Sparse autoencoders provide a promising unsupervised approach for extracting interpretable features from a language model by reconstructing activations from a sparse bottleneck layer. Since language models learn many concepts, autoencoders need to be very large to recover all relevant features. However, studying the properties of autoencoder scaling is difficult due to the need to balance reconstruction and sparsity objectives and the presence of dead latents. We propose using k-sparse autoencoders [Makhzani and Frey, 2013] to directly control sparsity, simplifying tuning and improving the reconstruction-sparsity frontier. Additionally, we find modifications that result in few dead latents, even at the largest scales we tried. Using these techniques, we find clean scaling laws with respect to autoencoder size and sparsity. We also introduce several new metrics for evaluating feature quality based on the recovery of hypothesized features, the explainability of activation patterns, and the sparsity of downstream effects. These metrics all generally improve with autoencoder size. To demonstrate the scalability of our approach, we train a 16 million latent autoencoder on GPT-4 activations for 40 billion tokens. We release training code and autoencoders for open-source models, as well as a visualizer.
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Probabilistic Methods · Everything Else
Whether deterministic or stochastic, models can be viewed as functions designed to approximate a specific quantity of interest. We introduce Minimal Empirical Variance Aggregation (MEVA), a data-driven framework that integrates predictions from various models, enhancing overall accuracy by leveraging the individual strengths of each. This non-intrusive, model-agnostic approach treats the contributing models as black boxes and accommodates outputs from diverse methodologies, including machine learning algorithms and traditional numerical solvers.We advocate for a point-wise linear aggregation process and consider two methods for optimizing this aggregate: Minimal Error Aggregation (MEA), which minimizes the prediction error, and Minimal Variance Aggregation (MVA), which focuses on reducing variance. We prove a theorem showing that MVA can be more robustly estimated from data than MEA, making MEVA superior to Minimal Empirical Error Aggregation (MEEA). Unlike MEEA, which interpolates target values directly, MEVA formulates aggregation as an error estimation problem, which can be performedusing any backbone learning paradigm. We demonstrate the versatility and effectiveness of our framework across various applications, including data science and partial differential equations, illustrating its ability to significantly enhance both robustness and accuracy.
Deep Learning · Generative Models and Autoencoders
In this paper, we introduce Plug-and-Play (PnP) Flow Matching, an algorithm for solving imaging inverse problems. PnP methods leverage the strength of pre-trained denoisers, often deep neural networks, by integrating them in optimization schemes. While they achieve state-of-the-art performance on various inverse problems in imaging, PnP approaches face inherent limitations on more generative tasks like inpainting. On the other hand, generative models such as Flow Matching pushed the boundary in image sampling yet lack a clear method for efficient use in image restoration. We propose to combine the PnP framework with Flow Matching (FM) by defining a time-dependent denoiser using a pre-trained FM model. Our algorithm alternates between gradient descent steps on the data-fidelity term, reprojections onto the learned FM path, and denoising. Notably, our method is computationally efficient and memory-friendly, as it avoids backpropagation through ODEs and trace computations. We evaluate its performance on denoising, super-resolution, deblurring, and inpainting tasks, demonstrating superior results compared to existing PnP algorithms and Flow Matching based state-of-the-art methods. Code available at https://github.com/annegnx/PnP-Flow.
In this paper, we introduce a novel analysis of neural networks based on geometric (Clifford) algebra and convex optimization. We show that optimal weights of deep ReLU neural networks are given by the wedge product of training samples when trained with standard regularized loss. Furthermore, the training problem reduces to convex optimization over wedge product features, which encode the geometric structure of the training dataset. This structure is given in terms of signed volumes of triangles and parallelotopes generated by data vectors. The convex problem finds a small subset of samples via $\ell_1$ regularization to discover only relevant wedge product features. Our analysis provides a novel perspective on the inner workings of deep neural networks and sheds light on the role of the hidden layers.
