Can a Language Model Learn Facts Continually in Its Weights?

Continual learning promises a language model that keeps acquiring knowledge after training, with each new fact written into its weights. Whether weight writes can support accumulation remains undecided. We follow invented facts written into Qwen3 models from creation through sequences of twenty to one hundred later writes, using held-out questions of five types, with the original model given the fact in its prompt as the reference. Across these experiments, the breadth of the training data determines the kind of knowledge created. Bare-statement training produces recitation, while diverse restatements reduce the recitation-to-use gap from 27.4 to 5.4 points without showing the model a conclusion. This difference carries into later writes: after twenty sequential writes, bare-statement facts retain 1% accuracy while facts written from broad study data retain 46%. We also find that facts can be behaviourally forgotten without being erased. Forgotten facts keep most of the log-probability added by their write, and under bare-statement training 70% of wrong answers about them contain the most recently written fact. The same writes barely degrade the model's use of facts in context, and a forgotten study fact supplied in the prompt recovers to 77-80% on its questions. These results describe knowledge that is stored but question-keyed: later writes redirect the questions that reached it. Damage to unrelated abilities tracks KL divergence from the original model, and the later writes cause interference regardless of how the earlier fact was stored. Broad data can create usable knowledge, and a frozen reference can preserve capability, but no intervention we tested, including those built on accurate local measurements of each write, keeps earlier facts reachable. When facts must be composed or survive later writes, the reliable channel is context rather than the weights.

Still: Amortized KV Cache Compaction in a Single Forward Pass

The KV cache is the memory bottleneck of long-horizon language model deployment. Practically, a deployable compactor must be lightweight enough to call during inference, expressive enough to preserve context under constraint, and reusable across a trajectory. Existing compaction methods satisfy only part of this requirement: selection methods are lightweight but subset-bound, while synthesis methods are expressive but rely on per-context optimization. Here we introduce Still, a small per-layer Perceiver trained once against a frozen base model that produces compact keys and values in a single forward pass. On Qwen and Gemma models, Still occupies the favorable side of the speed--quality frontier across compression ratios from $8\times$ to $200\times$ and context lengths from $8$k to $128$k. On the long-context RULER grid, Still exceeds the strongest baseline by 8--22 points. The same compact cache also supports free-form summarization, preserving most of the full-context gain on HELMET and winning a pairwise LongBench summarization comparison against KV-Distill. Because compaction is a forward pass, Still can be applied iteratively, entering a long-horizon regime unavailable to per-context methods. We show that amortization makes long-context cache compaction tractable, and synthesis makes its compact state useful at extreme compression.

Procedural Generation of Algorithm Discovery Tasks in Machine Learning

Automating the development of machine learning algorithms has the potential to unlock new breakthroughs. However, our ability to improve and evaluate algorithm discovery systems has thus far been limited by existing task suites. They suffer from many issues, such as: poor evaluation methodologies; data contamination; and containing saturated or very similar problems. Here, we introduce DiscoGen, a procedural generator of algorithm discovery tasks for machine learning, such as developing optimisers for reinforcement learning or loss functions for image classification. Motivated by the success of procedural generation in reinforcement learning, DiscoGen spans millions of tasks of varying difficulty and complexity from a range of machine learning fields. These tasks are specified by a small number of configuration parameters and can be used to optimise algorithm discovery agents (ADAs). We present DiscoBench, a benchmark consisting of a fixed, small subset of DiscoGen tasks for principled evaluation of ADAs. Finally, we propose a number of ambitious, impactful research directions enabled by DiscoGen, in addition to experiments demonstrating its use for prompt optimisation of an ADA. DiscoGen is released open-source at https://github.com/AlexGoldie/discogen.

