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.
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RELEX: Extrapolating LLM RLVR Training via Rank-1 Parameter Trajectories
This paper demonstrates that RLVR weight update trajectories are extremely low-rank and near-linearly predictable, with a rank-1 approximation capturing most downstream performance gains. The authors propose RELEX, a compute-efficient method that observes a short training window, estimates the rank-1 subspace, and extrapolates future checkpoints via linear regression—requiring no additional training. Evaluated on Qwen2.5-Math-1.5B, Qwen3-4B-Base, and Qwen3-8B-Base, RELEX matches or exceeds full RLVR performance using as few as 15% of training steps, and can extrapolate up to 10–20× beyond the observed prefix. The authors attribute the method's effectiveness to a denoising effect from rank-1 projection that discards stochastic optimization noise.
Language models linearly encode a 'value axis' tracking expected goal success, study finds
Researchers construct a 'value axis' in Qwen3-8B's activation space using synthetic in-context RL data, finding that this axis distinguishes high vs. low confidence, backtracking vs. non-backtracking rollouts, and correct vs. corrupted code. Steering along this axis causally modulates self-correction behavior and verbosity, while DPO training shifts the internal value of rewarded behaviors. Applied to real-world settings, the axis reveals that Qwen assigns low internal value to politically sensitive queries post-training and that SFT increases domain-specific confidence. The findings suggest LLMs linearly encode an estimate of expected goal success that shapes their generative behavior.
Hyperfitting Explained: Terminal Geometric Expansion in Final Transformer Layers Drives Diversity Gains
This paper investigates the 'hyperfitting' phenomenon—where fine-tuning LLMs to near-zero loss on small datasets improves open-ended generation and reduces repetition—and demonstrates it is mechanistically distinct from temperature scaling. Entropy-matched control experiments falsify both the temperature-equivalence and static vocabulary reweighting hypotheses, instead localizing the effect to a 'Terminal Expansion' in the final transformer block where feature-space dimensionality expands by ~80.8 dimensions, enabling promotion of deep-tail tokens via context-dependent rank reordering. The authors introduce Late-Stage LoRA, a targeted fine-tuning strategy updating only the final 5 layers, achieving robust generation with minimal parameter updates.
Language Models Need Sleep: Periodic Context Consolidation via Fast Weights and SSM Blocks
This paper proposes a sleep-like consolidation mechanism for transformer-based LLMs to address the quadratic scaling of attention with context length. During 'sleep' phases, the model performs N offline recurrent passes over accumulated context, updating fast weights in state-space model (SSM) blocks via a learned local rule, then clears the KV cache. The approach is evaluated on synthetic tasks (cellular automata, multi-hop graph retrieval) and math reasoning, where standard transformers and SSM-attention hybrids fail, with performance scaling with sleep duration N.
Activation-space directions for detecting and mitigating emergent misalignment across LLM families
Researchers fine-tuned four small instruction-tuned model families (Qwen2.5-1.5B, Gemma-2-2B, Llama-3.2-1B, Ministral-3B) on insecure code to induce emergent misalignment, then investigated whether a shared activation-space direction could detect and correct it. A difference-in-means direction achieves 99.6% separation of aligned vs. misaligned activations within each model, and causal steering by subtracting this direction reduces misaligned behavior by 21–51 points. Cross-architecture transfer via ridge regression yields large behavioral suppression but fails specificity controls, revealing a two-tier structure: within-model directions are causally specific and actionable, while cross-model directions are real but non-specific. The findings bound the utility of linear cross-architecture correction and recommend within-model probing for safety auditing.
Conservation laws from data symmetry in neural network gradient-flow training
A new arXiv preprint investigates whether intrinsic symmetries in training data produce conserved quantities during gradient-flow training of neural networks. The authors prove that for analytic, non-polynomial loss functions, data symmetries generically do not induce additional integrals of motion, but for MSE loss, data augmentation can yield extra conserved quantities. They introduce a framework of 'tensorizable networks'—architectures including linear, polynomial, and Lightning Attention networks—where parameter and input dependence can be separated via an intermediate representation.
AdamO optimizer and dynamical isometry regularization preserve plasticity in continual learning
A new arXiv preprint connects plasticity loss in continual learning to the empirical Neural Tangent Kernel and identifies dynamical isometry—keeping layer-wise Jacobian singular values near one—as a key mechanism for maintaining learning capacity under non-stationarity. The authors propose an isometry-promoting regularization scheme that can reactivate dormant ReLU units and introduce AdamO, an Adam-style optimizer that decouples isometry regularization from gradient updates analogously to AdamW. The methods are evaluated on supervised and reinforcement-learning continual-learning benchmarks, consistently matching or outperforming prior approaches. The work also reinterprets existing plasticity-preserving methods as targeting only partial isometry measures.
Looped World Models introduce iterative latent depth as a new scaling axis for world simulation
A new arXiv preprint introduces Looped World Models (LoopWM), a parameter-shared transformer architecture that iteratively refines latent environment states to achieve up to 100x parameter efficiency over conventional world models. The approach uses adaptive computation to scale depth dynamically per prediction step, addressing the tension between long-horizon simulation fidelity and deployment cost. The authors position iterative latent depth as a new scaling axis orthogonal to model size and training data.