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Aaron Mueller

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6 papers

2 author rows

ICLR Conference 2025 Conference Paper

Arithmetic Without Algorithms: Language Models Solve Math with a Bag of Heuristics

Yaniv Nikankin
Anja Reusch
Aaron Mueller
Yonatan Belinkov

Do large language models (LLMs) solve reasoning tasks by learning robust generalizable algorithms, or do they memorize training data? To investigate this question, we use arithmetic reasoning as a representative task. Using causal analysis, we identify a subset of the model (a circuit) that explains most of the model's behavior for basic arithmetic logic and examine its functionality. By zooming in on the level of individual circuit neurons, we discover a sparse set of important neurons that implement simple heuristics. Each heuristic identifies a numerical input pattern and outputs corresponding answers. We hypothesize that the combination of these heuristic neurons is the mechanism used to produce correct arithmetic answers. To test this, we categorize each neuron into several heuristic types---such as neurons that activate when an operand falls within a certain range---and find that the unordered combination of these heuristic types is the mechanism that explains most of the model's accuracy on arithmetic prompts. Finally, we demonstrate that this mechanism appears as the main source of arithmetic accuracy early in training. Overall, our experimental results across several LLMs show that LLMs perform arithmetic using neither robust algorithms nor memorization; rather, they rely on a ``bag of heuristics''.

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ICML Conference 2025 Conference Paper

MIB: A Mechanistic Interpretability Benchmark

Aaron Mueller
Atticus Geiger
Sarah Wiegreffe
Dana Arad
Iván Arcuschin
Adam Belfki
Yik Siu Chan
Jaden Fried Fiotto-Kaufman

How can we know whether new mechanistic interpretability methods achieve real improvements? In pursuit of lasting evaluation standards, we propose MIB, a Mechanistic Interpretability Benchmark, with two tracks spanning four tasks and five models. MIB favors methods that precisely and concisely recover relevant causal pathways or causal variables in neural language models. The circuit localization track compares methods that locate the model components—and connections between them—most important for performing a task (e. g. , attribution patching or information flow routes). The causal variable track compares methods that featurize a hidden vector, e. g. , sparse autoencoders (SAE) or distributed alignment search (DAS), and align those features to a task-relevant causal variable. Using MIB, we find that attribution and mask optimization methods perform best on circuit localization. For causal variable localization, we find that the supervised DAS method performs best, while SAEs features are not better than neurons, i. e. , non-featurized hidden vectors. These findings illustrate that MIB enables meaningful comparisons, and increases our confidence that there has been real progress in the field.

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ICLR Conference 2025 Conference Paper

NNsight and NDIF: Democratizing Access to Open-Weight Foundation Model Internals

Jaden Fried Fiotto-Kaufman
Alexander Russell Loftus
Eric Todd
Jannik Brinkmann
Koyena Pal
Dmitrii Troitskii
Michael Ripa
Adam Belfki

We introduce NNsight and NDIF, technologies that work in tandem to enable scientific study of the representations and computations learned by very large neural networks. NNsight is an open-source system that extends PyTorch to introduce deferred remote execution. The National Deep Inference Fabric (NDIF) is a scalable inference service that executes NNsight requests, allowing users to share GPU resources and pretrained models. These technologies are enabled by the Intervention Graph, an architecture developed to decouple experimental design from model runtime. Together, this framework provides transparent and efficient access to the internals of deep neural networks such as very large language models (LLMs) without imposing the cost or complexity of hosting customized models individually. We conduct a quantitative survey of the machine learning literature that reveals a growing gap in the study of the internals of large-scale AI. We demonstrate the design and use of our framework to address this gap by enabling a range of research methods on huge models. Finally, we conduct benchmarks to compare performance with previous approaches. Code, documentation, and tutorials are available at https://nnsight.net/.

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ICLR Conference 2025 Conference Paper

Sparse Feature Circuits: Discovering and Editing Interpretable Causal Graphs in Language Models

Samuel Marks
Can Rager
Eric J. Michaud
Yonatan Belinkov
David Bau
Aaron Mueller

We introduce methods for discovering and applying **sparse feature circuits**. These are causally implicated subnetworks of human-interpretable features for explaining language model behaviors. Circuits identified in prior work consist of polysemantic and difficult-to-interpret units like attention heads or neurons, rendering them unsuitable for many downstream applications. In contrast, sparse feature circuits enable detailed understanding of unanticipated mechanisms in neural networks. Because they are based on fine-grained units, sparse feature circuits are useful for downstream tasks: We introduce SHIFT, where we improve the generalization of a classifier by ablating features that a human judges to be task-irrelevant. Finally, we demonstrate an entirely unsupervised and scalable interpretability pipeline by discovering thousands of sparse feature circuits for automatically discovered model behaviors.

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ICLR Conference 2024 Conference Paper

Function Vectors in Large Language Models

Eric Todd
Millicent Li
Arnab Sen Sharma
Aaron Mueller
Byron C. Wallace
David Bau

We report the presence of a simple neural mechanism that represents an input-output function as a vector within autoregressive transformer language models (LMs). Using causal mediation analysis on a diverse range of in-context-learning (ICL) tasks, we find that a small number attention heads transport a compact representation of the demonstrated task, which we call a function vector (FV). FVs are robust to changes in context, i.e., they trigger execution of the task on inputs such as zero-shot and natural text settings that do not resemble the ICL contexts from which they are collected. We test FVs across a range of tasks, models, and layers and find strong causal effects across settings in middle layers. We investigate the internal structure of FVs and find while that they often contain information that encodes the output space of the function, this information alone is not sufficient to reconstruct an FV. Finally, we test semantic vector composition in FVs, and find that to some extent they can be summed to create vectors that trigger new complex tasks. Our findings show that compact, causal internal vector representations of function abstractions can be explicitly extracted from LLMs.

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TMLR Journal 2023 Journal Article

Inverse Scaling: When Bigger Isn't Better

Ian R. McKenzie
Alexander Lyzhov
Michael Martin Pieler
Alicia Parrish
Aaron Mueller
Ameya Prabhu
Euan McLean
Xudong Shen

Work on scaling laws has found that large language models (LMs) show predictable improvements to overall loss with increased scale (model size, training data, and compute). Here, we present evidence for the claim that LMs may show inverse scaling, or worse task performance with increased scale, e.g., due to flaws in the training objective and data. We present empirical evidence of inverse scaling on 11 datasets collected by running a public contest, the Inverse Scaling Prize, with a substantial prize pool. Through analysis of the datasets, along with other examples found in the literature, we identify four potential causes of inverse scaling: (i) preference to repeat memorized sequences over following in-context instructions, (ii) imitation of undesirable patterns in the training data, (iii) tasks containing an easy distractor task which LMs could focus on, rather than the harder real task, and (iv) correct but misleading few-shot demonstrations of the task. We release the winning datasets at inversescaling.com/data to allow for further investigation of inverse scaling. Our tasks have helped drive the discovery of U-shaped and inverted-U scaling trends, where an initial trend reverses, suggesting that scaling trends are less reliable at predicting the behavior of larger-scale models than previously understood. Overall, our results suggest that there are tasks for which increased model scale alone may not lead to progress, and that more careful thought needs to go into the data and objectives for training language models.

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