capability.

Recent advances in visual generation have made significant strides in producing content of exceptional quality. However, most methods suffer from a fundamental problem - a bottleneck of inference computational efficiency. Most of these algorithms involve multiple passes over a transformer model to generate tokens or denoise inputs. However, the model size is kept consistent throughout all iterations, which makes it computationally expensive. In this work, we aim to address this issue primarily through two key ideas - (a) not all parts of the generation process need equal compute, and we design a decode time model scaling schedule to utilize compute effectively, and (b) we can cache and reuse some of the computation. Combining these two ideas leads to using smaller models to process more tokens while large models process fewer tokens. These different-sized models do not increase the parameter size, as they share parameters. We rigorously experiment with ImageNet256times256 , UCF101, and Kinetics600 to showcase the efficacy of the proposed method for image/video generation and frame prediction. Our experiments show that with almost 3times less compute than baseline, our model obtains competitive performance.

Large Language Models (LLMs) exhibit a troubling duality, capable of both remarkable generalization and brittle, verbatim memorization of their training data. This unpredictability undermines their reliability in high-stakes applications. In this work, we propose a unified framework to understand, identify, and control these distinct reasoning modes. First, we introduce a theoretical model based on the Information Bottleneck (IB) principle, formalizing generalization as the learning of a compressed, task-relevant representation and memorization as a failure to compress. Building on this theory, we develop Dynamic Mode Steering (DMS), a novel inference-time algorithm which comprises two components: (1) a lightweight, causally-grounded linear probe that identifies the model's instantaneous reliance on memorization, and (2) a dynamic activation steering mechanism that nudges the model's computation towards pre-identified generalization circuits. We frame DMS as a form of adaptive, self-contrastive decoding. Experiments on reasoning and faithfulness tasks demonstrate that DMS significantly improves logical consistency and factual accuracy, thereby offering a principled approach to enhancing LLM reliability.

The representation disparity between visual generation and understanding imposes a critical gap in integrating these capabilities into a single framework. To bridge this gap, we introduce UniTok, a discrete visual tokenizer that encodes fine-grained details for generation while also capturing high-level semantics for understanding. Despite recent studies have shown that these objectives could induce loss conflicts in training, we reveal that the underlying bottleneck stems from limited representational capacity of discrete tokens. We address this by introducing multi-codebook quantization, which divides vector quantization with several independent sub-codebooks to expand the latent feature space, while avoiding training instability caused by overlarge codebooks. Our method significantly raises the upper limit of unified discrete tokenizers to match or even surpass domain-specific continuous tokenizers. For instance, UniTok achieves a remarkable rFID of 0.38 (versus 0.87 for SD-VAE) and a zero-shot accuracy of 78.6% (versus 76.2% for CLIP) on ImageNet. Our code is available at https://github.com/FoundationVision/UniTok.

Vision Transformers (ViTs) lack the hierarchical inductive biases inherent to Convolutional Neural Networks (CNNs), theoretically allowing them to maintain high-dimensional representations throughout all layers. However, recent observations suggest ViTs often spontaneously manifest a "U-shaped" entropy profile-compressing information in middle layers before expanding it for the final classification. In this work, we demonstrate that this "Inductive Bottleneck" is not an architectural artifact, but a data-dependent adaptation. By analyzing the layer-wise Effective Encoding Dimension (EED) of DINO-trained ViTs across datasets of varying compositional complexity (UC Merced, Tiny ImageNet, and CIFAR-100), we show that the depth of the bottleneck correlates strongly with the semantic abstraction required by the task. We find that while texture-heavy datasets preserve high-rank representations throughout, object-centric datasets drive the network to dampen high-frequency information in middle layers, effectively "learning" a bottleneck to isolate semantic features.

Although deep learning has made great progress in recent years, the exploding economic and environmental costs of training neural networks are becoming unsustainable. To address this problem, there has been a great deal of research on *algorithmically-efficient deep learning*, which seeks to reduce training costs not at the hardware or implementation level, but through changes in the semantics of the training program. In this paper, we present a structured and comprehensive overview of the research in this field. First, we formalize the *algorithmic speedup* problem, then we use fundamental building blocks of algorithmically efficient training to develop a taxonomy. Our taxonomy highlights commonalities of seemingly disparate methods and reveals current research gaps. Next, we present evaluation best practices to enable comprehensive, fair, and reliable comparisons of speedup techniques. To further aid research and applications, we discuss common bottlenecks in the training pipeline (illustrated via experiments) and offer taxonomic mitigation strategies for them. Finally, we highlight some unsolved research challenges and present promising future directions.

Despite widespread adoption, multimodal large language models (MLLMs) suffer performance degradation when encountering unfamiliar queries under distribution shifts. Existing methods to improve MLLM generalization typically require either more instruction data or larger advanced model architectures, both of which incur non-trivial human labor or computational costs. In this work, we take an alternative approach to enhance the robustness of MLLMs under distribution shifts, from a representation learning perspective. Inspired by the information bottleneck (IB) principle, we derive a variational lower bound of the IB for MLLMs and devise a practical implementation, Visual Instruction Bottleneck Tuning (Vittle). We then provide a theoretical justification of Vittle by revealing its connection to an information-theoretic robustness metric of MLLM. Empirical validation of three MLLMs on open-ended and closed-form question answering and object hallucination detection tasks over 45 datasets, including 30 shift scenarios, demonstrates that Vittle consistently improves the MLLM's robustness under shifts by pursuing the learning of a minimal sufficient representation.

To improve how neural networks function it is crucial to understand their learning process. The information bottleneck theory of deep learning proposes that neural networks achieve good generalization by compressing their representations to disregard information that is not relevant to the task. However, empirical evidence for this theory is conflicting, as compression was only observed when networks used saturating activation functions. In contrast, networks with non-saturating activation functions achieved comparable levels of task performance but did not show compression. In this paper we developed more robust mutual information estimation techniques, that adapt to hidden activity of neural networks and produce more sensitive measurements of activations from all functions, especially unbounded functions. Using these adaptive estimation techniques, we explored compression in networks with a range of different activation functions. With two improved methods of estimation, firstly, we show that saturation of the activation function is not required for compression, and the amount of compression varies between different activation functions. We also find that there is a large amount of variation in compression between different network initializations. Secondary, we see that L2 regularization leads to significantly increased compression, while preventing overfitting. Finally, we show that only compression of the last layer is positively correlated with generalization.