Miscellaneous Aspects of Machine Learning · Transfer, Multitask and Meta-learning
Neural Ordinary Differential Equations (NODEs) often struggle to adapt to new dynamic behaviors caused by parameter changes in the underlying physical system, even when these dynamics are similar to previously observed behaviors. This problem becomes more challenging when the changing parameters are unobserved, meaning their value or influence cannot be directly measured when collecting data. To address this issue, we introduce Neural Context Flow (NCF), a robust and interpretable Meta-Learning framework that includes uncertainty estimation. NCF uses Taylor expansion to enable contextual self-modulation, allowing context vectors to influence dynamics from other domains while also modulating themselves. After establishing theoretical guarantees, we empirically test NCF and compare it to related adaptation methods. Our results show that NCF achieves state-of-the-art Out-of-Distribution performance on 5 out of 6 linear and non-linear benchmark problems. Through extensive experiments, we explore the flexible model architecture of NCF and the encoded representations within the learned context vectors. Our findings highlight the potential implications of NCF for foundational models in the physical sciences, offering a promising approach to improving the adaptability and generalization of NODEs in various scientific applications.
Social Aspects · Trustworthy Machine Learning
Reward models (RMs) are a crucial component in the alignment of large language models’ (LLMs) outputs with human values. RMs approximate human preferences over possible LLM responses to the same prompt by predicting and comparing reward scores. However, as they are typically modified versions of LLMs with scalar output heads, RMs are large black boxes whose predictions are not explainable. More transparent RMs would enable improved trust in the alignment of LLMs. In this work, we propose to use contrastive explanations to explain any binary response comparison made by an RM. Specifically, we generate a diverse set of new comparisons similar to the original one to characterise the RM’s local behaviour. The perturbed responses forming the new comparisons are generated to explicitly modify manually specified high-level evaluation attributes, on which analyses of RM behaviour are grounded. In quantitative experiments, we validate the effectiveness of our method for finding high-quality contrastive explanations. We then showcase the qualitative usefulness of our method for investigating global sensitivity of RMs to each evaluation attribute, and demonstrate how representative examples can be automatically extracted to explain and compare behaviours of different RMs. We see our method as a flexible framework for RM explanation, providing a basis for more interpretable and trustworthy LLM alignment.
Deep Learning · Large Language Models
Recent advancements in large language models (LLMs) have resulted in increasingly anthropomorphic language concerning the ability of LLMs to reason. Whether \textit{reasoning} in LLMs should be understood to be inherently different is, however, widely debated. We propose utilizing a representation engineering approach wherein model activations are read from the residual stream of an LLM when processing a reasoning task. The activations are used to derive a control vector that is applied to the model as an inference-time intervention, modulating the representational space of the model, to improve performance on the specified task. We publish the code for deriving control vectors and analyzing model representations. The method allows us to improve performance on reasoning benchmarks and assess how control vectors influence the final logit distribution of a model via metrics such as KL divergence and entropy. We apply control vectors to Mistral-7B-Instruct and a range of Pythia models on an inductive, a deductive and mathematical reasoning task. We show that an LLM can, to a certain degree, be controlled to improve its perceived reasoning ability by modulating activations. The intervention is dependent upon the ability to reliably extract the model's typical state when correctly solving a task. Our results suggest that reasoning performance can be modulated in the same manner as other information-processing tasks performed by LLMs and demonstrate that we are capable of improving performance on specific tasks via a simple intervention on the residual stream with no additional training.
Deep Learning · Robustness
In the era of exceptionally data-hungry models, careful selection of the training data is essential to mitigate the extensive costs of deep learning. Data pruning offers a solution by removing redundant or uninformative samples from the dataset, which yields faster convergence and improved neural scaling laws. However, little is known about its impact on classification bias of the trained models. We conduct the first systematic study of this effect and reveal that existing data pruning algorithms can produce highly biased classifiers. We present theoretical analysis of the classification risk in a mixture of Gaussians to argue that choosing appropriate class pruning ratios, coupled with random pruning within classes has potential to improve worst-class performance. We thus propose DRoP, a distributionally robust approach to pruning and empirically demonstrate its performance on standard computer vision benchmarks. In sharp contrast to existing algorithms, our proposed method continues improving distributional robustness at a tolerable drop of average performance as we prune more from the datasets.