Sparks of Science: Hypothesis Generation Using Structured Paper Data

Generating novel and creative scientific hypotheses is a cornerstone in achieving Artificial General Intelligence. Large language and reasoning models have the potential to aid in the systematic creation, selection, and validation of scientifically informed hypotheses. However, current foundation models often struggle to produce scientific ideas that are both novel and feasible. One reason is the lack of a dedicated dataset that frames Scientific Hypothesis Generation (SHG) as a Natural Language Generation (NLG) task. In this paper, we introduce HypoGen, the first dataset of approximately 5500 structured problem-hypothesis pairs extracted from top-tier computer science conferences structured with a Bit-Flip-Spark schema, where the Bit is the conventional assumption, the Spark is the key insight or conceptual leap, and the Flip is the resulting counterproposal. HypoGen uniquely integrates an explicit Chain-of-Reasoning component that reflects the intellectual process from Bit to Flip. We demonstrate that framing hypothesis generation as conditional language modelling, with the model fine-tuned on Bit-Flip-Spark and the Chain-of-Reasoning (and where, at inference, we only provide the Bit), leads to improvements in the overall quality of the hypotheses. Our evaluation employs automated metrics and LLM judge rankings for overall quality assessment. We show that by fine-tuning on our HypoGen dataset we improve the novelty, feasibility, and overall quality of the generated hypotheses. The HypoGen dataset is publicly available at huggingface.co/datasets/UniverseTBD/hypogen-dr1.

From superposition to sparse codes: interpretable representations in neural networks

Understanding how information is represented in neural networks is a fundamental challenge in both neuroscience and artificial intelligence. Despite their nonlinear architectures, recent evidence suggests that neural networks encode features in superposition, meaning that input concepts are linearly overlaid within the network's representations. We present a perspective that explains this phenomenon and provides a foundation for extracting interpretable representations from neural activations. Our theoretical framework consists of three steps: (1) Identifiability theory shows that neural networks trained for classification recover latent features up to a linear transformation. (2) Sparse coding methods can extract disentangled features from these representations by leveraging principles from compressed sensing. (3) Quantitative interpretability metrics provide a means to assess the success of these methods, ensuring that extracted features align with human-interpretable concepts. By bridging insights from theoretical neuroscience, representation learning, and interpretability research, we propose an emerging perspective on understanding neural representations in both artificial and biological systems. Our arguments have implications for neural coding theories, AI transparency, and the broader goal of making deep learning models more interpretable.

Self-Attention as a Parametric Endofunctor: A Categorical Framework for Transformer Architectures

Self-attention mechanisms have revolutionised deep learning architectures, but their mathematical foundations remain incompletely understood. We establish that these mechanisms can be formalised through categorical algebra, presenting a framework that focuses on the linear components of self-attention. We prove that the query, key, and value maps in self-attention naturally form a parametric endofunctor in the 2-category $\mathbf{Para}(\mathbf{Vect})$ of parametric morphisms. We show that stacking multiple self-attention layers corresponds to constructing the free monad on this endofunctor. For positional encodings, we demonstrate that strictly additive position embeddings constitute monoid actions on the embedding space, while standard sinusoidal encodings, though not additive, possess a universal property among faithful position-preserving functors. We establish that the linear portions of self-attention exhibit natural equivariance properties with respect to permutations of input tokens. Finally, we prove that the ``circuits'' identified in mechanistic interpretability correspond precisely to compositions of parametric morphisms in our framework. This categorical perspective unifies geometric, algebraic, and interpretability-based approaches to transformer analysis, while making explicit the mathematical structures underlying attention mechanisms. Our treatment focuses exclusively on linear maps, setting aside nonlinearities like softmax and layer normalisation, which require more sophisticated categorical structures. Our results extend recent work on categorical foundations for deep learning while providing insights into the algebraic structure of attention mechanisms.