Attention based Transformer architecture has enabled significant advances in the field of natural language processing. In addition to new pre-training techniques, recent improvements crucially rely on working with a relatively larger embedding dimension for tokens. Unfortunately, this leads to models that are prohibitively large to be employed in the downstream tasks. In this paper we identify one of the important factors contributing to the large embedding size requirement. In particular, our analysis highlights that the scaling between the number of heads and the size of each head in the current architecture gives rise to a low-rank bottleneck in attention heads, causing this limitation. We further validate this in our experiments. As a solution we propose to set the head size of an attention unit to input sequence length, and independent of the number of heads, resulting in multi-head attention layers with provably more expressive power. We empirically show that this allows us to train models with a relatively smaller embedding dimension and with better performance scaling.

Recent Large Reasoning Models (LRMs), such as DeepSeek-R1 and OpenAI o1, have demonstrated strong performance gains by scaling up the length of Chain-of-Thought (CoT) reasoning during inference. However, a growing concern lies in their tendency to produce excessively long reasoning traces, which are often filled with redundant content (e.g., repeated definitions), over-analysis of simple problems, and superficial exploration of multiple reasoning paths for harder tasks. This inefficiency introduces significant challenges for training, inference, and real-world deployment (e.g., in agent-based systems), where token economy is critical. In this survey, we provide a comprehensive overview of recent efforts aimed at improving reasoning efficiency in LRMs, with a particular focus on the unique challenges that arise in this new paradigm. We identify common patterns of inefficiency, examine methods proposed across the LRM lifecycle, i.e., from pretraining to inference, and discuss promising future directions for research. To support ongoing development, we also maintain a real-time GitHub repository tracking recent progress in the field. We hope this survey serves as a foundation for further exploration and inspires innovation in this rapidly evolving area.

Pretraining large language models (LLMs) is resource-intensive, often requiring months of training time even with high-end GPU clusters. There are two approaches of mitigating such computational demands: reusing smaller models to train larger ones (upcycling), and training computationally efficient models like mixture-of-experts (MoE). In this paper, we study the upcycling of LLMs to MoE models, of which the scaling behavior remains underexplored. Through extensive experiments, we identify empirical scaling laws that describe how performance depends on dataset size and model configuration. Particularly, we show that, while scaling these factors improves performance, there is a novel interaction term between the dense and upcycled training dataset that limits the efficiency of upcycling at large computational budgets. Based on these findings, we provide guidance to scale upcycling, and establish conditions under which upcycling outperforms from-scratch trainings within budget constraints.

Despite the recent advances in personalized text-to-image (P-T2I) generative models, subject-driven T2I remains challenging. The primary bottlenecks include 1) Intensive training resource requirements, 2) Hyper-parameter sensitivity leading to inconsistent outputs, and 3) Balancing the intricacies of novel visual concept and composition alignment. We start by re-iterating the core philosophy of T2I diffusion models to address the above limitations. Predominantly, contemporary subject-driven T2I approaches hinge on Latent Diffusion Models (LDMs), which facilitate T2I mapping through cross-attention layers. While LDMs offer distinct advantages, P-T2I methods' reliance on the latent space of these diffusion models significantly escalates resource demands, leading to inconsistent results and necessitating numerous iterations for a single desired image. Recently, ECLIPSE has demonstrated a more resource-efficient pathway for training UnCLIP-based T2I models, circumventing the need for diffusion text-to-image priors. Building on this, we introduce lambda-ECLIPSE. Our method illustrates that effective P-T2I does not necessarily depend on the latent space of diffusion models. lambda-ECLIPSE achieves single, multi-subject, and edge-guided T2I personalization with just 34M parameters and is trained on a mere 74 GPU hours using 1.6M image-text interleaved data. Through extensive experiments, we also establish that lambda-ECLIPSE surpasses existing baselines in composition alignment while preserving concept alignment performance, even with significantly lower resource utilization.

We observe that the mapping between an image's representation in one model to its representation in another can be learned surprisingly well with just a linear layer, even across diverse models. Building on this observation, we propose text-to-concept, where features from a fixed pretrained model are aligned linearly to the CLIP space, so that text embeddings from CLIP's text encoder become directly comparable to the aligned features. With text-to-concept, we convert fixed off-the-shelf vision encoders to surprisingly strong zero-shot classifiers for free, with accuracy at times even surpassing that of CLIP, despite being much smaller models and trained on a small fraction of the data compared to CLIP. We show other immediate use-cases of text-to-concept, like building concept bottleneck models with no concept supervision, diagnosing distribution shifts in terms of human concepts, and retrieving images satisfying a set of text-based constraints. Lastly, we demonstrate the feasibility of concept-to-text, where vectors in a model's feature space are decoded by first aligning to the CLIP before being fed to a GPT-based generative model. Our work suggests existing deep models, with presumably diverse architectures and training, represent input samples relatively similarly, and a two-way communication across model representation spaces and to humans (through language) is viable.

Text-to-image models produce images that align well with natural language prompts, but compositional generation has long been a central challenge. Models often struggle to satisfy multiple concepts within a single prompt, frequently omitting some concepts and resulting in partial success. Such failures highlight the difficulty of jointly optimizing multiple concepts during reward optimization, where competing concepts can interfere with one another. To address this limitation, we propose Correlation-Weighted Multi-Reward Optimization (\ours), a framework that leverages the correlation structure among concept rewards to adaptively weight each attribute concept in optimization. By accounting for interactions among concepts, \ours balances competing reward signals and emphasizes concepts that are partially satisfied yet inconsistently generated across samples, improving compositional generation. Specifically, we decompose multi-concept prompts into pre-defined concept groups (\eg, objects, attributes, and relations) and obtain reward signals from dedicated reward models for each concept. We then adaptively reweight these rewards, assigning higher weights to conflicting or hard-to-satisfy concepts using correlation-based difficulty estimation. By focusing optimization on the most challenging concepts within each group, \ours encourages the model to consistently satisfy all requested attributes simultaneously. We apply our approach to train state-of-the-art diffusion models, SD3.5 and FLUX.1-dev, and demonstrate consistent improvements on challenging multi-concept benchmarks, including ConceptMix, GenEval 2, and T2I-CompBench.

