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Social Aspects · Accountability, Transparency, and Interpretability

Shahaf Bassan, Guy Amir, Meirav Zehavi, Guy Katz

Ensemble models are widely recognized in the ML community for their limited interpretability. For instance, while a single decision tree is considered interpretable, ensembles of trees (e.g., boosted trees) are often treated as black-boxes. Despite this folklore recognition, there remains a lack of rigorous mathematical understanding of what particularly makes an ensemble (un)-interpretable, including how fundamental factors like the (1) *number*, (2) *size*, and (3) *type* of base models influence its interpretability. In this work, we seek to bridge this gap by applying concepts from computational complexity theory to study the challenges of generating explanations for various ensemble configurations. Our analysis uncovers nuanced complexity patterns influenced by various factors. For example, we demonstrate that under standard complexity assumptions like P$\neq$NP, interpreting ensembles remains intractable even when base models are of constant size. Surprisingly, the complexity changes drastically with the number of base models: small ensembles of decision trees are efficiently interpretable, whereas ensembles of linear models remain intractable, even with a constant number of models. We believe that our findings provide a more robust foundation for understanding the interpretability of ensembles, emphasizing the benefits of examining it through a computational complexity lens.

Social Aspects · Accountability, Transparency, and Interpretability

Xiuyi Jia, Jinchi Li, Yunan Lu, Weiwei Li

Label distribution learning (LDL) is a novel machine learning paradigm that can handle label ambiguity. This paper focuses on the interpretability issue of label distribution learning. Existing local interpretability models are mainly designed for single-label learning problems and are difficult to directly interpret label distribution learning models. In response to this situation, we propose an improved local interpretable model-agnostic explanations algorithm that can effectively interpret any black-box model in label distribution learning.To address the label dependency problem, we introduce the feature attribution distribution matrix and derive the solution formula for explanations under the label distribution form. Meanwhile, to enhance the transparency and trustworthiness of the explanation algorithm, we provide an analytical solution and derive the boundary conditions for explanation convergence and stability. In addition, we design a feature selection scoring function and a fidelity metric for the explanation task of label distribution learning. A series of numerical experiments and human experiments were conducted to validate the performance of the proposed algorithm in practical applications. The experimental results demonstrate that the proposed algorithm achieves high fidelity, consistency, and trustworthiness in explaining LDL models.

Deep Learning · Large Language Models

Zeyu Gan, Yun Liao, Yong Liu

Test-time scaling, which is also often referred to as *slow-thinking*, has been demonstrated to enhance multi-step reasoning in large language models (LLMs). However, despite its widespread utilization, the mechanisms underlying slow-thinking methods remain poorly understood. This paper explores the mechanisms of external slow-thinking from a theoretical standpoint. We begin by examining the snowball error effect within the LLM reasoning process and connect it to the likelihood of correct reasoning using information theory. Building on this, we show that external slow-thinking methods can be interpreted as strategies to mitigate the error probability. We further provide a comparative analysis of popular external slow-thinking approaches, ranging from simple to complex, highlighting their differences and interrelationships. Our findings suggest that the efficacy of these methods is not primarily determined by the specific framework employed, and that expanding the search scope or the model's internal reasoning capacity may yield more sustained improvements in the long term. We open-source our code at https://github.com/ZyGan1999/Snowball-Errors-and-Probability.

Social Aspects · Accountability, Transparency, and Interpretability

Matthew Chen, Josh Engels, Max Tegmark

Sparse autoencoders (SAEs) aim to decompose language model representations into a sparse set of linear latent vectors. Recent works have improved SAEs using language model gradients, but these techniques require many expensive backward passes during training and still cause a significant increase in cross entropy loss when SAE reconstructions are inserted into the model. In this work, we improve on these limitations by taking a fundamentally different approach: we use low-rank adaptation (LoRA) to finetune the *language model itself* around a previously trained SAE. We analyze our method across SAE sparsity, SAE width, language model size, LoRA rank, and model layer on the Gemma Scope family of SAEs. In these settings, our method reduces the cross entropy loss gap by 30% - 55% when SAEs are inserted during the forward pass. We also find that compared to end-to-end (e2e) SAEs, our approach achieves the same downstream cross entropy loss 3$\times$ to 20$\times$ faster on Gemma-2-2B and 2$\times$ to 10$\times$ faster on Llama-3.2-1B. We further show that our technique improves downstream metrics and can adapt multiple SAEs at once. Our results demonstrate that improving model interpretability is not limited to post-hoc SAE training; Pareto improvements can also be achieved by directly optimizing the model itself.

