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Computer Vision · Segmentation

Qishuai Wen, Chun-Guang Li

State-of-the-art methods for Transformer-based semantic segmentation typically adopt Transformer decoders that are used to extract additional embeddings from image embeddings via cross-attention, refine either or both types of embeddings via self-attention, and project image embeddings onto the additional embeddings via dot-product. Despite their remarkable success, these empirical designs still lack theoretical justifications or interpretations, thus hindering potentially principled improvements. In this paper, we argue that there are fundamental connections between semantic segmentation and compression, especially between the Transformer decoders and Principal Component Analysis (PCA). From such a perspective, we derive a white-box, fully attentional DEcoder for PrIncipled semantiC segemenTation (DEPICT), with the interpretations as follows: 1) the self-attention operator refines image embeddings to construct an ideal principal subspace that aligns with the supervision and retains most information; 2) the cross-attention operator seeks to find a low-rank approximation of the refined image embeddings, which is expected to be a set of orthonormal bases of the principal subspace and corresponds to the predefined classes; 3) the dot-product operation yields compact representation for image embeddings as segmentation masks. Experiments conducted on dataset ADE20K find that DEPICT consistently outperforms its black-box counterpart, Segmenter, and it is light weight and more robust.

Interpretability

Divyansh Srivastava, Ge Yan, Lily Weng

Concept Bottleneck Models (CBMs) provide interpretable prediction by introducing an intermediate Concept Bottleneck Layer (CBL), which encodes human-understandable concepts to explain models' decision. Recent works proposed to utilize Large Language Models and pre-trained Vision-Language Models to automate the training of CBMs, making it more scalable and automated. However, existing approaches still fall short in two aspects: First, the concepts predicted by CBL often mismatch the input image, raising doubts about the faithfulness of interpretation. Second, it has been shown that concept values encode unintended information: even a set of random concepts could achieve comparable test accuracy to state-of-the-art CBMs. To address these critical limitations, in this work, we propose a novel framework called Vision-Language-Guided Concept Bottleneck Model (VLG-CBM) to enable faithful interpretability with the benefits of boosted performance. Our method leverages off-the-shelf open-domain grounded object detectors to provide visually grounded concept annotation, which largely enhances the faithfulness of concept prediction while further improving the model performance. In addition, we propose a new metric called Number of Effective Concepts (NEC) to control the information leakage and provide better interpretability. Extensive evaluations across five standard benchmarks show that our method, VLG-CBM, outperforms existing methods by at least 4.27\% and up to 51.09\% on *Accuracy at NEC=5* (denoted as ANEC-5), and by at least 0.45\% and up to 29.78\% on *average accuracy* (denoted as ANEC-avg), while preserving both faithfulness and interpretability of the learned concepts as demonstrated in extensive experiments.

Deep Learning · Representation Learning

Konstantinos Kogkalidis, Jean-Philippe Bernardy, Vikas Garg

We introduce a novel positional encoding strategy for Transformer-style models, addressing the shortcomings of existing, often ad hoc, approaches. Our framework implements a flexible mapping from the algebraic specification of a domain to a positional encoding scheme where positions are interpreted as orthogonal operators. This design preserves the structural properties of the source domain, thereby ensuring that the end-model upholds them. The framework can accommodate various structures, including sequences, grids and trees, but also their compositions. We conduct a series of experiments demonstrating the practical applicability of our method. Our results suggest performance on par with or surpassing the current state of the art, without hyper-parameter optimizations or ``task search'' of any kind.Code is available through https://aalto-quml.github.io/ape/.

Yihao Zhang, Zeming Wei, Jun Sun, Meng Sun

Since the rapid development of Large Language Models (LLMs) has achieved remarkable success, understanding and rectifying their internal complex mechanisms has become an urgent issue. Recent research has attempted to interpret their behaviors through the lens of inner representation. However, developing practical and efficient methods for applying these representations for general and flexible model editing remains challenging. In this work, we explore how to leverage insights from representation engineering to guide the editing of LLMs by deploying a representation discriminator as an editing oracle. We first identify the importance of a robust and reliable discriminator during editing, then propose an \textbf{A}dversarial \textbf{R}epresentation \textbf{E}ngineering (\textbf{ARE}) framework to provide a unified and interpretable approach for conceptual model editing without compromising baseline performance. Experiments on multiple tasks demonstrate the effectiveness of ARE in various model editing scenarios. Our code and data are available at \url{https://github.com/Zhang-Yihao/Adversarial-Representation-Engineering}.

