arXiv subjects

Mateja Jamnik

Publications and source records attributed to Mateja Jamnik.

At least 19 recordsLinked to original sources

arXiv2026

Persistent Sparse Autoencoders: Learning Feature-Specific Timescales in Language Model Representations

Sparse autoencoders (SAEs) decompose language model activations into sparse features, yet these models traditionally encode each token independently, failing to expose information that persists across a sequence. We first show that temporal persistence can naturally emerge in standard SAE features: after a feature activates, the hidden state remains aligned with its direction, and past activations help reconstruct later hidden states. How long this lasts varies widely across features. We therefore introduce Persistent Sparse Autoencoders (Persistent SAEs), an extension of standard SAEs that learns a persistence coefficient for each feature, allowing the model to learn feature-specific timescales from reconstruction alone. Our experiments show that Persistent SAEs retain competitive reconstruction quality while learning a spectrum of timescales: short-timescale (fast) features stay locally interpretable, whereas long-timescale (slow) features accumulate information that identifies the current context. Moreover, we show in a prompt-injection monitoring case study that slow features preserve injection-related signals and remain causally effective over long contexts. These results suggest that Persistent SAEs offer new opportunities for interpreting and monitoring language models via persistent sparse features.

cs.LG↗

arXiv2026

KnowsTFM: Knowledge-Informed Fine-Tuning of Small Tabular Foundation Models

Tabular foundation models have advanced deep learning for tabular data by delivering strong default performance across many small and medium tasks. Yet in niche domains, where data is scarce, high-dimensional, and shifted from the pretraining distribution, they may still fail to outperform carefully designed domain-specific methods. Many such domains also provide curated relational knowledge in the form of knowledge graphs and knowledge banks, but how to use this knowledge to improve and steer \textit{small} specialist tabular foundation models remains unclear. We address this problem through \textbf{Know}ledge-informed fine-tuning of \textbf{s}mall \textbf{T}abular \textbf{F}oundation \textbf{M}odels (\modelname). Specifically, we study nanoscale TabPFN- and TabICL-style variants, pretrained under controlled synthetic prior families and adapted using two complementary mechanisms: structural attention priors derived from knowledge graphs and parameter-efficient low-rank updates. We show that injecting domain-specific structural knowledge during fine-tuning yields meaningful gains over vanilla variants in specialist settings, whereas gains on general-domain tasks are marginal. We further observe that continual fine-tuning of frontier models can trigger collapse of pretrained knowledge and mechanisms.

cs.LG↗

arXiv2026

Data-driven Machine Learning Cannot Reach Symbolic-level Logical Reasoning -- The Limit of the Scaling Law

By promoting vectors to spheres and enabling explicit model construction, neural networks can perform symbolic-level syllogistic reasoning without training data. We identify two fundamental limitations that prevent conventional data-driven machine learning systems from achieving this capability: training data generated by the combination table cannot distinguish all 24 valid syllogism types, and end-to-end premise-to-conclusion mapping creates contradictory targets within neural components. Experiments with two representative conventional systems, GPT-5 using linguistic inputs and Euler Net using visual inputs, support this analysis. ChatGPT GPT-5 may reach 100% accuracy in syllogistic reasoning, but with hallucinations. Because the learning process terminates upon reaching 100% accuracy, the system cannot progress beyond empirical accuracy to symbolic level reasoning. Random test data reduced Euler Net's accuracy to 56%. Repeatedly expanding the training set increased its accuracy to 97%, with perfect performance on 8 syllogism types. However, because unintended inputs cannot be exhaustively covered, even 100% test accuracy does not imply symbolic-level reasoning. Since syllogistic reasoning underpins logical reasoning and human rationality, these results suggest that increasing data and training time alone cannot ensure symbolic level logical reasoning.

cs.AI↗

arXiv2026

The Standard Interpretable Model: A general theory of interpretable machine learning to deductively design interpretable methods using Lagrangian mechanics