General Machine Learning

Ayman Chaouki, Jesse Read, Albert Bifet

Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch \& Bound. However, most of these approaches rely on a Depth-First-Search strategy, which is inefficient when searching for DTs at high depths and requires the definition of a maximum depth hyperparameter. Best-First-Search was also employed by other methods to circumvent these issues. The downside of this strategy is its higher memory consumption, as such, it has to be designed in a fully efficient manner that takes full advantage of the problem's structure. We formulate the problem as an AND/OR graph search which we solve with a novel AO*-type algorithm called Branches. We prove both optimality and complexity guarantees for Branches and we show that it is more efficient than the state of the art theoretically and on a variety of experiments. Furthermore, Branches supports non-binary features unlike the other methods, we show that this property can further induce larger gains in computational efficiency.

Deep Learning · Graph Neural Networks

Masahiro Negishi, Thomas Gärtner, Pascal Welke

We investigate the distance function learned by message passing neural networks (MPNNs) in specific tasks, aiming to capture the _functional_ distance between prediction targets that MPNNs implicitly learn. This contrasts with previous work, which links MPNN distances on arbitrary tasks to _structural_ distances on graphs that ignore task-specific information. To address this gap, we distill the distance between MPNN embeddings into an interpretable graph distance. Our method uses optimal transport on the Weisfeiler Leman Labeling Tree (WILT), where the edge weights reveal subgraphs that strongly influence the distance between embeddings. This approach generalizes two well-known graph kernels and can be computed in linear time. Through extensive experiments, we demonstrate that MPNNs define the relative position of embeddings by focusing on a small set of subgraphs that are known to be functionally important in the domain.

Deep Learning · Large Language Models

Roman Abramov, Felix Steinbauer, Gjergji Kasneci

Transformers have achieved great success in numerous NLP tasks but continue to exhibit notable gaps in multi-step factual reasoning, especially when real-world knowledge is sparse. Recent advances in grokking have demonstrated that neural networks can transition from memorizing to perfectly generalizing once they detect underlying logical patterns -- yet these studies have primarily used small, synthetic tasks. In this paper, for the first time, we extend grokking to real-world factual data and address the challenge of dataset sparsity by augmenting existing knowledge graphs with carefully designed synthetic data to raise the ratio $\phi_r$ of inferred facts to atomic facts above the threshold required for grokking. Surprisingly, we find that even factually incorrect synthetic data can strengthen emergent reasoning circuits rather than degrade accuracy, as it forces the model to rely on relational structure rather than memorization. When evaluated on multi-hop reasoning benchmarks, our approach achieves up to 95--100\% accuracy on 2WikiMultiHopQA -- substantially improving over strong baselines and matching or exceeding current state-of-the-art results. We further provide an in-depth analysis of how increasing $\phi_r$ drives the formation of generalizing circuits inside Transformers. Our findings suggest that grokking-based data augmentation can unlock implicit multi-hop reasoning capabilities, opening the door to more robust and interpretable factual reasoning in large-scale language models.

Social Aspects · Accountability, Transparency, and Interpretability

Bart Bussmann, Noa Nabeshima, Adam Karvonen, Neel Nanda

Sparse autoencoders (SAEs) have emerged as a powerful tool for interpreting neural networks by extracting the concepts represented in their activations. However, choosing the size of the SAE dictionary (i.e. number of learned concepts) creates a tension: as dictionary size increases to capture more relevant concepts, sparsity incentivizes features to be split or absorbed into more specific features, leaving high-level features missing or warped. We introduce Matryoshka SAEs, a novel variant that addresses these issues by simultaneously training multiple nested dictionaries of increasing size, forcing the smaller dictionaries to independently reconstruct the inputs without using the larger dictionaries. This organizes features hierarchically - the smaller dictionaries learn general concepts, while the larger dictionaries learn more specific concepts, without incentive to absorb the high-level features. We train Matryoshka SAEs on Gemma-2-2B and TinyStories and find superior performance on sparse probing and targeted concept erasure tasks, more disentangled concept representations, and reduced feature absorption. While there is a minor tradeoff with reconstruction performance, we believe Matryoshka SAEs are a superior alternative for practical tasks, as they enable training arbitrarily large SAEs while retaining interpretable features at different levels of abstraction.

