Fergal Reid

James O' Neill, Fergal Reid

Looped, weight-tied Transformers reduce parameters by reusing a 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 SVD of teacher activations and refined with KL 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 32x 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 21.3x compression. For long math rollouts, on-policy refinement on student-generated prefixes raises MATH-500 at 4x from 0.43 to 0.66 and reduces no-answer generations.

Mayug Maniparambil, Arjun Karuvally, Terrence Sejnowski et al.

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.

James O'Neill, Robert Clancy, Mariia Matskevichus et al.

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.

Mayug Maniparambil, Nils Hoehing, Janak Kapuriya et al.

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.

Wenlong Wang, Fergal Reid

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.

Wenlong Wang, Fergal Reid

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.