Multi-Head Attention (MHA) is the core computational primitive underlying modern Large Language Models (LLMs). However, MHA suffers from a fundamental linear scaling limitation: H attention heads produce exactly H independent attention matrices, with no communication between heads during attention computation. This becomes problematic for multi-step reasoning, where correct answers depend on aggregating evidence from multiple parts of the context and composing latent token-to-token relations over a chain of intermediate inferences. To address this, we propose Interleaved Head Attention (IHA), which enables cross-head mixing by constructing P pseudo-heads per head (typically P=H), where each pseudo query/key/value is a learned linear combination of all H original queries, keys and values respectively. Interactions between pseudo-query and pseudo-key heads induce up to P^2 attention patterns per head with modest parameter overhead O(H^2P). We provide theory showing improved efficiency in terms of number of parameters on the synthetic Polynomial task (IHA uses Θ(kn^2) parameters vs. Θ(kn^2) for MHA) and on the synthetic order-sensitive CPM-3 task (IHA uses lceilN_{max}rceil heads vs. N_{max} for MHA). On real-world benchmarks, IHA improves Multi-Key retrieval on RULER by 10-20% (4k-16k) and, after fine-tuning for reasoning on OpenThoughts, improves GSM8K by 5.8% and MATH-500 by 2.8% (Majority Vote) over full attention.

Human cognition typically involves thinking through abstract, fluid concepts rather than strictly using discrete linguistic tokens. Current reasoning models, however, are constrained to reasoning within the boundaries of human language, processing discrete token embeddings that represent fixed points in the semantic space. This discrete constraint restricts the expressive power and upper potential of such reasoning models, often causing incomplete exploration of reasoning paths, as standard Chain-of-Thought (CoT) methods rely on sampling one token per step. In this work, we introduce Soft Thinking, a training-free method that emulates human-like "soft" reasoning by generating soft, abstract concept tokens in a continuous concept space. These concept tokens are created by the probability-weighted mixture of token embeddings, which form the continuous concept space, enabling smooth transitions and richer representations that transcend traditional discrete boundaries. In essence, each generated concept token encapsulates multiple meanings from related discrete tokens, implicitly exploring various reasoning paths to converge effectively toward the correct answer. Empirical evaluations on diverse mathematical and coding benchmarks consistently demonstrate the effectiveness and efficiency of Soft Thinking, improving pass@1 accuracy by up to 2.48 points while simultaneously reducing token usage by up to 22.4% compared to standard CoT. Qualitative analysis further reveals that Soft Thinking outputs remain highly interpretable and readable, highlighting the potential of Soft Thinking to break the inherent bottleneck of discrete language-based reasoning. Code is available at https://github.com/eric-ai-lab/Soft-Thinking.

Why do even the most powerful 7B-parameter embedding models struggle with simple retrieval tasks that the decades old BM25 handles with ease? Recent theory suggests that this happens because of a dimensionality bottleneck. This occurs when we force infinite linguistic nuances into small, fixed-length learned vectors. We developed NUMEN to break this bottleneck by removing the learning process entirely. Instead of training heavy layers to map text to a constrained space, NUMEN uses deterministic character hashing to project language directly onto high-dimensional vectors. This approach requires no training, supports an unlimited vocabulary, and allows the geometric capacity scale as needed. On the LIMIT benchmark, NUMEN achieves 93.90 % Recall@100 at 32,768 dimensions. This makes it the first dense retrieval model to officially surpass the sparse BM25 baseline 93.6 %. Our findings show that the real problem in dense retrieval isn't the architecture, but the embedding layer itself. The solution isn't necessarily smarter training, but simply providing more room to breathe.

Computational workloads composing traditional Transformer models are starkly bifurcated. Multi-Head Attention (MHA) is memory-bound, with low arithmetic intensity, while feedforward layers are compute-bound. This dichotomy has long motivated research into specialized hardware to mitigate the MHA bottleneck. This paper argues that recent architectural shifts, namely Multi-head Latent Attention (MLA) and Mixture-of-Experts (MoE), challenge the premise of specialized attention hardware. We make two key observations. First, the arithmetic intensity of MLA is over two orders of magnitude greater than that of MHA, shifting it close to a compute-bound regime well-suited for modern accelerators like GPUs. Second, by distributing MoE experts across a pool of accelerators, their arithmetic intensity can be tuned through batching to match that of the dense layers, creating a more balanced computational profile. These findings reveal a diminishing need for specialized attention hardware. The central challenge for next-generation Transformers is no longer accelerating a single memory-bound layer. Instead, the focus must shift to designing balanced systems with sufficient compute, memory capacity, memory bandwidth, and high-bandwidth interconnects to manage the diverse demands of large-scale models.

Adversarial examples, generated by carefully crafted perturbation, have attracted considerable attention in research fields. Recent works have argued that the existence of the robust and non-robust features is a primary cause of the adversarial examples, and investigated their internal interactions in the feature space. In this paper, we propose a way of explicitly distilling feature representation into the robust and non-robust features, using Information Bottleneck. Specifically, we inject noise variation to each feature unit and evaluate the information flow in the feature representation to dichotomize feature units either robust or non-robust, based on the noise variation magnitude. Through comprehensive experiments, we demonstrate that the distilled features are highly correlated with adversarial prediction, and they have human-perceptible semantic information by themselves. Furthermore, we present an attack mechanism intensifying the gradient of non-robust features that is directly related to the model prediction, and validate its effectiveness of breaking model robustness.

Parallel thinking enhances LLM reasoning by multi-path sampling and aggregation. In system-level evaluations, a global parallelism level N is allocated to all samples, typically set large to maximize overall dataset accuracy. However, due to sample heterogeneity, some samples can achieve comparable performance with a smaller N'< N, causing budget redundancy. This incompatibility between system-level efficacy and sample-level efficiency constitutes the overscaling curse. In this paper, we formalize and quantify the overscaling curse, showing its universality and severity in practice, and analyze its trigger mechanism. We then propose a lightweight method, T2, to break the overscaling curse, which utilizes latent representations to estimate the optimal parallelism level for each sample before decoding. Experiments show that T2 significantly reduces cost while maintaining comparable performance, enabling more efficient parallel thinking.