Deep Learning · Other Representation Learning

Damian Smith, Harvey Mannering, Antonia Marcu

A common belief in the representational comparison literature is that if two representations can be functionally aligned, they must capture similar information. In this paper we focus on model stitching and show that models can be functionally aligned, but represent very different information. Firstly, we show that discriminative models with very different biases can be stitched together. We then show that models trained to solve entirely different tasks on different data modalities, and even clustered random noise, can be successfully stitched into MNIST or ImageNet-trained models. We end with a discussion of the wider impact of our results on the community's current beliefs. Overall, our paper draws attention to the need to correctly interpret the results of such functional similarity measures and highlights the need for approaches that capture informational similarity.

Applications · Health / Medicine

Hung Manh Pham, Aaqib Saeed, Dong Ma

The accurate interpretation of Electrocardiogram (ECG) signals is pivotal for diagnosing cardiovascular diseases. Integrating ECG signals with accompanying textual reports further holds immense potential to enhance clinical diagnostics by combining physiological data and qualitative insights. However, this integration faces significant challenges due to inherent modality disparities and the scarcity of labeled data for robust cross-modal learning. To address these obstacles, we propose D-BETA, a novel framework that pre-trains ECG and text data using a contrastive masked auto-encoder architecture, uniquely combining generative and boosted discriminative capabilities for robust cross-modal representations. This is accomplished through masked modality modeling, specialized loss functions, and an improved negative sampling strategy tailored for cross-modal alignment. Extensive experiments on five public datasets across diverse downstream tasks demonstrate that D-BETA significantly outperforms existing methods, achieving an average AUC improvement of 15% in linear probing with only one percent of training data and 2% in zero-shot performance without requiring training data over state-of-the-art models. These results highlight the effectiveness of D-BETA, underscoring its potential to advance automated clinical diagnostics through multi-modal representations.

Deep Learning · Large Language Models

Tian Jin, Ellie Cheng, Zachary Ankner, Nikunj Saunshi, Blake Elias, Amir Yazdanbakhsh, Jonathan Ragan-Kelley, Suvinay Subramanian, Michael Carbin

Decoding with autoregressive language models traditionally occurs sequentially, generating one token after another. Recent attempts to introduce parallelism require a pre-determined structure in the generated content to implement parallel generation, such as by pattern-matching on bullet points. In this work, we present a new technique to automate parallel generation by dynamically exploiting the semantic independence of generation outputs to implement asynchronous decoding. We introduce an annotation language Pasta-Lang for language models to initiate asynchronous decoding at inference time. We also develop an accompanying Pasta-Lang interpreter that performs on-the-fly asynchronous decoding, effectively implementing parallel generation and speeding up inference. We present an instruction-finetuning dataset with Pasta-Lang-annotated responses for teaching LLMs to annotate semantic independence with Pasta-Lang as well as the methodology for creating the dataset. Our evaluation shows using the interpreter with a Pasta-Lang-equipped model achieves significant speedup while maintaining the same generation quality.

Applications · Neuroscience, Cognitive Science

Amin Nejatbakhsh, Yixin Wang

Neural circuits produce signals that are complex and nonlinear. To facilitate the understanding of neural dynamics, a popular approach is to fit state space models (SSM) to the data and analyze the dynamics of the low-dimensional latent variables. Despite the power of SSM to explain the dynamics of neural circuits, these models have been shown to merely capture statistical associations in the data and cannot be causally interpreted. Therefore, an important research problem is to build models that can predict neural dynamics under causal manipulations. Here, we propose interventional state-space models (iSSM), a class of causal models that can predict neural responses to novel perturbations. We draw on recent advances in causal dynamical systems and present theoretical results for the identifiability of iSSM. In simulations of the motor cortex, we show that iSSM can recover the true latents and the underlying dynamics. In addition, we illustrate two applications of iSSM in biological datasets. First, we applied iSSM to a dataset of calcium recordings from ALM neurons in mice during photostimulation. Second, we applied iSSM to a dataset of electrophysiological recordings from macaque dlPFC during micro-stimulation. In both cases, we show that iSSM outperforms SSM and results in identifiable parameters. The code is available at https://github.com/amin-nejat/issm.