Deep Learning · Generative Models and Autoencoders
We introduce a novel method for generating 360° panoramas from text prompts or images. Our approach leverages recent advances in 3D generation by employing multi-view diffusion models to jointly synthesize the six faces of a cubemap. Unlike previous methods that rely on processing equirectangular projections or autoregressive generation, our method treats each face as a standard perspective image, simplifying the generation process and enabling the use of existing multi-view diffusion models. We demonstrate that these models can be adapted to produce high-quality cubemaps without requiring correspondence-aware attention layers. Our model allows for fine-grained text control, generates high resolution panorama images and generalizes well beyond its training set, whilst achieving state-of-the-art results, both qualitatively and quantitatively.
Deep Learning · Large Language Models
We introduce the "Belief State Transformer", a next-token predictor that takes both a prefix and suffix as inputs, with a novel objective of predicting both the next token for the prefix and the previous token for the suffix. The Belief State Transformer effectively learns to solve challenging problems that conventional forward-only transformers struggle with, in a domain-independent fashion. Key to this success is learning a compact belief state that captures all relevant information necessary for accurate predictions.Empirical ablations show that each component of the model is essential in difficult scenarios where standard Transformers fall short. For the task of story writing with known prefixes and suffixes, our approach outperforms the Fill-in-the-Middle method for reaching known goals and demonstrates improved performance even when the goals are unknown. Altogether, the Belief State Transformer enables more efficient goal-conditioned decoding, better test-time inference, and high-quality text representations on small scale problems. Website: https://edwhu.github.io/bst-website
Applications · Physics
Understanding the physical world is a fundamental challenge in embodied AI, critical for enabling agents to perform complex tasks and operate safely in real-world environments. While Vision-Language Models (VLMs) have shown great promise in reasoning and task planning for embodied agents, their ability to comprehend physical phenomena remains extremely limited.To close this gap, we introduce PhysBench, a comprehensive benchmark designed to evaluate VLMs' physical world understanding capability across a diverse set of tasks. PhysBench contains 10,002 entries of interleaved video-image-text data, categorized into four major domains: physical object properties, physical object relationships, physical scene understanding, and physics-based dynamics, further divided into 19 subclasses and 8 distinct capability dimensions.Our extensive experiments, conducted on 75 representative VLMs, reveal that while these models excel in common-sense reasoning, they struggle with understanding the physical world---likely due to the absence of physical knowledge in their training data and the lack of embedded physical priors.To tackle the shortfall, we introduce PhysAgent, a novel framework that combines the generalization strengths of VLMs with the specialized expertise of vision models, significantly enhancing VLMs' physical understanding across a variety of tasks, including an 18.4\% improvement on GPT-4o.Furthermore, our results demonstrate that enhancing VLMs' physical world understanding capabilities can help embodied agents such as MOKA.We believe that PhysBench and PhysAgent offer valuable insights and contribute to bridging the gap between VLMs and physical world understanding. [Project Page is here](https://physbench.github.io/)
Social Aspects · Trustworthy Machine Learning
Recent studies show that image and video generation models can be prompted to reproduce copyrighted content from their training data, raising serious legal con- cerns about copyright infringement. Copyrighted characters (e.g., Mario, Batman) present a significant challenge: at least one lawsuit has already awarded damages based on the generation of such characters. Consequently, commercial services like DALL·E have started deploying interventions. However, little research has systematically examined these problems: (1) Can users easily prompt models to generate copyrighted characters, even if it is unintentional?; (2) How effective are the existing mitigation strategies? To address these questions, we introduce a novel evaluation framework with metrics that assess both the generated image’s similarity to copyrighted characters and its consistency with user intent, grounded in a set of popular copyrighted characters from diverse studios and regions. We show that state-of-the-art image and video generation models can still generate characters even if characters’ names are not explicitly mentioned, sometimes with only two generic keywords (e.g., prompting with “videogame, plumber” consistently gener- ates Nintendo’s Mario character). We also introduce semi-automatic techniques to identify such keywords or descriptions that trigger character generation. Using this framework, we evaluate mitigation strategies, including prompt rewriting and new approaches we propose. Our findings reveal that common methods, such as DALL·E’s prompt rewriting, are insufficient alone and require supplementary strategies like negative prompting. Our work provides empirical grounding for discussions on copyright mitigation strategies and offers actionable insights for model deployers implementing these safeguards.
