arXiv subjects

Fergal Reid

Publications and source records attributed to Fergal Reid.

16 recordsLinked to original sources

arXiv2026

Looped Transformers under the Jacobian Lens: Does the Global Workspace Survive Recurrence?

Recent work identifies a mid-depth band of verbalisable, causally potent representations in a standard feedforward transformer --- a functional analogue of a global workspace. Whether the same workspace functionality emerges when depth is implemented through recurrence rather than a stack of distinct layers remains unknown. Looped and depth-recurrent transformers provide a direct test of this question because they reuse the same weights across depth. We extend the Jacobian lens to iterated architectures using a virtual-unrolling adapter. We apply the full workspace suite --- lens fitting, readout, and eleven causal experiment families --- to Ouro-2.6B (48 layers looped 4 times, deeply supervised) and Huginn-0125 (a 4-layer core recurred 16 times, trained for latent reasoning), using Qwen3.6-27B (64 untied layers) as the standard baseline. We find that a workspace forms in the iterated part of each architecture, but that recurrence changes how it can be accessed. Ouro reconstructs workspace content in every loop, and linear transport cannot carry that content across loop boundaries; writes and ablations must therefore span every remaining loop. Huginn carries content forward across all sixteen recurrences, while reads, writes, and ablations act only within a sliding window of roughly two recurrences. Whether newly injected content can be verbalised tracks explicit per-iteration supervision; whether existing content can be steered does not.

cs.AI↗

arXiv2026

Protoreasoning in Tiny Transformers

We show that tiny transformers can profitably employ a simple form of Chain of Thought, which we call protoreasoning, allowing us to study step-by-step reasoning on ~1M-parameter models and opening up opportunities for much more detailed experimentation and analysis than is feasible for larger models. Current Large Language Models exhibit impressive step-by-step reasoning, but we have yet to understand its generality, i.e., when and how LLMs learn genuinely general algorithms rather than "bags of heuristics." Such questions are hard to settle on compute-intensive frontier models trained on opaque data. To work at model scales far below the threshold for natural-language competence, we define reasoning-friendly tasks on Dyck languages (sentences of correctly nested brackets). We find that protoreasoning traces substantially close the out-of-distribution generalization gap, and ablations confirm that the trace's content, not merely its extra tokens, drives the gain.

cs.CL↗

arXiv2026

Looped Latent Attention: Cross-Loop KV Compression for Looped Transformers

Looped, weight-tied Transformers reduce parameters by reusing a single block, but decoding still stores a separate K/V cache for every recurrence step. We show that this loop-indexed cache is highly structured. For a fixed token, layer and head, K/V vectors trace a short low-rank trajectory across loops, while the head and layer axes remain much flatter. We introduce Looped Latent Attention (\lla{}), a post-training cache codec that stores compact K and V latents and reconstructs loop-specific K/V vectors only when attention reads them. The default per-head codec compresses recurrence, while \lla{}-2D also folds heads into one latent for the extreme-compression regime. The codec is initialized from the SVD of teacher activations and refined with logit and attention-output distillation. At matched cache budget, per-head \lla{} outperforms head-axis MLA, cross-layer sharing, KV quantization and final-loop reuse, showing that the recurrent cache is low-rank but not safely collapsible to a single state. The same axis advantage holds on Ouro-2.6B-Thinking and transfers to Huginn-3.5B, where an SVD codec remains near-lossless to $32\times$ compression in decoder-independent evaluation. The cache reduction is exact. On one H200, the latent-store path increases measured Ouro-1.4B batch capacity at 4k context from 32 to 768 sequences at $21.3\times$ compression. Lastly, for long reasoning rollouts such as in MATH-500, on-policy refinement on student-generated prefixes raises accuracy at $4\times$ compression from 0.43 to 0.66 and reduces no-answer generations when compared to token-level off-policy distillation.

cs.LG↗

arXiv2026

Does Verbose Chain-of-Thought Really Help? In-Distribution Evidence that Content, Not Length, Matters