Federated Learning (FL) enables edge devices or clients to collaboratively train machine learning (ML) models without sharing their private data. Much of the existing work in FL focuses on efficiently learning a model for a single task. In this paper, we study simultaneous training of multiple FL models using a common set of clients. The few existing simultaneous training methods employ synchronous aggregation of client updates, which can cause significant delays because large models and/or slow clients can bottleneck the aggregation. On the other hand, a naive asynchronous aggregation is adversely affected by stale client updates. We propose FedAST, a buffered asynchronous federated simultaneous training algorithm that overcomes bottlenecks from slow models and adaptively allocates client resources across heterogeneous tasks. We provide theoretical convergence guarantees for FedAST for smooth non-convex objective functions. Extensive experiments over multiple real-world datasets demonstrate that our proposed method outperforms existing simultaneous FL approaches, achieving up to 46.0% reduction in time to train multiple tasks to completion.

Recent LLMs have significantly improved reasoning capabilities, primarily by including an explicit, lengthy Thinking process as part of generation. In this paper, we question whether this explicit thinking is necessary. Using the state-of-the-art DeepSeek-R1-Distill-Qwen, we find that bypassing the thinking process via simple prompting, denoted as NoThinking, can be surprisingly effective. When controlling for the number of tokens, NoThinking outperforms Thinking across a diverse set of seven challenging reasoning datasets--including mathematical problem solving, formal theorem proving, and coding--especially in low-budget settings, e.g., 51.3 vs. 28.9 on ACM 23 with 700 tokens. Notably, the performance of NoThinking becomes more competitive with pass@k as k increases. Building on this observation, we demonstrate that a parallel scaling approach that uses NoThinking to generate N outputs independently and aggregates them is highly effective. For aggregation, we use task-specific verifiers when available, or we apply simple best-of-N strategies such as confidence-based selection. Our method outperforms a range of baselines with similar latency using Thinking, and is comparable to Thinking with significantly longer latency (up to 9x). Together, our research encourages a reconsideration of the necessity of lengthy thinking processes, while also establishing a competitive reference for achieving strong reasoning performance in low-budget settings or at low latency using parallel scaling.

Large language models (LLMs) benefit from test-time scaling but are often hampered by high inference latency. Speculative decoding is a natural way to accelerate the scaling process; however, scaling along both the parallel and sequential dimensions poses significant challenges, including substantial memory-bound execution and synchronization overhead. We introduce ATTS (Asynchronous Test-Time Scaling), a statistically guaranteed adaptive scaling framework that follows the hypothesis testing process to address these challenges. By revisiting arithmetic intensity, ATTS identifies synchronization as the primary bottleneck. It enables asynchronous inference through online calibration and proposes an ordinal classification algorithm that supports a three-stage rejection sampling pipeline, scaling along both the sequential and parallel axes. Across experiments on the MATH, AMC23, AIME24, and AIME25 datasets and across multiple draft-target model families, we show that ATTS delivers up to 56.7x speedup in test-time scaling and a 4.14x throughput improvement, while maintaining accurate control of the rejection rate, reducing latency and memory overhead, and incurring no accuracy loss. By scaling both in parallel and sequential dimensions, we enable the 1.5B/70B draft/target model combination to achieve the performance of the state-of-the-art reasoning model o3-mini (high) on the AIME dataset. We have released the code at https://github.com/menik1126/asynchronous-test-time-scaling.

While generative models produce high-quality images of concepts learned from a large-scale database, a user often wishes to synthesize instantiations of their own concepts (for example, their family, pets, or items). Can we teach a model to quickly acquire a new concept, given a few examples? Furthermore, can we compose multiple new concepts together? We propose Custom Diffusion, an efficient method for augmenting existing text-to-image models. We find that only optimizing a few parameters in the text-to-image conditioning mechanism is sufficiently powerful to represent new concepts while enabling fast tuning (~6 minutes). Additionally, we can jointly train for multiple concepts or combine multiple fine-tuned models into one via closed-form constrained optimization. Our fine-tuned model generates variations of multiple, new concepts and seamlessly composes them with existing concepts in novel settings. Our method outperforms several baselines and concurrent works, regarding both qualitative and quantitative evaluations, while being memory and computationally efficient.

We prove theoretically that generalization improves not only through data scaling but also by compressing internal representations. To operationalize this insight, we introduce the Information Bottleneck Language Modeling (IBLM) objective, which reframes language modeling as a constrained optimization problem: minimizing representation entropy subject to optimal prediction performance. Empirically, we observe an emergent memorization-compression cycle during LLM pretraining, evidenced by oscillation positive/negative gradient alignment between cross-entropy and Matrix-Based Entropy (MBE), a measure of representation entropy. This pattern closely mirrors the predictive-compressive trade-off prescribed by IBLM and also parallels the biological alternation between awake learning and sleep consolidation. Motivated by this observation, we propose Gated Phase Transition (GAPT), a training algorithm that adaptively switches between memorization and compression phases. When applied to GPT-2 pretraining on FineWeb dataset, GAPT reduces MBE by 50% and improves cross-entropy by 4.8%. GAPT improves OOD generalizatino by 35% in a pretraining task on arithmetic multiplication. In a setting designed to simulate catastrophic forgetting, GAPT reduces interference by compressing and separating representations, achieving a 97% improvement in separation - paralleling the functional role of sleep consolidation.

We show that a variety of modern deep learning tasks exhibit a "double-descent" phenomenon where, as we increase model size, performance first gets worse and then gets better. Moreover, we show that double descent occurs not just as a function of model size, but also as a function of the number of training epochs. We unify the above phenomena by defining a new complexity measure we call the effective model complexity and conjecture a generalized double descent with respect to this measure. Furthermore, our notion of model complexity allows us to identify certain regimes where increasing (even quadrupling) the number of train samples actually hurts test performance.

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions of tokens. The standard approach is to represent each feature value as a d-dimensional embedding, introducing hundreds of billions of parameters for extremely high-cardinality features. This bottleneck has led to substantial progress in alternative embedding algorithms. Many of these methods, however, make the assumption that each feature uses an independent embedding table. This work introduces a simple yet highly effective framework, Feature Multiplexing, where one single representation space is used across many different categorical features. Our theoretical and empirical analysis reveals that multiplexed embeddings can be decomposed into components from each constituent feature, allowing models to distinguish between features. We show that multiplexed representations lead to Pareto-optimal parameter-accuracy tradeoffs for three public benchmark datasets. Further, we propose a highly practical approach called Unified Embedding with three major benefits: simplified feature configuration, strong adaptation to dynamic data distributions, and compatibility with modern hardware. Unified embedding gives significant improvements in offline and online metrics compared to highly competitive baselines across five web-scale search, ads, and recommender systems, where it serves billions of users across the world in industry-leading products.

