In this paper, we investigate how model distillation impacts the development of reasoning features in large language models (LLMs). To explore this, we train a crosscoder on Qwen-series models and their fine-tuned variants. Our results suggest that the crosscoder learns features corresponding to various types of reasoning, including self-reflection and computation verification. Moreover, we observe that distilled models contain unique reasoning feature directions, which could be used to steer the model into over-thinking or incisive-thinking mode. In particular, we perform analysis on four specific reasoning categories: (a) self-reflection, (b) deductive reasoning, (c) alternative reasoning, and (d) contrastive reasoning. Finally, we examine the changes in feature geometry resulting from the distillation process and find indications that larger distilled models may develop more structured representations, which correlate with enhanced distillation performance. By providing insights into how distillation modifies the model, our study contributes to enhancing the transparency and reliability of AI systems.

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.

In this paper, we introduce **harmonic loss** as an alternative to the standard cross-entropy loss for training neural networks and large language models (LLMs). Harmonic loss enables improved interpretability and faster convergence, owing to its scale invariance and finite convergence point by design, which can be interpreted as a class center. We first validate the performance of harmonic models across algorithmic, vision, and language datasets. Through extensive experiments, we demonstrate that models trained with harmonic loss outperform standard models by: (a) enhancing interpretability, (b) requiring less data for generalization, and (c) reducing grokking. Moreover, we compare a GPT-2 model trained with harmonic loss to the standard GPT-2, illustrating that the harmonic model develops more interpretable representations. Looking forward, we believe harmonic loss has the potential to become a valuable tool in domains with limited data availability or in high-stakes applications where interpretability and reliability are paramount, paving the way for more robust and efficient neural network models.

Mathematical reasoning is an increasingly important indicator of large language model (LLM) capabilities, yet we lack understanding of how LLMs process even simple mathematical tasks. To address this, we reverse engineer how three mid-sized LLMs compute addition. We first discover that numbers are represented in these LLMs as a generalized helix, which is strongly causally implicated for the tasks of addition and subtraction, and is also causally relevant for integer division, multiplication, and modular arithmetic. We then propose that LLMs compute addition by manipulating this generalized helix using the "Clock" algorithm: to solve $a+b$, the helices for $a$ and $b$ are manipulated to produce the $a+b$ answer helix which is then read out to model logits. We model influential MLP outputs, attention head outputs, and even individual neuron preactivations with these helices and verify our understanding with causal interventions. By demonstrating that LLMs represent numbers on a helix and manipulate this helix to perform addition, we present the first representation-level explanation of an LLM's mathematical capability.

Sparse autoencoders (SAEs) 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% to 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.

Mechanistic interpretability aims to understand the computational mechanisms underlying neural networks' capabilities in order to accomplish concrete scientific and engineering goals. Progress in this field thus promises to provide greater assurance over AI system behavior and shed light on exciting scientific questions about the nature of intelligence. Despite recent progress toward these goals, there are many open problems in the field that require solutions before many scientific and practical benefits can be realized: Our methods require both conceptual and practical improvements to reveal deeper insights; we must figure out how best to apply our methods in pursuit of specific goals; and the field must grapple with socio-technical challenges that influence and are influenced by our work. This forward-facing review discusses the current frontier of mechanistic interpretability and the open problems that the field may benefit from prioritizing. This review collects the perspectives of its various authors and represents a synthesis of their views by Apollo Research on behalf of Schmidt Sciences. The perspectives presented here do not necessarily reflect the views of any individual author or the institutions with which they are affiliated.

We aim to understand physics of skill learning, i.e., how skills are learned in neural networks during training. We start by observing the Domino effect, i.e., skills are learned sequentially, and notably, some skills kick off learning right after others complete learning, similar to the sequential fall of domino cards. To understand the Domino effect and relevant behaviors of skill learning, we take physicists' approach of abstraction and simplification. We propose three models with varying complexities -- the Geometry model, the Resource model, and the Domino model, trading between reality and simplicity. The Domino effect can be reproduced in the Geometry model, whose resource interpretation inspires the Resource model, which can be further simplified to the Domino model. These models present different levels of abstraction and simplification; each is useful to study some aspects of skill learning. The Geometry model provides interesting insights into neural scaling laws and optimizers; the Resource model sheds light on the learning dynamics of compositional tasks; the Domino model reveals the benefits of modularity. These models are not only conceptually interesting -- e.g., we show how Chinchilla scaling laws can emerge from the Geometry model, but also are useful in practice by inspiring algorithmic development -- e.g., we show how simple algorithmic changes, motivated by these toy models, can speed up the training of deep learning models.

Sparse autoencoders (SAEs) are a promising technique for decomposing language model activations into interpretable linear features. However, current SAEs fall short of completely explaining model performance, resulting in "dark matter": unexplained variance in activations. This work investigates dark matter as an object of study in its own right. Surprisingly, we find that much of SAE dark matter--about half of the error vector itself and >90% of its norm--can be linearly predicted from the initial activation vector. Additionally, we find that the scaling behavior of SAE error norms at a per token level is remarkably predictable: larger SAEs mostly struggle to reconstruct the same contexts as smaller SAEs. We build on the linear representation hypothesis to propose models of activations that might lead to these observations, including postulating a new type of "introduced error"; these insights imply that the part of the SAE error vector that cannot be linearly predicted ("nonlinear" error) might be fundamentally different from the linearly predictable component. To validate this hypothesis, we empirically analyze nonlinear SAE error and show that 1) it contains fewer not yet learned features, 2) SAEs trained on it are quantitatively worse, 3) it helps predict SAE per-token scaling behavior, and 4) it is responsible for a proportional amount of the downstream increase in cross entropy loss when SAE activations are inserted into the model. Finally, we examine two methods to reduce nonlinear SAE error at a fixed sparsity: inference time gradient pursuit, which leads to a very slight decrease in nonlinear error, and linear transformations from earlier layer SAE outputs, which leads to a larger reduction.

We show that these attractor representations optimize generalization to unseen examples by exploiting properties of knowledge graph relations (e.g. We find experimental support for such universality by showing that LLMs and simpler neural networks can be stitched, i.e., by stitching the first part of one model to the last part of another, mediated only by an affine or almost affine transformation. We hypothesize that this dynamic toward simplicity and generalization is driven by "intelligence from starvation": where overfitting is minimized by pressure to minimize the use of resources that are either scarce or competed for against other tasks. Large Language Models (LLMs), despite being primarily trained for next-token predictions, have shown impressive reasoning capabilities (Bubeck et al., 2023; Anthropic, 2024; Team et al., 2023). However, despite recent progress reviewed below, it is not well understood what knowledge LLMs represent internally and how they represent it. Improving such understanding could enable valuable progress relevant to transparency, interpretability, fairness and robustness, for example discovering and correcting inaccuracies to improve model reliability.

Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.