As Artificial Intelligence models grow in complexity, interpretability has become an indispensable tool for understanding, debugging, and controlling their computations. However, interpretability lacks general theories to deductively design interpretable methods. This gap between theories and methods results in a fragmented literature and inconsistent evaluation protocols. To fill this gap, we introduce the Standard Interpretable Model (SIM), a general theory grounded in Lagrangian mechanics that enables the deductive design of interpretable methods. Specifically, the SIM summarises, in a set of premises, what interpretability is for a target user. From these premises, the SIM systematically derives interpretability symmetries and corresponding constraints, which shape the landscape of a Lagrangian whose minima correspond to optimal interpretable models. To reach the minima, one can either update the parameter values of an opaque model to make it more interpretable or compile constraints into an interpretable architecture. We empirically show that the SIM identifies and solves limitations of existing methods (including traditional, concept-based, and mechanistic interpretability), highlights underexplored research directions, and informs the design of core programming interfaces. Beyond being a research method, the deductive nature of the SIM offers pedagogical grounding for interpretability curricula and may shift the scientific community's perspective of a discipline that has long been fragmented.

cs.LG↗

arXiv2026

CB-SLICE: Concept-Based Interpretable Error Slice Discovery

Despite strong average-case performance, deep learning models often exhibit systematic errors on specific population groups, known as error slices. Identifying these groups and the root causes of their failures is critical for model debugging and bias mitigation. However, existing error Slice Discovery Methods (SDMs) typically generate explanations disconnected from the model's inference process, thus only approximating the underlying error source and may be inaccurate. We address this limitation by leveraging Concept Bottleneck Models (CBMs), whose predictions are directly dependent on human-understandable semantic concepts. Since downstream task failures in CBMs commonly arise from concept mispredictions, concept representations provide a strong candidate for error slice identification, offering fine-grained explanations directly linked to the error source. Building on this insight, we introduce CB-SLICE, a concept-based SDM that groups samples with shared concept prediction failures and identifies the keyword concepts most responsible for each slice's failure mode. Across multiple benchmarks, we show that CB-SLICE outperforms state-of-the-art methods in uncovering well-known biases while providing richer and more faithful explanations of model errors.

cs.LG↗

arXiv2026

Training Language Agents to Learn from Experience

Language agents can adapt from experience in interactive environments, but current reflection-based methods can only self-correct within a single task instance. Whether such experience can be distilled into reusable lessons that improve performance on future unseen tasks remains unclear. We address this problem by introducing the In-context Training (ICT) task, a framework for evaluating cross-task self-improvement in language agents. In ICT, a reflector model observes trajectories collected by an actor model and generates system prompts intended to improve the actor's performance on future unseen tasks. We then propose an RL-based training pipeline for learning such reflections directly from experience, without human-provided examples. Across ALFWorld and MiniHack, our trained reflectors outperform an untrained baseline on most held-out task families, showing that the ability to learn from experience can itself be learned. In some cases, we observe generalisation beyond the benchmark on which the reflector was trained, to substantially different environments. Finally, we introduce MetaGym, a generic Python library for constructing meta-environments, enabling future research on self-improving language agents.

cs.LG↗

arXiv2026

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.

cs.LG↗

arXiv2026

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.

cs.CL↗

arXiv2026

Shaping the Future of Mathematics in the Age of AI

Artificial intelligence is transforming mathematics at a speed and scale that demand active engagement from the mathematical community. We examine five areas where this transformation is particularly pressing: values, practice, teaching, technology, and ethics. We offer recommendations on safeguarding our intellectual autonomy, rethinking our practice, broadening curricula, building academically oriented infrastructure, and developing shared ethical principles - with the aim of ensuring that the future of mathematics is shaped by the community itself.

math.HO↗

arXiv2026

Digging Deeper: Learning Multi-Level Concept Hierarchies

Although concept-based models promise interpretability by explaining predictions with human-understandable concepts, they typically rely on exhaustive annotations and treat concepts as flat and independent. To circumvent this, recent work has introduced Hierarchical Concept Embedding Models (HiCEMs) to explicitly model concept relationships, and Concept Splitting to discover sub-concepts using only coarse annotations. However, both HiCEMs and Concept Splitting are restricted to shallow hierarchies. We overcome this limitation with Multi-Level Concept Splitting (MLCS), which discovers multi-level concept hierarchies from only top-level supervision, and Deep-HiCEMs, an architecture that represents these discovered hierarchies and enables interventions at multiple levels of abstraction. Experiments across multiple datasets show that MLCS discovers human-interpretable concepts absent during training and that Deep-HiCEMs maintain high accuracy while supporting test-time concept interventions that can improve task performance.