Chain-of-thought (CoT) prompting improves LLM reasoning, but the source is contested: do the intermediate steps help because they carry useful semantic content, or because conditioning on more tokens buys extra computation before the model commits to an answer? We bring two lines of evidence to bear. First, in distribution: we repeatedly sample each model on the same question and pair a shorter with a longer of its own natural generations that follow the same reasoning plan, so nothing is rewritten and both traces are genuinely in-distribution. Across 25 models the extra tokens leave accuracy essentially unchanged for every independently-trained reasoner, and a blind analysis of the surplus tokens shows that what gain exists elsewhere tracks validation- and checking-content, not verbosity per se. Second, as a controlled intervention, we ask whether two traces expressing the same semantic content (the same facts, operations, and intermediate values, verified through directed acyclic graph equivalence) produce different outcomes when one is more verbose, using a dual-validator design across four targets and eight benchmarks with number-redacted completion and stratified bootstrap confidence intervals. Verbose traces do improve accuracy (25 of 32 benchmark-target cells are positive under at least one validator), but the effects are modest (typically 1-4 points) and depend on the quality of the verbose prose, not merely its length. Under maximum numerical redaction the effect is amplified (median 3.24x across four arithmetic benchmarks), and length-matched non-reasoning filler recovers none of it. Both lines converge: what matters is what the extra tokens do (the reasoning and validation content they carry), not how many there are, a picture neither a pure forward-pass-compute nor a pure semantic-content account fully explains.

cs.AI↗

arXiv2026

When RL Suppresses Its Own Vocabulary: Recovering Reasoning Diversity in Puzzle-to-Math Transfer

Reinforcement learning using verifiable rewards (RLVR) improves LLM reasoning, but the conditions under which it transfers across domains -- and why it does so -- remain under-explored. We study cross-domain transfer in a 7B model whose SFT and RL post-training stages use only constraint-satisfaction puzzles, with no mathematics problems in the post-training data. To analyze how transfer emerges, we introduce a reasoning primitive-level framework that combines a 9-class span classifier with motif extraction, allowing us to segment chain-of-thought traces into primitive motifs and track their evolution across training stages and domains. We find that puzzle SFT induces a reasoning-primitive vocabulary, yielding a $+7$pp \texttt{pass@32} gain on OlymMATH-Hard. Vanilla GSPO then composes these primitives into longer compute-verify chains, adding a further $+6$pp. However, this RL stage also suppresses exploratory primitives such as \textit{hypothesize} and \textit{backtrack}. To address this, we introduce a novelty bonus that rewards diverse correct rollouts, using perplexity under the reference model as a signal. This restores recovery primitives during RL and adds a further $+7$pp \texttt{pass@32} relative to vanilla GSPO. Finally, the end-to-end recipe raises the hard-math capability ceiling from $16.0\%$ at the OLMo3-7B-Instruct-SFT base to $36.0\%$, without adding any mathematics problems during the SFT or RL stages.

cs.LG↗

arXiv2026

TopoBench: Benchmarking LLMs on Hard Topological Reasoning

Solving topological grid puzzles requires reasoning over global spatial invariants such as connectivity, loop closure, and region symmetry and remains challenging for even the most powerful large language models (LLMs). To study these abilities under controlled settings, we introduce TopoBench, a benchmark of six puzzle families across three difficulty levels. We evaluate strong reasoning LLMs on TopoBench and find that even frontier models solve fewer than one quarter of hard instances, with two families nearly unsolved. To investigate whether these failures stem from reasoning limitations or from difficulty extracting and maintaining spatial constraints, we annotate 750 chain of thought traces with an error taxonomy that surfaces four candidate causal failure modes, then test them with targeted interventions simulating each error type. These interventions show that certain error patterns like premature commitment and constraint forgetting have a direct impact on the ability to solve the puzzle, while repeated reasoning is a benign effect of search. Finally we study mitigation strategies including prompt guidance, cell-aligned grid representations and tool-based constraint checking, finding that the bottleneck lies in extracting constraints from spatial representations and not in reasoning over them. Code and data are available at github.com/mayug/topobench-benchmark.