In this paper, we propose Knowledge Base augmented Language Model (KBLAM), a new method for augmenting Large Language Models (LLMs) with external knowledge. KBLAM works with a knowledge base (KB) constructed from a corpus of documents, transforming each piece of knowledge in the KB into continuous key-value vector pairs via pre-trained sentence encoders with linear adapters andintegrating them into pre-trained LLMs via a specialized rectangular attention mechanism. Unlike Retrieval-Augmented Generation, KBLAM eliminates external retrieval modules, and unlike in-context learning, its computational overhead scales linearly with KB size rather than quadratically. Our approach enables integrating a large KB of more than 10K triples into an 8B pre-trained LLM of only 8K context window on one single A100 80GB GPU and allows for dynamic updates without model fine-tuning or retraining. Experiments demonstrate KBLAM’s effectiveness in various tasks, including question-answering and open-ended reasoning, while providing interpretable insights into its use of the augmented knowledge. Code and datasets are available at https://github.com/microsoft/KBLaM/
Applications · Health
Adapting medical Large Language Models to local languages can reduce barriers to accessing healthcare services, but data scarcity remains a significant challenge, particularly for low-resource languages. To address this, we first construct a high-quality medical dataset and conduct analysis to ensure its quality. In order to leverage the generalization capability of multilingual LLMs to efficiently scale to more resource-constrained languages, we explore the internal information flow of LLMs from a multilingual perspective using Mixture of Experts (MoE) modularity. Technically, we propose a novel MoE routing method that employs language-specific experts and cross-lingual routing. Inspired by circuit theory, our routing analysis revealed a \textit{``Spread Out in the End``} information flow mechanism: while earlier layers concentrate cross-lingual information flow, the later layers exhibit language-specific divergence. This insight directly led to the development of the Post-MoE architecture, which applies sparse routing only in the later layers while maintaining dense others. Experimental results demonstrate that this approach enhances the generalization of multilingual models to other languages while preserving interpretability. Finally, to efficiently scale the model to 50 languages, we introduce the concept of \textit{language family} experts, drawing on linguistic priors, which enables scaling the number of languages without adding additional parameters.
We investigate the statistical and computational limits of prompt tuning for transformer-based foundation models. Our key contributions are that prompt tuning on *single-head* transformers with only a *single* self-attention layer: (i) is universal, and (ii) supports efficient (even almost-linear time) algorithms under the Strong Exponential Time Hypothesis (SETH). Statistically, we prove that prompt tuning on such the simplest possible transformers are universal approximators for sequence-to-sequence Lipschitz functions. In addition, we provide an exponential-in-$dL$ and -in-$(1/\epsilon)$ lower bound on the required soft-prompt tokens for prompt tuning to memorize any dataset with 1-layer, 1-head transformers. Computationally, we identify a phase transition in the efficiency of prompt tuning, determined by the norm of the *soft-prompt-induced* keys and queries, and provide an upper bound criterion. Beyond this criterion, no sub-quadratic (efficient) algorithm for prompt tuning exists under SETH. Within this criterion, we showcase our theory by proving the existence of almost-linear time prompt tuning inference algorithms. These fundamental limits provide important necessary conditions for designing expressive and efficient prompt tuning methods for practitioners.
Miscellaneous Aspects of Machine Learning · Representation Learning
Vision foundation models, particularly the ViT family, have revolutionized image understanding by providing rich semantic features. However, despite their success in 2D comprehension, their abilities on grasping 3D spatial relationships are still unclear.In this work, we evaluate and enhance the 3D awareness of ViT-based models. We begin by systematically assessing their ability to learn 3D equivariant features, specifically examining the consistency of semantic embeddings across different viewpoints. Our findings indicate that improved 3D equivariance leads to better performance on various downstream tasks, including pose estimation, tracking, and semantic transfer. Building on this insight, we propose a simple yet effective finetuning strategy based on 3D correspondences, which significantly enhances the 3D understanding of existing vision models. Remarkably, even finetuning on a single object for just one iteration results in substantial performance gains. Code is available on https://github.com/qq456cvb/3DCorrEnhance.