Interpretability

Aahlad Manas Puli, Nhi Nguyen, Rajesh Ranganath

Feature attributions attempt to highlight what inputs drive predictive power. Good attributions or explanations are thus those that produce inputs that retain this predictive power; accordingly, evaluations of explanations score their quality of prediction. However, evaluations produce scores better than what appears possible from the values in the explanation for a class of explanations, called encoding explanations. Probing for encoding remains a challenge because there is no general characterization of what gives the extra predictive power. We develop a definition of encoding that identifies this extra predictive power via conditional dependence and show that the definition fits existing examples of encoding. This definition implies, in contrast to encoding explanations, that non-encoding explanations contain all the informative inputs used to produce the explanation, giving them a “what you see is what you get” property, which makes them transparent and simple to use. Next, we prove that existing scores (ROAR, FRESH, EVAL-X) do not rank non-encoding explanations above encoding ones, and develop STRIPE-X which ranks them correctly. After empirically demonstrating the theoretical insights, we use STRIPE-X to show that despite prompting an LLM to produce non-encoding explanations for a sentiment analysis task, the LLM-generated explanations encode.

Deep Learning · Theory

Nikita Karagodin, Yury Polyanskiy, Philippe Rigollet

This work presents a modification of the self-attention dynamics proposed in Geshkovski et al to better reflect the practically relevant, causally masked attention used in transformer architectures for generative AI. This modification translates into an interacting particle system that cannot be interpreted as a mean-field gradient flow. Despite this loss of structure, we significantly strengthen the results of Geshkovski et al in this context: While previous rigorous results focused on cases where all three matrices (key, query, and value) were scaled identities, we prove asymptotic convergence to a single cluster for arbitrary key-query matrices and value matrix equal to the identity.Additionally, we establish a connection to the classical R\'enyi parking problem from combinatorial geometry to make initial theoretical steps towards demonstrating the existence of meta-stable states.

Interpretability

Richard Nock, Ehsan Amid, Frank Nielsen, Alexander Soen, Manfred Warmuth

Models of hyperbolic geometry have been successfully used in ML for two main tasks: embedding *models* in unsupervised learning (*e.g.* hierarchies) and embedding *data*. To our knowledge, there are no approaches that provide embeddings for supervised models; even when hyperbolic geometry provides convenient properties for expressing popular hypothesis classes, such as decision trees (and ensembles).In this paper, we propose a full-fledged solution to the problem in three independent contributions. The first linking the theory of losses for class probability estimation to hyperbolic embeddings in Poincar\'e disk model. The second resolving an issue for a clean, unambiguous embedding of (ensembles of) decision trees in this model. The third showing how to smoothly tweak the Poincar\'e hyperbolic distance to improve its encoding and visualization properties near the border of the disk, a crucial region for our application, while keeping hyperbolicity.This last step has substantial independent interest as it is grounded in a generalization of Leibniz-Newton's fundamental Theorem of calculus.

Graph Neural Networks

Maya Bechler-Speicher, Amir Globerson, Ran Gilad-Bachrach

Graph Neural Networks (GNNs) have emerged as the predominant approach for learning over graph-structured data. However, most GNNs operate as black-box models and require post-hoc explanations, which may not suffice in high-stakes scenarios where transparency is crucial.In this paper, we present a GNN that is interpretable by design. Our model, Graph Neural Additive Network (GNAN), is a novel extension of the interpretable class of Generalized Additive Models, and can be visualized and fully understood by humans. GNAN is designed to be fully interpretable, offering both global and local explanations at the feature and graph levels through direct visualization of the model. These visualizations describe exactly how the model uses the relationships between the target variable, the features, and the graph. We demonstrate the intelligibility of GNANs in a series of examples on different tasks and datasets. In addition, we show that the accuracy of GNAN is on par with black-box GNNs, making it suitable for critical applications where transparency is essential, alongside high accuracy.