cs.AI↗

arXiv2026

Tiny Recursive Reasoning with Mamba-2 Attention Hybrid

Recent work on recursive reasoning models like TRM demonstrates that tiny networks (7M parameters) can achieve strong performance on abstract reasoning tasks through latent recursion -- iterative refinement in hidden representation space without emitting intermediate tokens. This raises a natural question about operator choice: Mamba-2's state space recurrence is itself a form of iterative refinement, making it a natural candidate for recursive reasoning -- but does introducing Mamba-2 into the recursive scaffold preserve reasoning capability? We investigate this by replacing the Transformer blocks in TRM with Mamba-2 hybrid operators while maintaining parameter parity (6.83M vs 6.86M parameters). On ARC-AGI-1, we find that the hybrid improves pass@2 (the official metric) by +2.0\% (45.88\% vs 43.88\%) and consistently outperforms at higher K values (+4.75\% at pass@100), whilst maintaining pass@1 parity. This suggests improved candidate coverage -- the model generates correct solutions more reliably -- with similar top-1 selection. Our results validate that Mamba-2 hybrid operators preserve reasoning capability within the recursive scaffold, establishing SSM-based operators as viable candidates in the recursive operator design space and taking a first step towards understanding the best mixing strategies for recursive reasoning.

cs.AI↗

arXiv2026

Low-Rank Key Value Attention

The key-value (KV) cache is a primary memory bottleneck in Transformers. We propose Low-Rank Key-Value (LRKV) attention, which reduces KV cache memory by exploiting redundancy across attention heads, while being compute efficient. Each layer uses a shared full-rank KV projection augmented with low-rank, head-specific residuals, providing a continuous trade-off between complete sharing and full independence. After pretraining models of size 128M to 6.3B parameters, LRKV consistently achieves the lowest test loss among standard MHA, MQA/GQA, and MLA while using only 45-53\% of MHA's KV cache. LRKV reaches equivalent baseline quality 18-25\% faster (measured in training steps). After supervised midtraining, LRKV achieves the highest downstream task performance across ARC-Easy, ARC-Challenge, MMLU, GSM8K, and HumanEval benchmarks.

cs.LG↗

arXiv2012

Partitioning Breaks Communities

Considering a clique as a conservative definition of community structure, we examine how graph partitioning algorithms interact with cliques. Many popular community-finding algorithms partition the entire graph into non-overlapping communities. We show that on a wide range of empirical networks, from different domains, significant numbers of cliques are split across the separate partitions produced by these algorithms. We then examine the largest connected component of the subgraph formed by retaining only edges in cliques, and apply partitioning strategies that explicitly minimise the number of cliques split. We further examine several modern overlapping community finding algorithms, in terms of the interaction between cliques and the communities they find, and in terms of the global overlap of the sets of communities they find. We conclude that, due to the connectedness of many networks, any community finding algorithm that produces partitions must fail to find at least some significant structures. Moreover, contrary to traditional intuition, in some empirical networks, strong ties and cliques frequently do cross community boundaries; much community structure is fundamentally overlapping and unpartitionable in nature.

physics.soc-ph↗

arXiv2012

An Analysis of Anonymity in the Bitcoin System

Anonymity in Bitcoin, a peer-to-peer electronic currency system, is a complicated issue. Within the system, users are identified by public-keys only. An attacker wishing to de-anonymize its users will attempt to construct the one-to-many mapping between users and public-keys and associate information external to the system with the users. Bitcoin tries to prevent this attack by storing the mapping of a user to his or her public-keys on that user's node only and by allowing each user to generate as many public-keys as required. In this chapter we consider the topological structure of two networks derived from Bitcoin's public transaction history. We show that the two networks have a non-trivial topological structure, provide complementary views of the Bitcoin system and have implications for anonymity. We combine these structures with external information and techniques such as context discovery and flow analysis to investigate an alleged theft of Bitcoins, which, at the time of the theft, had a market value of approximately half a million U.S. dollars.

physics.soc-ph↗

arXiv2012

Efficient and reliable network tomography in heterogeneous networks using BitTorrent broadcasts and clustering algorithms