Compute Optimal Inference and Provable Amortisation Gap in Sparse Autoencoders

A recent line of work has shown promise in using sparse autoencoders (SAEs) to uncover interpretable features in neural network representations. However, the simple linear-nonlinear encoding mechanism in SAEs limits their ability to perform accurate sparse inference. In this paper, we investigate sparse inference and learning in SAEs through the lens of sparse coding. Specifically, we show that SAEs perform amortised sparse inference with a computationally restricted encoder and, using compressed sensing theory, we prove that this mapping is inherently insufficient for accurate sparse inference, even in solvable cases. Building on this theory, we empirically explore conditions where more sophisticated sparse inference methods outperform traditional SAE encoders. Our key contribution is the decoupling of the encoding and decoding processes, which allows for a comparison of various sparse encoding strategies. We evaluate these strategies on two dimensions: alignment with true underlying sparse features and correct inference of sparse codes, while also accounting for computational costs during training and inference. Our results reveal that substantial performance gains can be achieved with minimal increases in compute cost. We demonstrate that this generalises to SAEs applied to large language models (LLMs), where advanced encoders achieve similar interpretability. This work opens new avenues for understanding neural network representations and offers important implications for improving the tools we use to analyse the activations of large language models.

Disentangling Dense Embeddings with Sparse Autoencoders

Sparse autoencoders (SAEs) have shown promise in extracting interpretable features from complex neural networks. We present one of the first applications of SAEs to dense text embeddings from large language models, demonstrating their effectiveness in disentangling semantic concepts. By training SAEs on embeddings of over 420,000 scientific paper abstracts from computer science and astronomy, we show that the resulting sparse representations maintain semantic fidelity while offering interpretability. We analyse these learned features, exploring their behaviour across different model capacities and introducing a novel method for identifying ``feature families'' that represent related concepts at varying levels of abstraction. To demonstrate the practical utility of our approach, we show how these interpretable features can be used to precisely steer semantic search, allowing for fine-grained control over query semantics. This work bridges the gap between the semantic richness of dense embeddings and the interpretability of sparse representations. We open source our embeddings, trained sparse autoencoders, and interpreted features, as well as a web app for exploring them.

pathfinder: A Semantic Framework for Literature Review and Knowledge Discovery in Astronomy

The exponential growth of astronomical literature poses significant challenges for researchers navigating and synthesizing general insights or even domain-specific knowledge. We present Pathfinder, a machine learning framework designed to enable literature review and knowledge discovery in astronomy, focusing on semantic searching with natural language instead of syntactic searches with keywords. Utilizing state-of-the-art large language models (LLMs) and a corpus of 350,000 peer-reviewed papers from the Astrophysics Data System (ADS), Pathfinder offers an innovative approach to scientific inquiry and literature exploration. Our framework couples advanced retrieval techniques with LLM-based synthesis to search astronomical literature by semantic context as a complement to currently existing methods that use keywords or citation graphs. It addresses complexities of jargon, named entities, and temporal aspects through time-based and citation-based weighting schemes. We demonstrate the tool's versatility through case studies, showcasing its application in various research scenarios. The system's performance is evaluated using custom benchmarks, including single-paper and multi-paper tasks. Beyond literature review, Pathfinder offers unique capabilities for reformatting answers in ways that are accessible to various audiences (e.g. in a different language or as simplified text), visualizing research landscapes, and tracking the impact of observatories and methodologies. This tool represents a significant advancement in applying AI to astronomical research, aiding researchers at all career stages in navigating modern astronomy literature.

Designing an Evaluation Framework for Large Language Models in Astronomy Research

Large Language Models (LLMs) are shifting how scientific research is done. It is imperative to understand how researchers interact with these models and how scientific sub-communities like astronomy might benefit from them. However, there is currently no standard for evaluating the use of LLMs in astronomy. Therefore, we present the experimental design for an evaluation study on how astronomy researchers interact with LLMs. We deploy a Slack chatbot that can answer queries from users via Retrieval-Augmented Generation (RAG); these responses are grounded in astronomy papers from arXiv. We record and anonymize user questions and chatbot answers, user upvotes and downvotes to LLM responses, user feedback to the LLM, and retrieved documents and similarity scores with the query. Our data collection method will enable future dynamic evaluations of LLM tools for astronomy.