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Mateja Jamnik

Mateja Jamnik contributes to research discovery and scholarly infrastructure.

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Machine Learning Artificial Intelligence Logic in Computer Science Computation and Language Multiagent Systems Neural and Evolutionary Computing Software Engineering

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preprint2026arXiv

An AI Monkey Gets Grapes for Sure -- Sphere Neural Networks for Reliable Decision-Making

This paper compares three methodological categories of neural reasoning: LLM reasoning, supervised learning-based reasoning, and explicit model-based reasoning. LLMs remain unreliable and struggle with simple decision-making that animals can master without extensive corpora training. Through disjunctive syllogistic reasoning testing, we show that reasoning via supervised learning is less appealing than reasoning via explicit model construction. Concretely, we show that an Euler Net trained to achieve 100.00% in classic syllogistic reasoning can be trained to reach 100.00% accuracy in disjunctive syllogistic reasoning. However, the retrained Euler Net suffers severely from catastrophic forgetting (its performance drops to 6.25% on already-learned classic syllogistic reasoning), and its reasoning competence is limited to the pattern level. We propose a new version of Sphere Neural Networks that embeds concepts as circles on the surface of an n-dimensional sphere. These Sphere Neural Networks enable the representation of the negation operator via complement circles and achieve reliable decision-making by filtering out illogical statements that form unsatisfiable circular configurations. We demonstrate that the Sphere Neural Network can master 16 syllogistic reasoning tasks, including rigorous disjunctive syllogistic reasoning, while preserving the rigour of classical syllogistic reasoning. We conclude that neural reasoning with explicit model construction is the most reliable among the three methodological categories of neural reasoning.

preprint2026arXiv

Don't Lose Focus: Activation Steering via Key-Orthogonal Projections

Activation steering controls LLM behaviour towards target behaviour by intervening in internal representations, yet it often degrades reasoning and retrieval performance. We argue that a primary cause of this trade-off is attention rerouting: steering vectors alter query-key matching, shifting attention away from contextually important tokens toward less informative ones. To address this, we propose Steering via Key-Orthogonal Projections (SKOP), a steering method that constrains harmful attention rerouting without eliminating steering efficacy. SKOP achieves this by preserving attention patterns on a small set of focus tokens the model relies on for reasoning and retrieval, while allowing redistribution among less critical tail tokens. Across multiple steering benchmarks, we show that SKOP achieves the best joint steering-utility trade-off, reducing utility degradation by 5-7x while retaining over 95% of vanilla steering efficacy. Our results further suggest that, in long-context retrieval settings where vanilla steering approaches are ineffective, SKOP can maintain robust performance by avoiding attention rerouting.

preprint2026arXiv

Tabular Foundation Model for Generative Modelling

Generative modelling is a demanding test of foundation models, because it requires robust, holistic representation learning for a given data modality, rather than optimisation for a supervised prediction target alone. While recent work on tabular foundation models has achieved remarkable progress in predictive modelling, generative tabular foundation models remain underexplored. Existing tabular foundation generators, in particular, have not yet consistently matched strong dataset-specific generators in synthetic data quality. A key reason is their misalignment with the distinctive causal structural prior of heterogeneous tabular data. In this paper, we address this gap by introducing a novel tabular foundation model, \textbf{TabFORGE}, built on pretrained \textbf{Tab}ular \textbf{FO}undational \textbf{R}epresentations for \textbf{GE}neration. TabFORGE is designed to utilise the implicitly learned causal information underlying diverse tabular datasets in a unified latent space induced by a pretrained causality-aware feature encoder. It further decouples latent modelling from decoding through a two-stage design: we first pretrain a score-based diffusion transformer, and then pretrain a denoising-aligned decoder using the denoised latent embeddings. This design elegantly mitigates the distribution shifts in latent embeddings that typically arise between training and inference. We evaluate TabFORGE comprehensively against 22 benchmark methods on 45 real-world datasets. Our results show that TabFORGE effectively learns and leverages generalisable tabular representations, enabling efficient generation of high-quality synthetic tabular data, particularly with strong structural fidelity.