Sequential models, such as Recurrent Neural Networks and Neural Ordinary Differential Equations, have long suffered from slow training due to their inherent sequential nature. For many years this bottleneck has persisted, as many thought sequential models could not be parallelized. We challenge this long-held belief with our parallel algorithm that accelerates GPU evaluation of sequential models by up to 3 orders of magnitude faster without compromising output accuracy. The algorithm does not need any special structure in the sequential models' architecture, making it applicable to a wide range of architectures. Using our method, training sequential models can be more than 10 times faster than the common sequential method without any meaningful difference in the training results. Leveraging this accelerated training, we discovered the efficacy of the Gated Recurrent Unit in a long time series classification problem with 17k time samples. By overcoming the training bottleneck, our work serves as the first step to unlock the potential of non-linear sequential models for long sequence problems.

Recent advances in language modeling consist in pretraining highly parameterized neural networks on extremely large web-mined text corpora. Training and inference with such models can be costly in practice, which incentivizes the use of smaller counterparts. However, it has been observed that smaller models can suffer from saturation, characterized as a drop in performance at some advanced point in training followed by a plateau. In this paper, we find that such saturation can be explained by a mismatch between the hidden dimension of smaller models and the high rank of the target contextual probability distribution. This mismatch affects the performance of the linear prediction head used in such models through the well-known softmax bottleneck phenomenon. We measure the effect of the softmax bottleneck in various settings and find that models based on less than 1000 hidden dimensions tend to adopt degenerate latent representations in late pretraining, which leads to reduced evaluation performance.

The pervasive "memory wall" bottleneck is significantly amplified in modern large-scale Mixture-of-Experts (MoE) architectures. MoE's inherent architectural sparsity leads to sparse arithmetic compute and also introduces substantial activation memory overheads -- driven by large token routing buffers and the need to materialize and buffer intermediate tensors. This memory pressure limits the maximum batch size and sequence length that can fit on GPUs, and also results in excessive data movements that hinders performance and efficient model scaling. We present MoEBlaze, a memory-efficient MoE training framework that addresses these issues through a co-designed system approach: (i) an end-to-end token dispatch and MoE training method with optimized data structures to eliminate intermediate buffers and activation materializing, and (ii) co-designed kernels with smart activation checkpoint to mitigate memory footprint while simultaneously achieving better performance. We demonstrate that MoEBlaze can achieve over 4x speedups and over 50% memory savings compared to existing MoE frameworks.

Efficient parallelization of Large Language Models (LLMs) with long sequences is essential but challenging due to their significant computational and memory demands, particularly stemming from communication bottlenecks in attention mechanisms. While sequence parallelism (SP) has been introduced as a potential solution, existing methods often suffer from limited scalability or inefficiency, rendering their effectiveness. Ring-Attention demonstrates the potential for scaling sequence processing but faces significant limitations due to its reliance on peer-to-peer (P2P) communication and inefficient utilization of network resources. As the degree of SP increases, the quadratic decrease in computation time per step contrasts sharply with the linear reduction in communication volume, exacerbating communication bottlenecks. To address these challenges, we propose TokenRing, a fine-grained parallel framework that leverages bidirectional P2P communication to effectively overlap computation and data transmission. By partitioning the attention block and concurrently transmitting Query and block outputs (i.e., block_out and block_lse) within a fully connected mesh topology, TokenRing achieves significant reductions in communication overhead and better load balancing. These innovations improve the scalability and efficiency of distributed Transformer models, particularly for long-context sequences. Experimental results demonstrate that TokenRing enhances throughput and reduces communication latency. Moreover, its design adapts seamlessly to various multi-GPU interconnect solutions, such as Huawei Ascend, ensuring broad compatibility and cost-effectiveness for distributed LLM inference and training. The code is available at: https://github.com/ACA-Lab-SJTU/token-ring.

The availability of unprecedented unsupervised training data, along with neural scaling laws, has resulted in an unprecedented surge in model size and compute requirements for serving/training LLMs. However, the main performance bottleneck is increasingly shifting to memory bandwidth. Over the past 20 years, peak server hardware FLOPS has been scaling at 3.0x/2yrs, outpacing the growth of DRAM and interconnect bandwidth, which have only scaled at 1.6 and 1.4 times every 2 years, respectively. This disparity has made memory, rather than compute, the primary bottleneck in AI applications, particularly in serving. Here, we analyze encoder and decoder Transformer models and show how memory bandwidth can become the dominant bottleneck for decoder models. We argue for a redesign in model architecture, training, and deployment strategies to overcome this memory limitation.

The dominant paradigm for Audio-Text Retrieval (ATR) relies on mini-batch-based contrastive learning. This process, however, is inherently limited by what we formalize as the Gradient Locality Bottleneck (GLB), which structurally prevents models from leveraging out-of-batch knowledge and thus impairs fine-grained and long-tail learning. While external knowledge-enhanced methods can alleviate the GLB, we identify a critical, unaddressed side effect: the Representation-Drift Mismatch (RDM), where a static knowledge base becomes progressively misaligned with the evolving model, turning guidance into noise. To address this dual challenge, we propose the Adaptive Self-improving Knowledge (ASK) framework, a model-agnostic, plug-and-play solution. ASK breaks the GLB via multi-grained knowledge injection, systematically mitigates RDM through dynamic knowledge refinement, and introduces a novel adaptive reliability weighting scheme to ensure consistent knowledge contributes to optimization. Experimental results on two benchmark datasets with superior, state-of-the-art performance justify the efficacy of our proposed ASK framework.

