Decomposing MLP Activations into Interpretable Features via Semi-Nonnegative Matrix Factorization

A central goal for mechanistic interpretability has been to identify the right units of analysis in large language models (LLMs) that causally explain their outputs. While early work focused on individual neurons, evidence that neurons often encode multiple concepts has motivated a shift toward analyzing directions in activation space. A key question is how to find directions that capture interpretable features in an unsupervised manner. Current methods rely on dictionary learning with sparse autoencoders (SAEs), commonly trained over residual stream activations to learn directions from scratch. However, SAEs often struggle in causal evaluations and lack intrinsic interpretability, as their learning is not explicitly tied to the computations of the model. Here, we tackle these limitations by directly decomposing MLP activations with semi-nonnegative matrix factorization (SNMF), such that the learned features are (a) sparse linear combinations of co-activated neurons, and (b) mapped to their activating inputs, making them directly interpretable. Experiments on Llama 3.1, Gemma 2 and GPT-2 show that SNMF derived features outperform SAEs and a strong supervised baseline (difference-in-means) on causal steering, while aligning with human-interpretable concepts. Further analysis reveals that specific neuron combinations are reused across semantically-related features, exposing a hierarchical structure in the MLP's activation space. Together, these results position SNMF as a simple and effective tool for identifying interpretable features and dissecting concept representations in LLMs.

Resa: Transparent Reasoning Models via SAEs

How cost-effectively can we elicit strong reasoning in language models by leveraging their underlying representations? We answer this question with Resa, a family of 1.5B reasoning models trained via a novel and efficient sparse autoencoder tuning (SAE-Tuning) procedure. This method first trains an SAE to capture reasoning abilities from a source model, and then uses the trained SAE to guide a standard supervised fine-tuning process to elicit such abilities in a target model, all using verified question-answer data without any reasoning traces. Notably, when applied to certain base models before further RL post-training, SAE-Tuning retains >97% of its RL-trained counterpart's reasoning performance while reducing training costs by >2000x to roughly \$1 and training time by >450x to around 20 minutes. Furthermore, when applied to lightly RL-trained models (e.g., within 1 hour on 2 GPUs), it enables reasoning performance such as 43.33% Pass@1 on AIME24 and 90% Pass@1 on AMC23 for only around \$1 additional cost. Surprisingly, the reasoning abilities extracted via SAEs are potentially both generalizable and modular. Generality means abilities extracted from one dataset still elevate performance on a larger and overlapping corpus. Modularity means abilities extracted from Qwen or Qwen-Math can be attached to the R1-Distill model at test time, without any retraining, and yield comparable gains. Extensive ablations validate these findings and all artifacts are fully open-sourced.

Advanced fraud detection using machine learning models: enhancing financial transaction security

The rise of digital payments has accelerated the need for intelligent and scalable systems to detect fraud. This research presents an end-to-end, feature-rich machine learning framework for detecting credit card transaction anomalies and fraud using real-world data. The study begins by merging transactional, cardholder, merchant, and merchant category datasets from a relational database to create a unified analytical view. Through the feature engineering process, we extract behavioural signals such as average spending, deviation from historical patterns, transaction timing irregularities, and category frequency metrics. These features are enriched with temporal markers such as hour, day of week, and weekend indicators to expose all latent patterns that indicate fraudulent behaviours. Exploratory data analysis reveals contextual transaction trends across all the dataset features. Using the transactional data, we train and evaluate a range of unsupervised models: Isolation Forest, One Class SVM, and a deep autoencoder trained to reconstruct normal behavior. These models flag the top 1% of reconstruction errors as outliers. PCA visualizations illustrate each models ability to separate anomalies into a two-dimensional latent space. We further segment the transaction landscape using K-Means clustering and DBSCAN to identify dense clusters of normal activity and isolate sparse, suspicious regions.

Training Superior Sparse Autoencoders for Instruct Models

As large language models (LLMs) grow in scale and capability, understanding their internal mechanisms becomes increasingly critical. Sparse autoencoders (SAEs) have emerged as a key tool in mechanistic interpretability, enabling the extraction of human-interpretable features from LLMs. However, existing SAE training methods are primarily designed for base models, resulting in reduced reconstruction quality and interpretability when applied to instruct models. To bridge this gap, we propose $\underline{\textbf{F}}$inetuning-$\underline{\textbf{a}}$ligned $\underline{\textbf{S}}$equential $\underline{\textbf{T}}$raining ($\textit{FAST}$), a novel training method specifically tailored for instruct models. $\textit{FAST}$ aligns the training process with the data distribution and activation patterns characteristic of instruct models, resulting in substantial improvements in both reconstruction and feature interpretability. On Qwen2.5-7B-Instruct, $\textit{FAST}$ achieves a mean squared error of 0.6468 in token reconstruction, significantly outperforming baseline methods with errors of 5.1985 and 1.5096. In feature interpretability, $\textit{FAST}$ yields a higher proportion of high-quality features, for Llama3.2-3B-Instruct, $21.1\%$ scored in the top range, compared to $7.0\%$ and $10.2\%$ for $\textit{BT(P)}$ and $\textit{BT(F)}$. Surprisingly, we discover that intervening on the activations of special tokens via the SAEs leads to improvements in output quality, suggesting new opportunities for fine-grained control of model behavior. Code, data, and 240 trained SAEs are available at https://github.com/Geaming2002/FAST.