preprint2022arXiv

Autoformalization with Large Language Models

Autoformalization is the process of automatically translating from natural language mathematics to formal specifications and proofs. A successful autoformalization system could advance the fields of formal verification, program synthesis, and artificial intelligence. While the long-term goal of autoformalization seemed elusive for a long time, we show large language models provide new prospects towards this goal. We make the surprising observation that LLMs can correctly translate a significant portion ($25.3\%$) of mathematical competition problems perfectly to formal specifications in Isabelle/HOL. We demonstrate the usefulness of this process by improving a previously introduced neural theorem prover via training on these autoformalized theorems. Our methodology results in a new state-of-the-art result on the MiniF2F theorem proving benchmark, improving the proof rate from $29.6\%$ to $35.2\%$.

preprint2022arXiv

Encoding Concepts in Graph Neural Networks

The opaque reasoning of Graph Neural Networks induces a lack of human trust. Existing graph network explainers attempt to address this issue by providing post-hoc explanations, however, they fail to make the model itself more interpretable. To fill this gap, we introduce the Concept Encoder Module, the first differentiable concept-discovery approach for graph networks. The proposed approach makes graph networks explainable by design by first discovering graph concepts and then using these to solve the task. Our results demonstrate that this approach allows graph networks to: (i) attain model accuracy comparable with their equivalent vanilla versions, (ii) discover meaningful concepts that achieve high concept completeness and purity scores, (iii) provide high-quality concept-based logic explanations for their prediction, and (iv) support effective interventions at test time: these can increase human trust as well as significantly improve model performance.

preprint2022arXiv

Representational Systems Theory: A Unified Approach to Encoding, Analysing and Transforming Representations

The study of representations is of fundamental importance to any form of communication, and our ability to exploit them effectively is paramount. This article presents a novel theory -- Representational Systems Theory -- that is designed to abstractly encode a wide variety of representations from three core perspectives: syntax, entailment, and their properties. By introducing the concept of a construction space, we are able to encode each of these core components under a single, unifying paradigm. Using our Representational Systems Theory, it becomes possible to structurally transform representations in one system into representations in another. An intrinsic facet of our structural transformation technique is representation selection based on properties that representations possess, such as their relative cognitive effectiveness or structural complexity. A major theoretical barrier to providing general structural transformation techniques is a lack of terminating algorithms. Representational Systems Theory permits the derivation of partial transformations when no terminating algorithm can produce a full transformation. Since Representational Systems Theory provides a universal approach to encoding representational systems, a further key barrier is eliminated: the need to devise system-specific structural transformation algorithms, that are necessary when different systems adopt different formalisation approaches. Consequently, Representational Systems Theory is the first general framework that provides a unified approach to encoding representations, supports representation selection via structural transformations, and has the potential for widespread practical application.

preprint2022arXiv

Thor: Wielding Hammers to Integrate Language Models and Automated Theorem Provers

In theorem proving, the task of selecting useful premises from a large library to unlock the proof of a given conjecture is crucially important. This presents a challenge for all theorem provers, especially the ones based on language models, due to their relative inability to reason over huge volumes of premises in text form. This paper introduces Thor, a framework integrating language models and automated theorem provers to overcome this difficulty. In Thor, a class of methods called hammers that leverage the power of automated theorem provers are used for premise selection, while all other tasks are designated to language models. Thor increases a language model's success rate on the PISA dataset from $39\%$ to $57\%$, while solving $8.2\%$ of problems neither language models nor automated theorem provers are able to solve on their own. Furthermore, with a significantly smaller computational budget, Thor can achieve a success rate on the MiniF2F dataset that is on par with the best existing methods. Thor can be instantiated for the majority of popular interactive theorem provers via a straightforward protocol we provide.