cs.LG↗

arXiv2026

Hierarchical Concept-based Interpretable Models

Modern deep neural networks remain challenging to interpret due to the opacity of their latent representations, impeding model understanding, debugging, and debiasing. Concept Embedding Models (CEMs) address this by mapping inputs to human-interpretable concept representations from which tasks can be predicted. Yet, CEMs fail to represent inter-concept relationships and require concept annotations at different granularities during training, limiting their applicability. In this paper, we introduce Hierarchical Concept Embedding Models (HiCEMs), a new family of CEMs that explicitly model concept relationships through hierarchical structures. To enable HiCEMs in real-world settings, we propose Concept Splitting, a method for automatically discovering finer-grained sub-concepts from a pretrained CEM's embedding space without requiring additional annotations. This allows HiCEMs to generate fine-grained explanations from limited concept labels, reducing annotation burdens. Our evaluation across multiple datasets, including a user study and experiments on PseudoKitchens, a newly proposed concept-based dataset of 3D kitchen renders, demonstrates that (1) Concept Splitting discovers human-interpretable sub-concepts absent during training that can be used to train highly accurate HiCEMs, and (2) HiCEMs enable powerful test-time concept interventions at different granularities, leading to improved task accuracy.

cs.LG↗

arXiv2026

Towards Spatial Transcriptomics-driven Pathology Foundation Models

Spatial transcriptomics (ST) provides spatially resolved measurements of gene expression, enabling characterization of the molecular landscape of human tissue beyond histological assessment as well as localized readouts that can be aligned with morphology. Concurrently, the success of multimodal foundation models that integrate vision with complementary modalities suggests that morphomolecular coupling between local expression and morphology can be systematically used to improve histological representations themselves. We introduce Spatial Expression-Aligned Learning (SEAL), a vision-omics self-supervised learning framework that infuses localized molecular information into pathology vision encoders. Rather than training new encoders from scratch, SEAL is designed as a parameter-efficient vision-omics finetuning method that can be flexibly applied to widely used pathology foundation models. We instantiate SEAL by training on over 700,000 paired gene expression spot-tissue region examples spanning tumor and normal samples from 14 organs. Tested across 38 slide-level and 15 patch-level downstream tasks, SEAL provides a drop-in replacement for pathology foundation models that consistently improves performance over widely used vision-only and ST prediction baselines on slide-level molecular status, pathway activity, and treatment response prediction, as well as patch-level gene expression prediction tasks. Additionally, SEAL encoders exhibit robust domain generalization on out-of-distribution evaluations and enable new cross-modal capabilities such as gene-to-image retrieval. Our work proposes a general framework for ST-guided finetuning of pathology foundation models, showing that augmenting existing models with localized molecular supervision is an effective and practical step for improving visual representations and expanding their cross-modal utility.

cs.CV↗

arXiv2026

Actionable Interpretability Must Be Defined in Terms of Symmetries

This paper argues that interpretability research in Artificial Intelligence (AI) is fundamentally ill-posed as existing definitions of interpretability fail to describe how interpretability can be formally tested or designed for. We posit that actionable definitions of interpretability must be formulated in terms of *symmetries* that inform model design and lead to testable conditions. Under a probabilistic view, we hypothesise that four symmetries (inference equivariance, information invariance, concept-closure invariance, and structural invariance) suffice to (i) formalise interpretable models as a subclass of probabilistic models, (ii) yield a unified formulation of interpretable inference (e.g., alignment, interventions, and counterfactuals) as a form of Bayesian inversion, and (iii) provide a formal framework to verify compliance with safety standards and regulations.

cs.AI↗

arXiv2026

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.

cs.AI↗

arXiv2025

A Matter of Interest: Understanding Interestingness of Math Problems in Humans and Language Models