Recent advancements in slow thinking reasoning models have shown exceptional performance in complex reasoning tasks. However, these models often exhibit overthinking (generating redundant reasoning steps for simple problems), leading to excessive computational resource usage. While current mitigation strategies uniformly reduce reasoning tokens, they risk degrading performance on challenging tasks that require extended reasoning. This paper introduces Difficulty-Adaptive Slow Thinking (DAST), a novel framework that enables models to autonomously adjust the length of Chain-of-Thought (CoT) based on problem difficulty. We first propose a Token Length Budget (TLB) metric to quantify difficulty, then leverage budget-aware reward shaping and budget preference optimization to implement DAST. DAST penalizes overlong responses for simple tasks while incentivizing sufficient reasoning for complex problems. Experiments on diverse datasets and model scales demonstrate that DAST effectively mitigates overthinking (reducing token usage by over 30\% on average) while preserving reasoning accuracy on complex problems. Our codes and models are available at https://github.com/AnonymousUser0520/AnonymousRepo01.

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

Current text-to-image diffusion models have achieved groundbreaking results in image generation tasks. However, the unavoidable inclusion of sensitive information during pre-training introduces significant risks such as copyright infringement and privacy violations in the generated images. Machine Unlearning (MU) provides a effective way to the sensitive concepts captured by the model, has been shown to be a promising approach to addressing these issues. Nonetheless, existing MU methods for concept erasure encounter two primary bottlenecks: 1) generalization issues, where concept erasure is effective only for the data within the unlearn set, and prompts outside the unlearn set often still result in the generation of sensitive concepts; and 2) utility drop, where erasing target concepts significantly degrades the model's performance. To this end, this paper first proposes a concept domain correction framework for unlearning concepts in diffusion models. By aligning the output domains of sensitive concepts and anchor concepts through adversarial training, we enhance the generalizability of the unlearning results. Secondly, we devise a concept-preserving scheme based on gradient surgery. This approach alleviates the parts of the unlearning gradient that contradict the relearning gradient, ensuring that the process of unlearning minimally disrupts the model's performance. Finally, extensive experiments validate the effectiveness of our model, demonstrating our method's capability to address the challenges of concept unlearning in diffusion models while preserving model utility.

Scaling the size of language models to tens of billions of parameters has led to impressive performance on a wide range of tasks. At generation, these models are used auto-regressively, requiring a forward pass for each generated token, and thus reading the full set of parameters from memory. This memory access forms the primary bottleneck for generation and it worsens as the model size increases. Moreover, executing a forward pass for multiple tokens in parallel often takes nearly the same time as it does for just one token. These two observations lead to the development of speculative sampling, where a second smaller model is used to draft a few tokens, that are then validated or rejected using a single forward pass of the large model. Unfortunately, this method requires two models that share the same tokenizer and thus limits its adoption. As an alternative, we propose to use parallel decoding as a way to draft multiple tokens from a single model with no computational cost, nor the need for a second model. Our approach only requires an additional input token that marks the words that will be generated simultaneously. We show promising performance (up to 30% speed-up) while requiring only as few as O(d_{emb}) additional parameters.

Adding memory to pretrained language models typically requires architectural changes or weight modification. We present Prometheus Mind, which retrofits memory to a frozen Qwen3-4B using 11 modular adapters (530MB, 7% overhead) -- fully reversible by removing the adapters. Building this system required solving four problems: (1) Extraction -- we develop Contrastive Direction Discovery (CDD), which finds semantic directions via minimal pairs without labeled data. (2) Training -- end-to-end optimization collapses; stage-wise training of each adapter on simple proxy tasks succeeds. (3) Injection -- learned encoders fail to generalize; we find that lm_head-weight rows already provide the mapping we need, requiring no training. (4) Hidden state collapse -- transformers make ``wife'' and ``brother'' 0.98+ similar; we train projections to recover distinction (0.98 rightarrow 0.09). On PrometheusExtract-132 (132 cases), the system achieves 94.4% retrieval on clean inputs (n=54, 95% CI: [84.9%, 98.1%]), degrading to 19.4% on informal inputs with ellipsis, filler words, or implicit subjects (n=36). The primary bottleneck is relation classification (47.3% accuracy), responsible for most extraction errors.

Large language models allocate uniform computation across all tokens, ignoring that some sequences are trivially predictable while others require deep reasoning. We introduce ConceptMoE, which dynamically merges semantically similar tokens into concept representations, performing implicit token-level compute allocation. A learnable chunk module identifies optimal boundaries by measuring inter-token similarity, compressing sequences by a target ratio R before they enter the compute-intensive concept model. Crucially, the MoE architecture enables controlled evaluation: we reallocate saved computation to match baseline activated FLOPs (excluding attention map computation) and total parameters, isolating genuine architectural benefits. Under these conditions, ConceptMoE consistently outperforms standard MoE across language and vision-language tasks, achieving +0.9 points on language pretraining, +2.3 points on long context understanding, and +0.6 points on multimodal benchmarks. When converting pretrained MoE during continual training with layer looping, gains reach +5.5 points, demonstrating practical applicability. Beyond performance, ConceptMoE reduces attention computation by up to R^2times and KV cache by Rtimes. At R=2, empirical measurements show prefill speedups reaching 175\% and decoding speedups up to 117\% on long sequences. The minimal architectural modifications enable straightforward integration into existing MoE, demonstrating that adaptive concept-level processing fundamentally improves both effectiveness and efficiency of large language models.

Many interpretable AI approaches have been proposed to provide plausible explanations for a model's decision-making. However, configuring an explainable model that effectively communicates among computational modules has received less attention. A recently proposed shared global workspace theory showed that networks of distributed modules can benefit from sharing information with a bottlenecked memory because the communication constraints encourage specialization, compositionality, and synchronization among the modules. Inspired by this, we propose Concept-Centric Transformers, a simple yet effective configuration of the shared global workspace for interpretability, consisting of: i) an object-centric-based memory module for extracting semantic concepts from input features, ii) a cross-attention mechanism between the learned concept and input embeddings, and iii) standard classification and explanation losses to allow human analysts to directly assess an explanation for the model's classification reasoning. We test our approach against other existing concept-based methods on classification tasks for various datasets, including CIFAR100, CUB-200-2011, and ImageNet, and we show that our model achieves better classification accuracy than all baselines across all problems but also generates more consistent concept-based explanations of classification output.