Optimization · Discrete and Combinatorial Optimization

Jourdain Lamperski, Haeseong Yang, Oleg Prokopyev

We consider the *max-min eigenvalue augmentation* problem: given $n \times n$ symmetric positive semidefinite matrices $M,A_1,\ldots, A_m$ and a positive integer $k < m$, the goal is to choose a subset $I \subset \{1,\ldots,m\}$ of cardinality at most $k$ that maximizes the minimum eigenvalue of the matrix $M + \sum_{i \in I} A_i$. The problem captures both the *Bayesian E-optimal design* and *maximum algebraic connectivity augmentation* problems. In contrast to the existing work, we do not assume that the *augmentation matrices* are rank-one matrices, and we focus on the setting in which $k < n$. We show that a *simple* randomized rounding method provides a constant-factor approximation if the *optimal increase* is sufficiently large, specifically, if $\mathrm{OPT} - \lambda_{\mathrm{min}}(M) = \Omega(R \ln k)$, where $\mathrm{OPT}$ is the optimal value, and $R$ is the maximum trace of an augmentation matrix. To establish the guarantee, we derive a matrix concentration inequality that is of independent interest. The inequality can be interpreted as an *intrinsic dimension* analog of the matrix Chernoff inequality for the minimum eigenvalue of a sum of independent random positive semidefinite matrices; such an inequality has already been established for the maximum eigenvalue, but not for the minimum eigenvalue.

General Machine Learning · Causality

Raanan Yehezkel Rohekar, Yaniv Gurwicz, Sungduk Yu, Estelle Aflalo Guez, Vasudev Lal

Are generative pre-trained transformer (GPT) models, trained only to predict the next token, implicitly learning a world model from which sequences are generated one token at a time? We address this question by deriving a causal interpretation of the attention mechanism in GPT and presenting a causal world model that arises from this interpretation. Furthermore, we propose that GPT models, at inference time, can be utilized for zero-shot causal structure learning for input sequences, and introduce a corresponding confidence score. Empirical tests were conducted in controlled environments using the setups of the Othello and Chess strategy games. A GPT, pre-trained on real-world games played with the intention of winning, was tested on out-of-distribution synthetic data consisting of sequences of random legal moves. We find that the GPT model is likely to generate legal next moves for out-of-distribution sequences for which a causal structure is encoded in the attention mechanism with high confidence. In cases where it generates illegal moves, it also fails to capture a causal structure.

Social Aspects · Accountability, Transparency, and Interpretability

Adam Karvonen, Can Rager, Johnny Lin, Curt Tigges, Joseph Bloom, David Chanin, Yeu-Tong Lau, Eoin Farrell, Callum McDougall, Kola Ayonrinde 等

Sparse autoencoders (SAEs) are a popular technique for interpreting language model activations, and there is extensive recent work on improving SAE effectiveness. However, most prior work evaluates progress using unsupervised proxy metrics with unclear practical relevance. We introduce SAEBench, a comprehensive evaluation suite that measures SAE performance across eight diverse metrics, spanning interpretability, feature disentanglement and practical applications like unlearning. To enable systematic comparison, we open-source a suite of over 200 SAEs across seven recently proposed SAE architectures and training algorithms. Our evaluation reveals that gains on proxy metrics do not reliably translate to better practical performance. For instance, while Matryoshka SAEs slightly underperform on existing proxy metrics, they substantially outperform other architectures on feature disentanglement metrics; moreover, this advantage grows with SAE scale. By providing a standardized framework for measuring progress in SAE development, SAEBench enables researchers to study scaling trends and make nuanced comparisons between different SAE architectures and training methodologies. Our interactive interface enables researchers to flexibly visualize relationships between metrics across hundreds of open-source SAEs at www.neuronpedia.org/sae-bench

Social Aspects · Accountability, Transparency, and Interpretability

Subhash Kantamneni, Josh Engels, Senthooran Rajamanoharan, Max Tegmark, Neel Nanda

Sparse autoencoders (SAEs) are a popular method for interpreting concepts represented in large language model (LLM) activations. However, there is a lack of evidence regarding the validity of their interpretations due to the lack of a ground truth for the concepts used by an LLM, and a growing number of works have presented problems with current SAEs. One alternative source of evidence would be demonstrating that SAEs improve performance on downstream tasks beyond existing baselines. We test this by applying SAEs to the real-world task of LLM activation probing in four regimes: data scarcity, class imbalance, label noise, and covariate shift. Due to the difficulty of detecting concepts in these challenging settings, we hypothesize that SAEs’ basis of interpretable, concept-level latents should provide a useful inductive bias. However, although SAEs occasionally perform better than baselines on individual datasets, we are unable to design ensemble methods combining SAEs with baselines that consistently outperform ensemble methods solely using baselines. Additionally, although SAEs initially appear promising for identifying spurious correlations, detecting poor dataset quality, and training multi-token probes, we are able to achieve similar results with simple non-SAE baselines as well. Though we cannot discount SAEs’ utility on other tasks, our findings highlight the shortcomings of current SAEs and the need to rigorously evaluate interpretability methods on downstream tasks with strong baselines.

