We show that training a single d-dimensional steering vector per layer with reinforcement learning, while freezing all base weights, matches the accuracy of fully RL-tuned reasoning models on mathematical-reasoning tasks.On an 8 billion-parameter model this adds only ≈ 0.0016% additional parameters and reproduces performance across a range of base models and mathematical-reasoning benchmarks.These results tighten the upper bound on the parameter budget required for high-level chain-of-thought reasoning, indicating that millions of adapter weights are unnecessary.The minimal trainable footprint reduces optimizer memory and inter-GPU communication, lowering the overall cost of fine-tuning.Moreover, a logit-lens analysis shows that the learned vectors amplify coherent token directions, providing clearer insight into the model’s internal computations.

Sparse Autoencoders (SAEs) have proven to be powerful tools for interpreting neural networks by decomposing hidden representations into disentangled, interpretable features via sparsity constraints. However, conventional SAEs are constrained by the fixed sparsity level chosen during training; meeting different sparsity requirements therefore demands separate models and increases the computational footprint during both training and evaluation. We introduce a novel training objective, HierarchicalTopK, which trains a single SAE to optimise reconstructions across multiple sparsity levels simultaneously. Experiments with Gemma-2 2B demonstrate that our approach achieves Pareto-optimal trade-offs between sparsity and explained variance, outperforming traditional SAEs trained at individual sparsity levels. Further analysis shows that HierarchicalTopK preserves high interpretability scores even at higher sparsity. The proposed objective thus closes an important gap between flexibility and interpretability in SAE design.

Advancing the frontier of subquadratic architectures for Language Models (LMs) is crucial in the rapidly evolving field of natural language processing. Current innovations, including State Space Models, were initially celebrated for surpassing Transformer performance on language modeling tasks. However, these models have revealed deficiencies in essential In-Context Learning capabilities – a domain where the Transformer traditionally shines. The Based model emerged as a hybrid solution, blending a Linear Transformer with a kernel inspired by the Taylor expansion of exponential functions, augmented by convolutional networks. Mirroring the Transformer’s in-context adeptness, it became a strong contender in the field. In our work, we present a singular, elegant alteration to the Based kernel that amplifies its In-Context Learning abilities evaluated with the Multi-Query Associative Recall task and overall language modeling process, as demonstrated on the Pile dataset.