Shaoqi Wang, Chunjie Yang, Siwei Lou

Neural networks (NN) are extensively studied in cutting-edge soft sensor models due to their feature extraction and function approximation capabilities. Current research into network-based methods primarily focuses on models' offline accuracy. Notably, in industrial soft sensor context, online optimizing stability and interpretability are prioritized, followed by accuracy. This requires a clearer understanding of network's training process. To bridge this gap, we propose a novel NN named the Approximated Orthogonal Projection Unit (AOPU) which has solid mathematical basis and presents superior training stability. AOPU truncates the gradient backpropagation at dual parameters, optimizes the trackable parameters updates, and enhances the robustness of training. We further prove that AOPU attains minimum variance estimation in NN, wherein the truncated gradient approximates the natural gradient. Empirical results on two chemical process datasets clearly show that AOPU outperforms other models in achieving stable convergence, marking a significant advancement in soft sensor field.

Ruiqi Zhong, Heng Wang, Dan Klein, Jacob Steinhardt

To make sense of massive data, we often first fit simplified models and then interpret the parameters; for example, we cluster the text embeddings and then interpret the mean parameters of each cluster.However, these parameters are often high-dimensional and hard to interpret.To make model parameters directly interpretable, we introduce a family of statistical models---including clustering, time series, and classification models---parameterized by *natural language predicates*. For example, a cluster of text about COVID could be parameterized by the predicate ``*discusses COVID*''.To learn these statistical models effectively, we develop a model-agnostic algorithm that optimizes continuous relaxations of predicate parameters with gradient descent and discretizes them by prompting language models (LMs).Finally, we apply our framework to a wide range of problems: taxonomizing user chat dialogues, characterizing how they evolve across time, finding categories where one language model is better than the other, clustering math problems based on subareas, and explaining visual features in memorable images.Our framework is highly versatile, applicable to both textual and visual domains, can be easily steered to focus on specific properties (e.g. subareas), and explains sophisticated concepts that classical methods (e.g. n-gram analysis) struggle to produce.

Interpretability

Roland S. Zimmermann, David Klindt, Wieland Brendel

In today’s era, whatever we can measure at scale, we can optimize. So far, measuring the interpretability of units in deep neural networks (DNNs) for computer vision still requires direct human evaluation and is not scalable. As a result, the inner workings of DNNs remain a mystery despite the remarkable progress we have seen in their applications. In this work, we introduce the first scalable method to measure the per-unit interpretability in vision DNNs. This method does not require any human evaluations, yet its prediction correlates well with existing human interpretability measurements. We validate its predictive power through an interventional human psychophysics study. We demonstrate the usefulness of this measure by performing previously infeasible experiments: (1) A large-scale interpretability analysis across more than 70 million units from 835 computer vision models, and (2) an extensive analysis of how units transform during training. We find an anticorrelation between a model's downstream classification performance and per-unit interpretability, which is also observable during model training. Furthermore, we see that a layer's location and width influence its interpretability.

Interpretability

Yiming Lei, Zilong Li, Junping Zhang, Hongming Shan

The explainability of deep neural networks (DNNs) is critical for trust and reliability in AI systems. Path-based attribution methods, such as integrated gradients (IG), aim to explain predictions by accumulating gradients along a path from a baseline to the target image. However, noise accumulated during this process can significantly distort the explanation. While existing methods primarily concentrate on finding alternative paths to circumvent noise, they overlook a critical issue: intermediate-step images frequently diverge from the distribution of training data, further intensifying the impact of noise. This work presents a novel Denoising Diffusion Path (DDPath) to tackle this challenge by harnessing the power of diffusionmodels for denoising. By exploiting the inherent ability of diffusion models to progressively remove noise from an image, DDPath constructs a piece-wise linear path. Each segment of this path ensures that samples drawn from a Gaussian distribution are centered around the target image. This approach facilitates a gradual reduction of noise along the path. We further demonstrate that DDPath adheres to essential axiomatic properties for attribution methods and can be seamlessly integrated with existing methods such as IG. Extensive experimental results demonstrate that DDPath can significantly reduce noise in the attributions—resulting in clearer explanations—and achieves better quantitative results than traditional path-based methods.

