6arXiv cs.AI (Artificial Intelligence)·
Theoretical framework reveals low-dimensional invariant manifolds governing Transformer inductive reasoning dynamics
A new arXiv preprint presents a theoretical framework explaining how Transformers develop inductive reasoning abilities by proving that training dynamics of attention models are confined to a low-dimensional invariant manifold. The framework unifies several synthetic inductive tasks (in-context n-grams, multi-hop reasoning) and characterizes how data statistics govern competition between in-context and in-weights learning. The authors show that random initializations determine which circuit 'wins' when multiple solutions exist, and that the manifold's coordinate frame can automatically detect learned circuits in trained models. The work advances mechanistic interpretability by casting circuit formation as a tractable low-dimensional dynamical phenomenon.
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LOTUS: Looped Transformers bridge latent and explicit chain-of-thought reasoning at 3B scale
Researchers introduce LOTUS (Looped Transformers with parallel supervision on latents), a latent chain-of-thought method that processes reasoning steps in hidden states rather than decoded tokens. LOTUS is claimed to be the first latent-CoT approach to match explicit CoT performance at the 3B parameter scale, while reducing thought-phase latency by 2.5x–6.9x. The method uses a looped (recurrent-depth) Transformer backbone with parallel cross-entropy supervision on gold CoT-step tokens at each latent position, and the latent space is shown to be interpretable by projecting through the base LM head to recover reasoning steps.
Local linear structures in LLM weights and activations are dynamic, not fixed global directions
A new arXiv paper investigates the nature of linear structures in transformer weights and activations, finding strong local low-rank task-gradient structure but rejecting the hypothesis that fixed task planes exist. The authors show that useful bases drift substantially within 100 optimization steps, yet early recovery updates form a trajectory-prefix basis capturing 77% of LoRA recovery displacement. They also establish a formal connection between parameter perturbations and activation steering, finding a 0.58 cosine similarity between gradient-step-induced activation shifts and CAA steering vectors, suggesting linear structures are evolving local geometries rather than stable global task directions.
Equilibrium Reasoners: Learning Attractors Enables Scalable Reasoning
This paper introduces Equilibrium Reasoners (EqR), a framework that formalizes test-time compute scaling through learned task-conditioned attractors in latent space, where stable fixed points correspond to valid solutions. EqR scales along two axes—depth (more iterations) and breadth (aggregating stochastic trajectories)—without requiring external verifiers or task-specific priors. On Sudoku-Extreme, unrolling up to 40,000 equivalent layers boosts accuracy from 2.6% (feedforward baseline) to over 99%. The work provides a mechanistic lens for understanding why iterative latent models generalize beyond memorized patterns.
FlashMorph: Learned layer selection for converting Transformers to hybrid attention models
This arXiv paper introduces FlashMorph, a method for converting standard Transformer models into hybrid attention architectures by optimally selecting which layers retain full attention versus linear attention. Rather than using heuristic placement patterns, FlashMorph frames layer selection as a budget-constrained subset optimization, jointly learning layerwise gates on synthetic long-context retrieval data with a linearization regularization term. Experiments show FlashMorph finds more effective hybrid configurations that preserve long-context recall and general benchmark performance while reducing selection cost compared to prior methods. The work addresses a practical efficiency problem in deploying long-context models at scale.
Positional vs. Symbolic Attention Heads: Learning Dynamics, RoPE Geometry, and Length Generalization
Researchers train a decoder-only Transformer (GPT-J) on two structurally equivalent multi-hop reasoning tasks to study how attention heads specialize into positional or symbolic roles during learning. They find that successful task learning correlates with the emergence of 'pure' heads—exclusively positional or symbolic—and provide theoretical constructions showing how single-layer RoPE-based attention realizes these functions geometrically. A novel 'discrepancy' metric formalizes the robustness difference between the two head types, with symbolic mechanisms shown to extrapolate more reliably to longer sequences than positional ones. The findings have implications for understanding length generalization failures in RoPE-based models.
Dynamic short convolutions yield 1.33–1.60× compute advantage over standard Transformers
A new arXiv preprint introduces dynamic short convolutions as an architectural primitive for Transformers, using input-dependent filters to combine locality bias with increased expressivity. Experiments across 150M–2B parameter language models show consistent perplexity improvements over standard Transformers and static convolution variants, with scaling-law fits indicating a 1.33× compute advantage when applied to key/query/value vectors and 1.60× when added after every linear layer. The technique also improves linear RNNs (Mamba-2, Gated DeltaNet) and mixture-of-experts architectures, with custom Triton kernels making training practical.
Analysis-driven transformer linearization outperforms prior baselines on LLaMA and Qwen up to 32B
A new arXiv paper analyzes why post-hoc linearization of causal self-attention degrades model quality, identifying key-dependent rank-1 orthogonal projections as the mechanism softmax relies on and explaining why delta-style networks outperform gated accumulation. The authors introduce structural interventions—sink tokens, short convolutions, and fixed-budget cache routing—applied in a frozen-backbone regime. Scaling across LLaMA and Qwen models up to 32B parameters, the approach outperforms prior post-hoc linearization baselines on MMLU and matches long-context retrieval of adaptive-caching frameworks.
In-Context Reward Adaptation for Robust Preference Modeling
This paper proposes In-Context Reward Adaptation (ICRA), a transformer-based framework that infers reward structures from small sets of preference demonstrations at inference time, without retraining. The key finding is that standard transformers exhibit asymptotic bias toward ground-truth rewards, but incorporating human response time as an auxiliary signal resolves this limitation and enables generalization to unseen preference domains. The approach addresses a core limitation of static RLHF reward models, which fail to handle heterogeneous or shifting human value distributions.