In the area of network performance and discovery, network tomography focuses on reconstructing network properties using only end-to-end measurements at the application layer. One challenging problem in network tomography is reconstructing available bandwidth along all links during multiple source/multiple destination transmissions. The traditional measurement procedures used for bandwidth tomography are extremely time consuming. We propose a novel solution to this problem. Our method counts the fragments exchanged during a BitTorrent broadcast. While this measurement has a high level of randomness, it can be obtained very efficiently, and aggregated into a reliable metric. This data is then analyzed with state-of-the-art algorithms, which reliably reconstruct logical clusters of nodes inter-connected by high bandwidth, as well as bottlenecks between these logical clusters. Our experiments demonstrate that the proposed two-phase approach efficiently solves the presented problem for a number of settings on a complex grid infrastructure.

cs.DC↗

arXiv2012

Percolation Computation in Complex Networks

K-clique percolation is an overlapping community finding algorithm which extracts particular structures, comprised of overlapping cliques, from complex networks. While it is conceptually straightforward, and can be elegantly expressed using clique graphs, certain aspects of k-clique percolation are computationally challenging in practice. In this paper we investigate aspects of empirical social networks, such as the large numbers of overlapping maximal cliques contained within them, that make clique percolation, and clique graph representations, computationally expensive. We motivate a simple algorithm to conduct clique percolation, and investigate its performance compared to current best-in-class algorithms. We present improvements to this algorithm, which allow us to perform k-clique percolation on much larger empirical datasets. Our approaches perform much better than existing algorithms on networks exhibiting pervasively overlapping community structure, especially for higher values of k. However, clique percolation remains a hard computational problem; current algorithms still scale worse than some other overlapping community finding algorithms.

cs.SI↗

arXiv2011

Supporting the Curation of Twitter User Lists

Twitter introduced lists in late 2009 as a means of curating tweets into meaningful themes. Lists were quickly adopted by media companies as a means of organising content around news stories. Thus the curation of these lists is important, they should contain the key information gatekeepers and present a balanced perspective on the story. Identifying members to add to a list on an emerging topic is a delicate process. From a network analysis perspective there are a number of views on the Twitter network that can be explored, e.g. followers, retweets mentions etc. We present a process for integrating these views in order to recommend authoritative commentators to include on a list. This process is evaluated on manually curated lists about unrest in Bahrain and the Iowa caucuses for the 2012 US election.

cs.SI↗

arXiv2011

Diffusion in Networks With Overlapping Community Structure

In this work we study diffusion in networks with community structure. We first replicate and extend work on networks with non-overlapping community structure. We then study diffusion on network models that have overlapping community structure. We study contagions in the standard SIR model, and complex contagions thought to be better models of some social diffusion processes. Finally, we investigate diffusion on empirical networks with known overlapping community structure, by analysing the structure of such networks, and by simulating contagion on them. We find that simple and complex contagions can spread fast in networks with overlapping community structure. We also find that short paths exist through overlapping community structure on empirical networks.

physics.soc-ph↗

arXiv2011

Seeding for pervasively overlapping communities

In some social and biological networks, the majority of nodes belong to multiple communities. It has recently been shown that a number of the algorithms that are designed to detect overlapping communities do not perform well in such highly overlapping settings. Here, we consider one class of these algorithms, those which optimize a local fitness measure, typically by using a greedy heuristic to expand a seed into a community. We perform synthetic benchmarks which indicate that an appropriate seeding strategy becomes increasingly important as the extent of community overlap increases. We find that distinct cliques provide the best seeds. We find further support for this seeding strategy with benchmarks on a Facebook network and the yeast interactome.

physics.soc-ph↗

arXiv2010

Detecting highly overlapping community structure by greedy clique expansion

In complex networks it is common for each node to belong to several communities, implying a highly overlapping community structure. Recent advances in benchmarking indicate that existing community assignment algorithms that are capable of detecting overlapping communities perform well only when the extent of community overlap is kept to modest levels. To overcome this limitation, we introduce a new community assignment algorithm called Greedy Clique Expansion (GCE). The algorithm identifies distinct cliques as seeds and expands these seeds by greedily optimizing a local fitness function. We perform extensive benchmarks on synthetic data to demonstrate that GCE's good performance is robust across diverse graph topologies. Significantly, GCE is the only algorithm to perform well on these synthetic graphs, in which every node belongs to multiple communities. Furthermore, when put to the task of identifying functional modules in protein interaction data, and college dorm assignments in Facebook friendship data, we find that GCE performs competitively.

physics.data-an↗