SWAT-NN: Simultaneous Weights and Architecture Training for Neural Networks in a Latent Space

Designing neural networks typically relies on manual trial and error or a neural architecture search (NAS) followed by weight training. The former is time-consuming and labor-intensive, while the latter often discretizes architecture search and weight optimization. In this paper, we propose a fundamentally different approach that simultaneously optimizes both the architecture and the weights of a neural network. Our framework first trains a universal multi-scale autoencoder that embeds both architectural and parametric information into a continuous latent space, where functionally similar neural networks are mapped closer together. Given a dataset, we then randomly initialize a point in the embedding space and update it via gradient descent to obtain the optimal neural network, jointly optimizing its structure and weights. The optimization process incorporates sparsity and compactness penalties to promote efficient models. Experiments on synthetic regression tasks demonstrate that our method effectively discovers sparse and compact neural networks with strong performance.

Improving LLM Reasoning through Interpretable Role-Playing Steering

Role-playing has emerged as an effective technique for enhancing the reasoning capabilities of large language models (LLMs). However, existing methods primarily rely on prompt engineering, which often lacks stability and interpretability. In this paper, we introduce Sparse Autoencoder Role-Playing Steering (SRPS), a novel framework that identifies and manipulates internal model features associated with role-playing behavior. Our approach extracts latent representations from role-play prompts, selects the most relevant features based on activation patterns, and constructs a steering vector that can be injected into the model's residual stream with controllable intensity. Our method enables fine-grained control over role-specific behavior and offers insights into how role information influences internal model activations. Extensive experiments across various reasoning benchmarks and model sizes demonstrate consistent performance gains. Notably, in the zero-shot chain-of-thought (CoT) setting, the accuracy of Llama3.1-8B on CSQA improves from 31.86% to 39.80%, while Gemma2-9B on SVAMP increases from 37.50% to 45.10%. These results highlight the potential of SRPS to enhance reasoning ability in LLMs, providing better interpretability and stability compared to traditional prompt-based role-playing.

Guided Graph Compression for Quantum Graph Neural Networks

Graph Neural Networks (GNNs) are effective for processing graph-structured data but face challenges with large graphs due to high memory requirements and inefficient sparse matrix operations on GPUs. Quantum Computing (QC) offers a promising avenue to address these issues and inspires new algorithmic approaches. In particular, Quantum Graph Neural Networks (QGNNs) have been explored in recent literature. However, current quantum hardware limits the dimension of the data that can be effectively encoded. Existing approaches either simplify datasets manually or use artificial graph datasets. This work introduces the Guided Graph Compression (GGC) framework, which uses a graph autoencoder to reduce both the number of nodes and the dimensionality of node features. The compression is guided to enhance the performance of a downstream classification task, which can be applied either with a quantum or a classical classifier. The framework is evaluated on the Jet Tagging task, a classification problem of fundamental importance in high energy physics that involves distinguishing particle jets initiated by quarks from those by gluons. The GGC is compared against using the autoencoder as a standalone preprocessing step and against a baseline classical GNN classifier. Our numerical results demonstrate that GGC outperforms both alternatives, while also facilitating the testing of novel QGNN ansatzes on realistic datasets.

Transferring Features Across Language Models With Model Stitching

In this work, we demonstrate that affine mappings between residual streams of language models is a cheap way to effectively transfer represented features between models. We apply this technique to transfer the weights of Sparse Autoencoders (SAEs) between models of different sizes to compare their representations. We find that small and large models learn highly similar representation spaces, which motivates training expensive components like SAEs on a smaller model and transferring to a larger model at a FLOPs savings. For example, using a small-to-large transferred SAE as initialization can lead to 50% cheaper training runs when training SAEs on larger models. Next, we show that transferred probes and steering vectors can effectively recover ground truth performance. Finally, we dive deeper into feature-level transferability, finding that semantic and structural features transfer noticeably differently while specific classes of functional features have their roles faithfully mapped. Overall, our findings illustrate similarities and differences in the linear representation spaces of small and large models and demonstrate a method for improving the training efficiency of SAEs.

Sparse Autoencoders, Again?

Is there really much more to say about sparse autoencoders (SAEs)? Autoencoders in general, and SAEs in particular, represent deep architectures that are capable of modeling low-dimensional latent structure in data. Such structure could reflect, among other things, correlation patterns in large language model activations, or complex natural image manifolds. And yet despite the wide-ranging applicability, there have been relatively few changes to SAEs beyond the original recipe from decades ago, namely, standard deep encoder/decoder layers trained with a classical/deterministic sparse regularizer applied within the latent space. One possible exception is the variational autoencoder (VAE), which adopts a stochastic encoder module capable of producing sparse representations when applied to manifold data. In this work we formalize underappreciated weaknesses with both canonical SAEs, as well as analogous VAEs applied to similar tasks, and propose a hybrid alternative model that circumvents these prior limitations. In terms of theoretical support, we prove that global minima of our proposed model recover certain forms of structured data spread across a union of manifolds. Meanwhile, empirical evaluations on synthetic and real-world datasets substantiate the efficacy of our approach in accurately estimating underlying manifold dimensions and producing sparser latent representations without compromising reconstruction error. In general, we are able to exceed the performance of equivalent-capacity SAEs and VAEs, as well as recent diffusion models where applicable, within domains such as images and language model activation patterns.

Evaluating Sparse Autoencoders: From Shallow Design to Matching Pursuit

Sparse autoencoders (SAEs) have recently become central tools for interpretability, leveraging dictionary learning principles to extract sparse, interpretable features from neural representations whose underlying structure is typically unknown. This paper evaluates SAEs in a controlled setting using MNIST, which reveals that current shallow architectures implicitly rely on a quasi-orthogonality assumption that limits the ability to extract correlated features. To move beyond this, we introduce a multi-iteration SAE by unrolling Matching Pursuit (MP-SAE), enabling the residual-guided extraction of correlated features that arise in hierarchical settings such as handwritten digit generation while guaranteeing monotonic improvement of the reconstruction as more atoms are selected.