Social Aspects · Fairness, Equity, Justice and Safety
The Balanced Stable Marriage (BSM) problem aims to find a stable matching in a two-sided market that minimizes the maximum dissatisfaction among two sides. The classical Deferred Acceptance algorithm merely produces an unfair stable marriage, providing optimal partners for one side while partially assigning pessimal partners to the other. Solving BSM is NP-hard, thwarting attempts to resolve the problem exactly. As the instance size increases in practice, recent studies have explored heuristics for finding a fair stable marriage but have not found an exact optimal solution for BSM efficiently. Nevertheless, in this paper we propose an efficient algorithm, Isorropia, that returns the exact optimal solution to practical BSM problem instances. Isorropia constructs two sets of candidate rotations from which it builds three sets of promising antichains, and performs local search on those three sets of promising antichains. Our extensive experimental study shows that Isorropia surpasses the time-efficiency of baselines that return the exact solution by up to three orders of magnitude.
In the era of Large Language Models (LLMs), Mixture-of-Experts (MoE) architectures offer a promising approach to managing computational costs while scaling up model parameters. Conventional MoE-based LLMs typically employ static Top-K routing, which activates a fixed and equal number of experts for each token regardless of their significance within the context. In this paper, we propose a novel Ada-K routing strategy that dynamically adjusts the number of activated experts for each token, thereby improving the balance between computational efficiency and model performance. Specifically, our strategy incorporates learnable and lightweight allocator modules that decide customized expert resource allocation tailored to the contextual needs for each token. These allocators are designed to be fully pluggable, making it broadly applicable across all mainstream MoE-based LLMs. We leverage the Proximal Policy Optimization (PPO) algorithm to facilitate an end-to-end learning process for this non-differentiable decision-making framework. Extensive evaluations on four popular baseline models demonstrate that our Ada-K routing method significantly outperforms conventional Top-K routing. Compared to Top-K, our method achieves over 25% reduction in FLOPs and more than 20% inference speedup while still improving performance across various benchmarks. Moreover, the training of Ada-K is highly efficient. Even for Mixtral-8x22B, a MoE-based LLM with more than 140B parameters, the training time is limited to 8 hours. Detailed analysis shows that harder tasks, middle layers, and content words tend to activate more experts, providing valuable insights for future adaptive MoE system designs. Both the training code and model checkpoints will be publicly available.
Applications · Physics
Weather forecasting has seen a shift in methods from numerical simulations to data-driven systems. While initial research in the area focused on deterministic forecasting, recent works have used diffusion models to produce skillful ensemble forecasts. These models are trained on a single forecasting step and rolled out autoregressively. However, they are computationally expensive and accumulate errors for high temporal resolution due to the many rollout steps. We address these limitations with Continuous Ensemble Forecasting, a novel and flexible method for sampling ensemble forecasts in diffusion models. The method can generate temporally consistent ensemble trajectories completely in parallel, with no autoregressive steps. Continuous Ensemble Forecasting can also be combined with autoregressive rollouts to yield forecasts at an arbitrary fine temporal resolution without sacrificing accuracy. We demonstrate that the method achieves competitive results for global weather forecasting with good probabilistic properties.
Miscellaneous Aspects of Machine Learning · Everything Else
As language models (LMs) become increasingly sophisticated and existing benchmarks approach saturation, the need for rigorous evaluation methods grows more pressing. Many evaluations lack the statistical rigour needed to draw meaningful conclusions, leading to a potential over-confidence in results that might not hold up under scrutiny or replication. This post advocates for bringing fundamental statistical principles to language model evaluation, demonstrating how basic statistical analysis can provide more reliable insights into model capabilities and limitations.We show how to conduct this type of analysis using a recent paper as a case study. We hope this post serves as a tutorial for LM researchers aiming to enhance the rigor of their empirical evaluations.