Generative Models · Diffusion models

Byoungwoo Park, Jungwon Choi, Sungbin Lim, Juho Lee

Recent advancements in diffusion models and diffusion bridges primarily focus on finite-dimensional spaces, yet many real-world problems necessitate operations in infinite-dimensional function spaces for more natural and interpretable formulations. In this paper, we present a theory of stochastic optimal control (SOC) tailored to infinite-dimensional spaces, aiming to extend diffusion-based algorithms to function spaces. Specifically, we demonstrate how Doob’s $h$-transform, the fundamental tool for constructing diffusion bridges, can be derived from the SOC perspective and expanded to infinite dimensions. This expansion presents a challenge, as infinite-dimensional spaces typically lack closed-form densities. Leveraging our theory, we establish that solving the optimal control problem with a specific objective function choice is equivalent to learning diffusion-based generative models. We propose two applications: 1) learning bridges between two infinite-dimensional distributions and 2) generative models for sampling from an infinite-dimensional distribution. Our approach proves effective for diverse problems involving continuous function space representations, such as resolution-free images, time-series data, and probability density functions.

Miscellaneous Aspects of Machine Learning · Unsupervised and Semi-supervised Learning

Eduardo Laber, Miguel Batista

Average-link is widely recognized as one of the most popular and effective methods for building hierarchical agglomerative clustering. The available theoretical analyses show that this method has a much better approximation than other popular heuristics, as single-linkage and complete-linkage, regarding variants of Dasgupta's cost function [STOC 2016]. However, these analyses do not separate average-link from a random hierarchy and they are not appealing for metric spaces since every hierarchical clustering has a $1/2$ approximation with regard to the variant of Dasgupta's functionthat is employed for dissimilarity measures [Moseley and Yang 2020]. In this paper, we present a comprehensive study of the performance of \avglink \, in metric spaces, regarding several natural criteria that capture separability and cohesion, and are more interpretable than Dasgupta's cost function and its variants. We also present experimental results with real datasets that, together with our theoretical analyses, suggest that average-link is a better choice than other related methods when both cohesion and separability are important goals.

Generative Models · In Context Learning

Aleksandar Petrov, Tom Lamb, Alasdair Paren, Philip Torr, Adel Bibi

Zero-shot and in-context learning enable solving tasks without model fine-tuning, making them essential for developing generative model solutions. Therefore, it is crucial to understand whether a pretrained model can be prompted to approximate any function, i.e., whether it is a universal in-context approximator. While it was recently shown that transformer models do possess this property, these results rely on their attention mechanism. Hence, these findings do not apply to fully recurrent architectures like RNNs, LSTMs, and the increasingly popular SSMs. We demonstrate that RNNs, LSTMs, GRUs, Linear RNNs, and linear gated architectures such as Mamba and Hawk/Griffin can also serve be universal in-context approximators. To streamline our argument, we introduce a programming language called LSRL that compiles to these fully recurrent architectures. LSRL may be of independent interest for further studies of fully recurrent models, such as constructing interpretability benchmarks. We also study the role of multiplicative gating and observe that architectures incorporating such gating (e.g., LSTMs, GRUs, Hawk/Griffin) can implement certain operations more stably, making them more viable candidates for practical in-context universal approximation.

Neuroscience, Cognitive Science

Yenho Chen, Noga Mudrik, Kyle A. Johnsen, Sankaraleengam Alagapan, Adam Charles, Christopher Rozell

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve according to simple locally linear dynamics. However, existing methods for latent variable estimation are not robust to dynamical noise and system nonlinearity due to noise-sensitive inference procedures and limited model formulations. This can lead to inconsistent results on signals with similar dynamics, limiting the model's ability to provide scientific insight. In this work, we address these limitations and propose a probabilistic approach to latent variable estimation in decomposed models that improves robustness against dynamical noise. Additionally, we introduce an extended latent dynamics model to improve robustness against system nonlinearities. We evaluate our approach on several synthetic dynamical systems, including an empirically-derived brain-computer interface experiment, and demonstrate more accurate latent variable inference in nonlinear systems with diverse noise conditions. Furthermore, we apply our method to a real-world clinical neurophysiology dataset, illustrating the ability to identify interpretable and coherent structure where previous models cannot.