Reasoning models have demonstrated remarkable progress in solving complex and logic-intensive tasks by generating extended Chain-of-Thoughts (CoTs) prior to arriving at a final answer. Yet, the emergence of this "slow-thinking" paradigm, with numerous tokens generated in sequence, inevitably introduces substantial computational overhead. To this end, it highlights an urgent need for effective acceleration. This survey aims to provide a comprehensive overview of recent advances in efficient reasoning. It categorizes existing works into three key directions: (1) shorter - compressing lengthy CoTs into concise yet effective reasoning chains; (2) smaller - developing compact language models with strong reasoning capabilities through techniques such as knowledge distillation, other model compression techniques, and reinforcement learning; and (3) faster - designing efficient decoding strategies to accelerate inference. A curated collection of papers discussed in this survey is available in our GitHub repository.

Language models are increasingly capable, yet still fail at a seemingly simple task of multi-digit multiplication. In this work, we study why, by reverse-engineering a model that successfully learns multiplication via implicit chain-of-thought, and report three findings: (1) Evidence of long-range structure: Logit attributions and linear probes indicate that the model encodes the necessary long-range dependencies for multi-digit multiplication. (2) Mechanism: the model encodes long-range dependencies using attention to construct a directed acyclic graph to ``cache'' and ``retrieve'' pairwise partial products. (3) Geometry: the model implements partial products in attention heads by forming Minkowski sums between pairs of digits, and digits are represented using a Fourier basis, both of which are intuitive and efficient representations that the standard fine-tuning model lacks. With these insights, we revisit the learning dynamics of standard fine-tuning and find that the model converges to a local optimum that lacks the required long-range dependencies. We further validate this understanding by introducing an auxiliary loss that predicts the ``running sum'' via a linear regression probe, which provides an inductive bias that enables the model to successfully learn multi-digit multiplication. In summary, by reverse-engineering the mechanisms of an implicit chain-of-thought model we uncover a pitfall for learning long-range dependencies in Transformers and provide an example of how the correct inductive bias can address this issue.

Recent advancements have demonstrated that the performance of large language models (LLMs) can be significantly enhanced by scaling computational resources at test time. A common strategy involves generating multiple Chain-of-Thought (CoT) trajectories and aggregating their outputs through various selection mechanisms. This raises a fundamental question: can models with lower complexity leverage their superior generation throughput to outperform similarly sized Transformers for a fixed computational budget? To address this question and overcome the lack of strong subquadratic reasoners, we distill pure and hybrid Mamba models from pretrained Transformers. Trained on only 8 billion tokens, our distilled models show strong performance and scaling on mathematical reasoning datasets while being much faster at inference for large batches and long sequences. Despite the zero-shot performance hit due to distillation, both pure and hybrid Mamba models can scale their coverage and accuracy performance past their Transformer teacher models under fixed time budgets, opening a new direction for scaling inference compute.

Recent developments in machine translation and multilingual text generation have led researchers to adopt trained metrics such as COMET or BLEURT, which treat evaluation as a regression problem and use representations from multilingual pre-trained models such as XLM-RoBERTa or mBERT. Yet studies on related tasks suggest that these models are most efficient when they are large, which is costly and impractical for evaluation. We investigate the trade-off between multilinguality and model capacity with RemBERT, a state-of-the-art multilingual language model, using data from the WMT Metrics Shared Task. We present a series of experiments which show that model size is indeed a bottleneck for cross-lingual transfer, then demonstrate how distillation can help addressing this bottleneck, by leveraging synthetic data generation and transferring knowledge from one teacher to multiple students trained on related languages. Our method yields up to 10.5% improvement over vanilla fine-tuning and reaches 92.6% of RemBERT's performance using only a third of its parameters.

Recent advances in text-to-image diffusion models have enabled the photorealistic generation of images from text prompts. Despite the great progress, existing models still struggle to generate compositional multi-concept images naturally, limiting their ability to visualize human imagination. While several recent works have attempted to address this issue, they either introduce additional training or adopt guidance at inference time. In this work, we consider a more ambitious goal: natural multi-concept generation using a pre-trained diffusion model, and with almost no extra cost. To achieve this goal, we identify the limitations in the text embeddings used for the pre-trained text-to-image diffusion models. Specifically, we observe concept dominance and non-localized contribution that severely degrade multi-concept generation performance. We further design a minimal low-cost solution that overcomes the above issues by tweaking (not re-training) the text embeddings for more realistic multi-concept text-to-image generation. Our Correction by Similarities method tweaks the embedding of concepts by collecting semantic features from most similar tokens to localize the contribution. To avoid mixing features of concepts, we also apply Cross-Token Non-Maximum Suppression, which excludes the overlap of contributions from different concepts. Experiments show that our approach outperforms previous methods in text-to-image, image manipulation, and personalization tasks, despite not introducing additional training or inference costs to the diffusion steps.

We present a simple, highly modularized network architecture for image classification. Our network is constructed by repeating a building block that aggregates a set of transformations with the same topology. Our simple design results in a homogeneous, multi-branch architecture that has only a few hyper-parameters to set. This strategy exposes a new dimension, which we call "cardinality" (the size of the set of transformations), as an essential factor in addition to the dimensions of depth and width. On the ImageNet-1K dataset, we empirically show that even under the restricted condition of maintaining complexity, increasing cardinality is able to improve classification accuracy. Moreover, increasing cardinality is more effective than going deeper or wider when we increase the capacity. Our models, named ResNeXt, are the foundations of our entry to the ILSVRC 2016 classification task in which we secured 2nd place. We further investigate ResNeXt on an ImageNet-5K set and the COCO detection set, also showing better results than its ResNet counterpart. The code and models are publicly available online.

This paper investigates the scaling properties of autoregressive next-pixel prediction, a simple, end-to-end yet under-explored framework for unified vision models. Starting with images at resolutions of 32x32, we train a family of Transformers using IsoFlops profiles across compute budgets up to 7e19 FLOPs and evaluate three distinct target metrics: next-pixel prediction objective, ImageNet classification accuracy, and generation quality measured by Fr'echet Distance. First, optimal scaling strategy is critically task-dependent. At a fixed 32x32 resolution alone, the optimal scaling properties for image classification and image generation diverge, where generation optimal setup requires the data size grow three to five times faster than for the classification optimal setup. Second, as image resolution increases, the optimal scaling strategy indicates that the model size must grow much faster than data size. Surprisingly, by projecting our findings, we discover that the primary bottleneck is compute rather than the amount of training data. As compute continues to grow four to five times annually, we forecast the feasibility of pixel-by-pixel modeling of images within the next five years.