Applications · Computer Vision

Peng Wang, Yong Li, Lin Zhao, Xiu-Shen Wei

Fine-grained hashing has become a powerful solution for rapid and efficient image retrieval, particularly in scenarios requiring high discrimination between visually similar categories. To enable each hash bit to correspond to specific visual attributes, we propose a novel method that harnesses learnable queries for attribute-aware hash code learning. This method deploys a tailored set of queries to capture and represent nuanced attribute-level information within the hashing process, thereby enhancing both the interpretability and relevance of each hash bit. Building on this query-based optimization framework, we incorporate an auxiliary branch to help alleviate the challenges of complex landscape optimization often encountered with low-bit hash codes. This auxiliary branch models high-order attribute interactions, reinforcing the robustness and specificity of the generated hash codes. Experimental results on benchmark datasets demonstrate that our method generates attribute-aware hash codes and consistently outperforms state-of-the-art techniques in retrieval accuracy and robustness, especially for low-bit hash codes, underscoring its potential in fine-grained image hashing tasks.

Social Aspects · Accountability, Transparency, and Interpretability

Emiliano Penaloza, Tianyue Zhang, Laurent Charlin, Mateo Espinosa Zarlenga

Concept Bottleneck Models (CBMs) propose toenhance the trustworthiness of AI systems byconstraining their decisions on a set of humanunderstandable concepts. However, CBMs typically rely on datasets with assumedly accurateconcept labels—an assumption often violated inpractice which we show can significantly degradeperformance. To address this, we introduce theConcept Preference Optimization (CPO) objective, a new loss function based on Direct Preference Optimization, which effectively mitigatesthe negative impact of concept mislabeling onCBM performance. We provide an analysis onsome key properties of the CPO objective showing it directly optimizes for the concept’s posteriordistribution, and contrast it against Binary CrossEntropy (BCE) where we show CPO is inherentlyless sensitive to concept noise. We empiricallyconfirm our analysis finding that CPO consistentlyoutperforms BCE in three real-world datasets withand without added label noise

Applications · Everything Else

Haohan Zou, Jie Feng, Hao Zhao, Yuanyuan Shi

Despite advances in learning-based methods, finding valid Lyapunov functions for nonlinear dynamical systems remains challenging. Current neural network approaches face two main issues: challenges in scalable verification and limited interpretability. To address these, we propose an end-to-end framework using transformers to construct analytical Lyapunov functions (local), which simplifies formal verification, enhances interpretability, and provides valuable insights for control engineers. Our framework consists of a transformer-based trainer that generates candidate Lyapunov functions and a falsifier that verifies candidate expressions and refines the model via risk-seeking policy gradient. Unlike Alfarano et al. (2024), which utilizes pre-training and seeks global Lyapunov functions for low-dimensional systems, our model is trained from scratch via reinforcement learning (RL) and succeeds in finding local Lyapunov functions for *high-dimensional* and *non-polynomial* systems. Given the symbolic nature of the Lyapunov function candidates, we employ efficient optimization methods for falsification during training and formal verification tools for the final verification. We demonstrate the efficiency of our approach on a range of nonlinear dynamical systems with up to ten dimensions and show that it can discover Lyapunov functions not previously identified in the control literature. Full implementation is available on [Github](https://github.com/JieFeng-cse/Analytical-Lyapunov-Function-Discovery).

Applications · Computer Vision

Yinpeng Chen, Dongdong Chen, Xiyang Dai, Mengchen Liu, Yinan Feng, Youzuo Lin, Lu Yuan, Zicheng Liu

In this paper, we empirically demonstrate that natural images can be reconstructed with high fidelity from compressed representations using a simple first-order norm-plus-linear autoregressive (FINOLA) process—without relying on explicit positional information. Through systematic analysis, we observe that the learned coefficient matrices ($\mathbf{A}$ and $\mathbf{B}$) in FINOLA are typically invertible, and their product, $\mathbf{AB}^{-1}$, is diagonalizable across training runs. This structure enables a striking interpretation: FINOLA’s latent dynamics resemble a system of one-way wave equations evolving in a compressed latent space. Under this framework, each image corresponds to a unique solution of these equations. This offers a new perspective on image invariance, suggesting that the underlying structure of images may be governed by simple, invariant dynamic laws. Our findings shed light on a novel avenue for understanding and modeling visual data through the lens of latent-space dynamics and wave propagation.