Thomas Dooms

Thomas Dooms, Ing Jyh Tsang, Jose Oramas

Modern machine learning models are able to outperform humans on a variety of non-trivial tasks. However, as the complexity of the models increases, they consume significant amounts of power and still struggle to generalize effectively to unseen data. Local learning, which focuses on updating subsets of a model's parameters at a time, has emerged as a promising technique to address these issues. Recently, a novel local learning algorithm, called Forward-Forward, has received widespread attention due to its innovative approach to learning. Unfortunately, its application has been limited to smaller datasets due to scalability issues. To this end, we propose The Trifecta, a collection of three simple techniques that synergize exceptionally well and drastically improve the Forward-Forward algorithm on deeper networks. Our experiments demonstrate that our models are on par with similarly structured, backpropagation-based models in both training speed and test accuracy on simple datasets. This is achieved by the ability to learn representations that are informative locally, on a layer-by-layer basis, and retain their informativeness when propagated to deeper layers in the architecture. This leads to around 84% accuracy on CIFAR-10, a notable improvement (25%) over the original FF algorithm. These results highlight the potential of Forward-Forward as a genuine competitor to backpropagation and as a promising research avenue.

ML Nissen Gonzalez, Melwina Albuquerque, Laurence Wroe et al.

Mechanistic interpretability aims to break models into meaningful parts; verifying that two such parts implement the same computation is a prerequisite. Existing similarity measures evaluate either empirical behaviour, leaving them blind to out-of-distribution mechanisms, or basis-dependent parameters, meaning they disregard weight-space symmetries. To address these issues for the class of tensor-based models, we introduce a weight-based metric, tensor similarity, that is invariant to such symmetries. This metric captures global functional equivalence and accounts for cross-layer mechanisms using an efficient recursive algorithm. Empirically, tensor similarity tracks functional training dynamics, such as grokking and backdoor insertion, with higher fidelity than existing metrics. This reduces measuring similarity and verifying faithfulness into a solved algebraic problem rather than one of empirical approximation.

Ward Gauderis, Thomas Dooms, Steven T. Holmer et al.

Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be objectively verified, compared, or composed. We introduce compositional interpretability, a category-theoretic framework grounded in the principles of compositionality and minimum description length. Compositional interpretations are pairs of syntactic and semantic mappings that must commute to enforce consistency between a model's decomposition and its observed behaviour. We deconstruct explanation quality into measures of faithfulness and complexity to cast interpretability as a constrained optimisation problem, and introduce compressive refinement to systematically restructure models into simpler parts without altering their function. Finally, we prove a parsimony criterion under which syntactic compression theoretically guarantees more concise, human-aligned explanations. Our framework situates prominent mechanistic methods as subclasses of refinement, and clarifies why their compressibility heuristics tend to align with human interpretability. Our work provides a measurable, optimisable foundation for automating the discovery and evaluation of mechanistic explanations.

Lennart Finke, Chandan Sreedhara, Thomas Dooms et al.

We present SimpleStories, a large synthetic story dataset in simple language, consisting of 2 million samples each in English and Japanese. Through parameterizing prompts at multiple levels of abstraction, we achieve control over story characteristics at scale, inducing syntactic and semantic diversity. Ablations on a newly trained model suite show improved sample efficiency and model interpretability compared to the TinyStories dataset. We open-source all constituent parts of model creation, hoping to enable novel ways to study the end-to-end training process. As a byproduct, we move the frontier regarding the fewest-parameter language model that outputs grammatical natural language.

Thomas Dooms, Ward Gauderis, Geraint Wiggins et al.

Sparse autoencoders have become a standard tool for uncovering interpretable latent representations in neural networks. Yet salient concepts often span manifolds that current linear methods cannot capture without post hoc analysis. This paper uses quadratic latents to close this gap: we implement these with bilinear autoencoders, which decompose activations into low-rank quadratic forms, compose linearly in weight space, and admit input-independent geometric analysis. This qualitative difference in what concepts quadratic latents can detect challenges the standard linear representation hypothesis. Our experiments and visualisations show that multi-dimensional geometries are highly prevalent and that composite latents capture them well, systematically improving reconstruction error in language models. Furthermore, we show that autoencoders with varying geometric priors recover the same input subspace despite their dictionary entries being distinct. Practically, these models serve as an unsupervised tool for manifold discovery, which we demonstrate through an interactive online visualizer for Qwen 3.5. This is a step toward nonlinear but mathematically tractable latent representations whose composition is expressive and interpretable by design.

Thomas Dooms, Ward Gauderis, Geraint A. Wiggins et al.

We propose $χ$-net, an intrinsically interpretable architecture combining the compositional multilinear structure of tensor networks with the expressivity and efficiency of deep neural networks. $χ$-nets retain equal accuracy compared to their baseline counterparts. Our novel, efficient diagonalisation algorithm, ODT, reveals linear low-rank structure in a multilayer SVHN model. We leverage this toward formal weight-based interpretability and model compression.

Thomas Dooms, Ward Gauderis

Sparse autoencoders are a standard tool for uncovering interpretable latent representations in neural networks. Yet, their interpretation depends on the inputs, making their isolated study incomplete. Polynomials offer a solution; they serve as algebraic primitives that can be analysed without reference to input and can describe structures ranging from linear concepts to complicated manifolds. This work uses bilinear autoencoders to efficiently decompose representations into quadratic polynomials. We discuss improvements that induce importance ordering, clustering, and activation sparsity. This is an initial step toward nonlinear yet analysable latents through their algebraic properties.

Thomas Dooms, Daniel Wilhelm

Sparse auto-encoders (SAEs) have become a prevalent tool for interpreting language models' inner workings. However, it is unknown how tightly SAE features correspond to computationally important directions in the model. This work empirically shows that many RES-JB SAE features predominantly correspond to simple input statistics. We hypothesize this is caused by a large class imbalance in training data combined with a lack of complex error signals. To reduce this behavior, we propose a method that disentangles token reconstruction from feature reconstruction. This improvement is achieved by introducing a per-token bias, which provides an enhanced baseline for interesting reconstruction. As a result, significantly more interesting features and improved reconstruction in sparse regimes are learned.

Michael T. Pearce, Thomas Dooms, Alice Rigg

Gated Linear Units (GLUs) have become a common building block in modern foundation models. Bilinear layers drop the non-linearity in the "gate" but still have comparable performance to other GLUs. An attractive quality of bilinear layers is that they can be fully expressed in terms of a third-order tensor and linear operations. Leveraging this, we develop a method to decompose the bilinear tensor into a set of sparsely interacting eigenvectors that show promising interpretability properties in preliminary experiments for shallow image classifiers (MNIST) and small language models (Tiny Stories). Since the decomposition is fully equivalent to the model's original computations, bilinear layers may be an interpretability-friendly architecture that helps connect features to the model weights. Application of our method may not be limited to pretrained bilinear models since we find that language models such as TinyLlama-1.1B can be finetuned into bilinear variants.