preprint2020arXiv

Abstract Diagrammatic Reasoning with Multiplex Graph Networks

Abstract reasoning, particularly in the visual domain, is a complex human ability, but it remains a challenging problem for artificial neural learning systems. In this work we propose MXGNet, a multilayer graph neural network for multi-panel diagrammatic reasoning tasks. MXGNet combines three powerful concepts, namely, object-level representation, graph neural networks and multiplex graphs, for solving visual reasoning tasks. MXGNet first extracts object-level representations for each element in all panels of the diagrams, and then forms a multi-layer multiplex graph capturing multiple relations between objects across different diagram panels. MXGNet summarises the multiple graphs extracted from the diagrams of the task, and uses this summarisation to pick the most probable answer from the given candidates. We have tested MXGNet on two types of diagrammatic reasoning tasks, namely Diagram Syllogisms and Raven Progressive Matrices (RPM). For an Euler Diagram Syllogism task MXGNet achieves state-of-the-art accuracy of 99.8%. For PGM and RAVEN, two comprehensive datasets for RPM reasoning, MXGNet outperforms the state-of-the-art models by a considerable margin.

preprint2020arXiv

Learned Low Precision Graph Neural Networks

Deep Graph Neural Networks (GNNs) show promising performance on a range of graph tasks, yet at present are costly to run and lack many of the optimisations applied to DNNs. We show, for the first time, how to systematically quantise GNNs with minimal or no loss in performance using Network Architecture Search (NAS). We define the possible quantisation search space of GNNs. The proposed novel NAS mechanism, named Low Precision Graph NAS (LPGNAS), constrains both architecture and quantisation choices to be differentiable. LPGNAS learns the optimal architecture coupled with the best quantisation strategy for different components in the GNN automatically using back-propagation in a single search round. On eight different datasets, solving the task of classifying unseen nodes in a graph, LPGNAS generates quantised models with significant reductions in both model and buffer sizes but with similar accuracy to manually designed networks and other NAS results. In particular, on the Pubmed dataset, LPGNAS shows a better size-accuracy Pareto frontier compared to seven other manual and searched baselines, offering a 2.3 times reduction in model size but a 0.4% increase in accuracy when compared to the best NAS competitor. Finally, from our collected quantisation statistics on a wide range of datasets, we suggest a W4A8 (4-bit weights, 8-bit activations) quantisation strategy might be the bottleneck for naive GNN quantisations.

preprint2020arXiv

Probabilistic Dual Network Architecture Search on Graphs

We present the first differentiable Network Architecture Search (NAS) for Graph Neural Networks (GNNs). GNNs show promising performance on a wide range of tasks, but require a large amount of architecture engineering. First, graphs are inherently a non-Euclidean and sophisticated data structure, leading to poor adaptivity of GNN architectures across different datasets. Second, a typical graph block contains numerous different components, such as aggregation and attention, generating a large combinatorial search space. To counter these problems, we propose a Probabilistic Dual Network Architecture Search (PDNAS) framework for GNNs. PDNAS not only optimises the operations within a single graph block (micro-architecture), but also considers how these blocks should be connected to each other (macro-architecture). The dual architecture (micro- and marco-architectures) optimisation allows PDNAS to find deeper GNNs on diverse datasets with better performance compared to other graph NAS methods. Moreover, we use a fully gradient-based search approach to update architectural parameters, making it the first differentiable graph NAS method. PDNAS outperforms existing hand-designed GNNs and NAS results, for example, on the PPI dataset, PDNAS beats its best competitors by 1.67 and 0.17 in F1 scores.

preprint2020arXiv

Towards Graph Representation Learning in Emergent Communication

Recent findings in neuroscience suggest that the human brain represents information in a geometric structure (for instance, through conceptual spaces). In order to communicate, we flatten the complex representation of entities and their attributes into a single word or a sentence. In this paper we use graph convolutional networks to support the evolution of language and cooperation in multi-agent systems. Motivated by an image-based referential game, we propose a graph referential game with varying degrees of complexity, and we provide strong baseline models that exhibit desirable properties in terms of language emergence and cooperation. We show that the emerged communication protocol is robust, that the agents uncover the true factors of variation in the game, and that they learn to generalize beyond the samples encountered during training.

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