Chaoya Jiang, Hongrui Jia, Haiyang Xu, Wei Ye, Mengfan Dong, Ming Yan, Ji Zhang, Fei Huang, Shikun Zhang

This paper presents MaVEn, an innovative Multi-granularity Visual Encoding framework designed to enhance the capabilities of Multimodal Large Language Models (MLLMs) in multi-image reasoning. Current MLLMs primarily focus on single-image visual understanding, limiting their ability to interpret and integrate information across multiple images. MaVEn addresses this limitation by combining discrete visual symbol sequences, which abstract coarse-grained semantic concepts, with traditional continuous representation sequences that model fine-grained features. This dual approach bridges the semantic gap between visual and textual data, thereby improving the model's ability to process and interpret information from multiple images effectively. Additionally, we design a dynamic reduction mechanism by for long-sequence continuous features to enhance multi-image processing efficiency. Experimental results demonstrate that MaVEn significantly enhances MLLMs' understanding in complex multi-image scenarios, while also improving performance in single-image contexts.

Causality

Joowon Lee, Jared Huling, Guanhua Chen

Estimating individualized treatment rules (ITRs) is fundamental in causal inference, particularly for precision medicine applications. Traditional ITR estimation methods rely on inverse probability weighting (IPW) to address confounding factors and $L_{1}$-penalization for simplicity and interpretability. However, IPW can introduce statistical bias without precise propensity score modeling, while $L_1$-penalization makes the objective non-smooth, leading to computational bias and requiring subgradient methods. In this paper, we propose a unified ITR estimation framework formulated as a constrained, weighted, and smooth convex optimization problem. The optimal ITR can be robustly and effectively computed by projected gradient descent. Our comprehensive theoretical analysis reveals that weights that balance the spectrum of a `weighted design matrix' improve both the optimization and likelihood landscapes, yielding improved computational and statistical estimation guarantees. In particular, this is achieved by distributional covariate balancing weights, which are model-free alternatives to IPW. Extensive simulations and applications demonstrate that our framework achieves significant gains in both robustness and effectiveness for ITR learning against existing methods.

Interpretability

Curt Tigges, Michael Hanna, Qinan Yu, Stella Biderman

Most currently deployed LLMs undergo continuous training or additional finetuning. By contrast, most research into LLMs' internal mechanisms focuses on models at one snapshot in time (the end of pre-training), raising the question of whether their results generalize to real-world settings. Existing studies of mechanisms over time focus on encoder-only or toy models, which differ significantly from most deployed models. In this study, we track how model mechanisms, operationalized as circuits, emerge and evolve across 300 billion tokens of training in decoder-only LLMs, in models ranging from 70 million to 2.8 billion parameters. We find that task abilities and the functional components that support them emerge consistently at similar token counts across scale. Moreover, although such components may be implemented by different attention heads over time, the overarching algorithm that they implement remains. Surprisingly, both these algorithms and the types of components involved therein tend to replicate across model scale. Finally, we find that circuit size correlates with model size and can fluctuate considerably over time even when the same algorithm is implemented. These results suggest that circuit analyses conducted on small models at the end of pre-training can provide insights that still apply after additional training and over model scale.

Interpretability

Claudia Shi, Nicolas Beltran Velez, Achille Nazaret, Carolina Zheng, Adrià Garriga-Alonso, Andrew Jesson, Maggie Makar, David Blei

Large language models (LLMs) demonstrate surprising capabilities, but we do not understand how they are implemented. One hypothesis suggests that these capabilities are primarily executed by small subnetworks within the LLM, known as circuits. But how can we evaluate this hypothesis?In this paper, we formalize a set of criteria that a circuit is hypothesized to meet and develop a suite of hypothesis tests to evaluate how well circuits satisfy them. The criteria focus on the extent to which the LLM's behavior is preserved, the degree of localization of this behavior, and whether the circuit is minimal.We apply these tests to six circuits described in the research literature. We find that synthetic circuits -- circuits that are hard-coded in the model -- align with the idealized properties. Circuits discovered in Transformer models satisfy the criteria to varying degrees.To facilitate future empirical studies of circuits, we created the \textit{circuitry} package, a wrapper around the \textit{TransformerLens} library, which abstracts away lower-level manipulations of hooks and activations. The software is available at \url{https://github.com/blei-lab/circuitry}.