The evolution of mathematics is shaped importantly by interestingness: researchers choose which problems to pursue, and students choose which problems to engage with, based on expectations of interest and challenge. As AI systems, particularly large language models (LLMs) that operate flexibly over natural language and formal mathematics, are increasingly used in mathematics research and education, it becomes crucial to characterize how closely their judgments align with people from different mathematical backgrounds. We study whether LLMs align with human interestingness judgments by comparing LLM ratings with those of two populations, crowdsourced participants with college math experience and International Math Olympiad competitors. Although many LLMs broadly agree with human notions of interestingness, they largely fail to match the distribution of human judgments. They also weakly align with why humans find problems interesting, with low correlation to human-selected rationales. Finally, we evaluate LLMs' ability to generate interesting problems and find that, after filtering for validity, LLMs are able to generate engaging problems. We conclude with takeaways, including the need for multi-LLM human-AI collaborative systems, that highlight both the promise and current limits of LLMs as partners in mathematical reasoning.

cs.AI↗

arXiv2025

TabStruct: Measuring Structural Fidelity of Tabular Data

Evaluating tabular generators remains a challenging problem, as the unique causal structural prior of heterogeneous tabular data does not lend itself to intuitive human inspection. Recent work has introduced structural fidelity as a tabular-specific evaluation dimension to assess whether synthetic data complies with the causal structures of real data. However, existing benchmarks often neglect the interplay between structural fidelity and conventional evaluation dimensions, thus failing to provide a holistic understanding of model performance. Moreover, they are typically limited to toy datasets, as quantifying existing structural fidelity metrics requires access to ground-truth causal structures, which are rarely available for real-world datasets. In this paper, we propose a novel evaluation framework that jointly considers structural fidelity and conventional evaluation dimensions. We introduce a new evaluation metric, $\textbf{global utility}$, which enables the assessment of structural fidelity even in the absence of ground-truth causal structures. In addition, we present $\textbf{TabStruct}$, a comprehensive evaluation benchmark offering large-scale quantitative analysis on 13 tabular generators from nine distinct categories, across 29 datasets. Our results demonstrate that global utility provides a task-independent, domain-agnostic lens for tabular generator performance. We release the TabStruct benchmark suite, including all datasets, evaluation pipelines, and raw results. Code is available at https://github.com/SilenceX12138/TabStruct.

cs.LG↗

arXiv2025

Oruga: An Avatar of Representational Systems Theory

Humans use representations flexibly. We draw diagrams, change representations and exploit creative analogies across different domains. We want to harness this kind of power and endow machines with it to make them more compatible with human use. Previously we developed Representational Systems Theory (RST) to study the structure and transformations of representations. In this paper we present Oruga (caterpillar in Spanish; a symbol of transformation), an implementation of various aspects of RST. Oruga consists of a core of data structures corresponding to concepts in RST, a language for communicating with the core, and an engine for producing transformations using a method we call structure transfer. In this paper we present an overview of the core and language of Oruga, with a brief example of the kind of transformation that structure transfer can execute.

cs.AI↗

arXiv2025

Structure Transfer: an Inference-Based Calculus for the Transformation of Representations

Representation choice is of fundamental importance to our ability to communicate and reason effectively. A major unsolved problem, addressed in this paper, is how to devise representational-system (RS) agnostic techniques that drive representation transformation and choice. We present a novel calculus, called structure transfer, that enables representation transformation across diverse RSs. Specifically, given a source representation drawn from a source RS, the rules of structure transfer allow us to generate a target representation for a target RS. The generality of structure transfer comes in part from its ability to ensure that the source representation and the generated target representation satisfy any specified relation (such as semantic equivalence). This is done by exploiting schemas, which encode knowledge about RSs. Specifically, schemas can express preservation of information across relations between any pair of RSs, and this knowledge is used by structure transfer to derive a structure for the target representation which ensures that the desired relation holds. We formalise this using Representational Systems Theory, building on the key concept of a construction space. The abstract nature of construction spaces grants them the generality to model RSs of diverse kinds, including formal languages, geometric figures and diagrams, as well as informal notations. Consequently, structure transfer is a system-agnostic calculus that can be used to identify alternative representations in a wide range of practical settings.

cs.LG↗