Thomas F Burns

Thomas F Burns

I introduce a novel associative memory model named Correlated Dense Associative Memory (CDAM), which integrates both auto- and hetero-association in a unified framework for continuous-valued memory patterns. Employing an arbitrary graph structure to semantically link memory patterns, CDAM is theoretically and numerically analysed, revealing four distinct dynamical modes: auto-association, narrow hetero-association, wide hetero-association, and neutral quiescence. Drawing inspiration from inhibitory modulation studies, I employ anti-Hebbian learning rules to control the range of hetero-association, extract multi-scale representations of community structures in graphs, and stabilise the recall of temporal sequences. Experimental demonstrations showcase CDAM's efficacy in handling real-world data, replicating a classical neuroscience experiment, performing image retrieval, and simulating arbitrary finite automata.

Thomas F Burns, Tomoki Fukai, Christopher J Earls

Large language models (LLMs) demonstrate an impressive ability to utilise information within the context of their input sequences to appropriately respond to data unseen by the LLM during its training procedure. This ability is known as in-context learning (ICL). Humans and non-human animals demonstrate similar abilities, however their neural architectures differ substantially from LLMs. Despite this, a critical component within LLMs, the attention mechanism, resembles modern associative memory models, widely used in and influenced by the computational neuroscience community to model biological memory systems. Using this connection, we introduce an associative memory model capable of performing ICL. We use this as inspiration for a novel residual stream architecture which allows information to directly flow between attention heads. We test this architecture during training within a two-layer Transformer and show its ICL abilities manifest more quickly than without this modification. We then apply our architecture in small language models with 8 million and 1 billion parameters, focusing on attention head values, with results also indicating improved performance at these larger and more naturalistic scales.

Thomas F Burns

Common evaluation paradigms for language models focus on scoring single responses through accuracy metrics or proper scoring rules, failing to capture the full richness of a model's belief state. Recent work illustrates that language models hallucinate in-part because they are optimised to be good test-takers under binary scoring schemes that reward any answer over abstention. While this insight naturally leads to penalty-based approaches, they ignore crucial distinctions in how models distribute uncertainty, for example between hedging toward incorrect answers versus hedging toward "I don't know" responses. A novel evaluation metric, the Distributional Correctness Score (DCS), is introduced to solve this problem, i.e., of not considering a model's entire probability distribution over answer choices. DCS naturally distinguishes between harmful overconfidence in wrong answers and uncertainty expressed through abstention, providing scores in an interpretable default range. Through theoretical analysis and illustrative examples, DCS is demonstrated to offer a more nuanced and aligned evaluation paradigm that incentivises models to express genuine uncertainty rather than guessing. Adapting 12 existing evaluation benchmarks to DCS's variants and measuring performance on six language models reveals that for half of the tested benchmarks scores are negative across all tested models, indicating significant tendencies towards hallucination.

Thomas F Burns, Letitia Parcalabescu, Stephan Wäldchen et al.

Scaling data quantity is essential for large language models (LLMs), yet recent findings show that data quality can significantly boost performance and training efficiency. We introduce a German-language dataset curation pipeline that combines heuristic and model-based filtering techniques with synthetic data generation. We use our pipeline to create Aleph-Alpha-GermanWeb, a large-scale German pre-training dataset which draws from: (1) Common Crawl web data, (2) FineWeb2, and (3) synthetically-generated data conditioned on actual, organic web data. We evaluate our dataset by pre-training both a 1B Llama-style model and an 8B tokenizer-free hierarchical autoregressive transformer (HAT). A comparison on German-language benchmarks, including MMMLU, shows significant performance gains of Aleph-Alpha-GermanWeb over FineWeb2 alone. This advantage holds at the 8B scale even when FineWeb2 is enriched by human-curated high-quality data sources such as Wikipedia. Our findings support the growing body of evidence that model-based data curation and synthetic data generation can significantly enhance LLM pre-training datasets.

Thomas F Burns, Tomoki Fukai

Hopfield networks are artificial neural networks which store memory patterns on the states of their neurons by choosing recurrent connection weights and update rules such that the energy landscape of the network forms attractors around the memories. How many stable, sufficiently-attracting memory patterns can we store in such a network using $N$ neurons? The answer depends on the choice of weights and update rule. Inspired by setwise connectivity in biology, we extend Hopfield networks by adding setwise connections and embedding these connections in a simplicial complex. Simplicial complexes are higher dimensional analogues of graphs which naturally represent collections of pairwise and setwise relationships. We show that our simplicial Hopfield networks increase memory storage capacity. Surprisingly, even when connections are limited to a small random subset of equivalent size to an all-pairwise network, our networks still outperform their pairwise counterparts. Such scenarios include non-trivial simplicial topology. We also test analogous modern continuous Hopfield networks, offering a potentially promising avenue for improving the attention mechanism in Transformer models.

Thomas F Burns, Robert Tang

Gridworlds have been long-utilised in AI research, particularly in reinforcement learning, as they provide simple yet scalable models for many real-world applications such as robot navigation, emergent behaviour, and operations research. We initiate a study of gridworlds using the mathematical framework of reconfigurable systems and state complexes due to Abrams, Ghrist & Peterson. State complexes represent all possible configurations of a system as a single geometric space, thus making them conducive to study using geometric, topological, or combinatorial methods. The main contribution of this work is a modification to the original Abrams, Ghrist & Peterson setup which we introduce to capture agent braiding and thereby more naturally represent the topology of gridworlds. With this modification, the state complexes may exhibit geometric defects (failure of Gromov's Link Condition). Serendipitously, we discover these failures occur exactly where undesirable or dangerous states appear in the gridworld. Our results therefore provide a novel method for seeking guaranteed safety limitations in discrete task environments with single or multiple agents, and offer useful safety information (in geometric and topological forms) for incorporation in or analysis of machine learning systems. More broadly, our work introduces tools from geometric group theory and combinatorics to the AI community and demonstrates a proof-of-concept for this geometric viewpoint of the task domain through the example of simple gridworld environments.