Large language models exhibit exceptional generalization capabilities, primarily attributed to the utilization of diversely sourced data. However, conventional practices in integrating this diverse data heavily rely on heuristic schemes, lacking theoretical guidance. This research tackles these limitations by investigating strategies based on low-cost proxies for data mixtures, with the aim of streamlining data curation to enhance training efficiency. Specifically, we propose a unified scaling law, termed BiMix, which accurately models the bivariate scaling behaviors of both data quantity and mixing proportions. We conduct systematic experiments and provide empirical evidence for the predictive power and fundamental principles of BiMix. Notably, our findings reveal that entropy-driven training-free data mixtures can achieve comparable or even better performance than more resource-intensive methods. We hope that our quantitative insights can shed light on further judicious research and development in cost-effective language modeling.

This paper introduces a theoretical framework for a Transformer-augmented, sectional Mixture-of-Experts (MoE) architecture that aims to enhance computational efficiency while preserving model scalability. Unlike conventional MoE models, which route entire token embeddings to selected experts, our approach portions the embedding dimension itself -- assigning segments of each token's representation to dedicated experts. To combat losses in token representation, we utilize a pre-expert transformer layer to recompute attention across tokens and reduce the sequence length dimensionality. We extend our theory by deriving optimal scaling laws that a non-linear relationship between the number of experts and factors such as model dimensionality, sequence length, and system overhead. These formulations yield closed-form and numerically-solvable expressions for identifying the optimal expert count under given architectural and hardware constraints. As a result, our framework not only provides theoretical bounds for computing efficiency with varying frameworks but also guides practical design choices for scaling large models effectively. While empirical validation is pending, we present a comprehensive experimental road map to evaluate the framework's efficiency, scalability, and practicality in future work.

Scaling laws have shaped recent advances in machine learning by enabling predictable scaling of model performance based on model size, computation, and data volume. Concurrently, the rise in computational cost for AI has motivated model compression techniques, notably quantization and sparsification, which have emerged to mitigate the steep computational demands associated with large-scale training and inference. This paper investigates the interplay between scaling laws and compression formats, exploring whether a unified scaling framework can accurately predict model performance when training occurs over various compressed representations, such as sparse, scalar-quantized, sparse-quantized or even vector-quantized formats. Our key contributions include validating a general scaling law formulation and showing that it is applicable both individually but also composably across compression types. Based on this, our main finding is demonstrating both theoretically and empirically that there exists a simple "capacity" metric -- based on the representation's ability to fit random Gaussian data -- which can robustly predict parameter efficiency across multiple compressed representations. On the practical side, we extend our formulation to directly compare the accuracy potential of different compressed formats, and to derive better algorithms for training over sparse-quantized formats.

Convolution models with long filters have demonstrated state-of-the-art reasoning abilities in many long-sequence tasks but lag behind the most optimized Transformers in wall-clock time. A major bottleneck is the Fast Fourier Transform (FFT)--which allows long convolutions to run in O(N logN) time in sequence length N but has poor hardware utilization. In this paper, we study how to optimize the FFT convolution. We find two key bottlenecks: the FFT does not effectively use specialized matrix multiply units, and it incurs expensive I/O between layers of the memory hierarchy. In response, we propose FlashFFTConv. FlashFFTConv uses a matrix decomposition that computes the FFT using matrix multiply units and enables kernel fusion for long sequences, reducing I/O. We also present two sparse convolution algorithms--1) partial convolutions and 2) frequency-sparse convolutions--which can be implemented simply by skipping blocks in the matrix decomposition, enabling further opportunities for memory and compute savings. FlashFFTConv speeds up exact FFT convolutions by up to 7.93times over PyTorch and achieves up to 4.4times speedup end-to-end. Given the same compute budget, FlashFFTConv allows Hyena-GPT-s to achieve 2.3 points better perplexity on the PILE and M2-BERT-base to achieve 3.3 points higher GLUE score--matching models with twice the parameter count. FlashFFTConv also achieves 96.1% accuracy on Path-512, a high-resolution vision task where no model had previously achieved better than 50%. Furthermore, partial convolutions enable longer-sequence models--yielding the first DNA model that can process the longest human genes (2.3M base pairs)--and frequency-sparse convolutions speed up pretrained models while maintaining or improving model quality.

Compute scaling for language model (LM) pretraining has outpaced the growth of human-written texts, leading to concerns that data will become the bottleneck to LM scaling. To continue scaling pretraining in this data-constrained regime, we propose that explicitly modeling and inferring the latent thoughts that underlie the text generation process can significantly improve pretraining data efficiency. Intuitively, our approach views web text as the compressed final outcome of a verbose human thought process and that the latent thoughts contain important contextual knowledge and reasoning steps that are critical to data-efficient learning. We empirically demonstrate the effectiveness of our approach through data-constrained continued pretraining for math. We first show that synthetic data approaches to inferring latent thoughts significantly improve data efficiency, outperforming training on the same amount of raw data (5.7\% rightarrow 25.4\% on MATH). Furthermore, we demonstrate latent thought inference without a strong teacher, where an LM bootstraps its own performance by using an EM algorithm to iteratively improve the capability of the trained LM and the quality of thought-augmented pretraining data. We show that a 1B LM can bootstrap its performance across at least three iterations and significantly outperform baselines trained on raw data, with increasing gains from additional inference compute when performing the E-step. The gains from inference scaling and EM iterations suggest new opportunities for scaling data-constrained pretraining.

Solving math word problems depends on how to articulate the problems, the lens through which models view human linguistic expressions. Real-world settings count on such a method even more due to the diverse practices of the same mathematical operations. Earlier works constrain available thinking processes by limited prediction strategies without considering their significance in acquiring mathematical knowledge. We introduce Attention-based THought Expansion Network Architecture (ATHENA) to tackle the challenges of real-world practices by mimicking human thought expansion mechanisms in the form of neural network propagation. A thought expansion recurrently generates the candidates carrying the thoughts of possible math expressions driven from the previous step and yields reasonable thoughts by selecting the valid pathways to the goal. Our experiments show that ATHENA achieves a new state-of-the-art stage toward the ideal model that is compelling in variant questions even when the informativeness in training examples is restricted.