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A hybrid transformer with constant-cost attention read from fixed-size dynamical memory units

AspireAI community · arXiv (cs.AI)
Transformers keep an explicit token history, so the KV cache and the cost of a new token grow with context, while state space models compress the past into a fixed recurrent state at the cost of addressability. The Dynamical Memory Transformer separates the two jobs: the encoder uses several memory units, each a dynamical system with a complex diagonal recurrent matrix and an input-dependent leak rate controlling its updates, while the decoder uses attention to read and combine their outputs without passing through the token history. The recurrence admits an associative scan with O(T) total work and O(log T) parallel depth at fixed dimensions, and during autoregressive inference the recurrent states and convolution cache stay fixed in size. The authors compare against Mamba and Transformer and are candid about the trade: DMT wins several cognitive tasks and shows stronger length extrapolation on selective copy, but remains behind Mamba on language modeling while staying close to Transformer.
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One distance function matched sparse-autoencoder features across layers and compressed feature circuits into supernodes
Two sparse-autoencoder analyses have resisted scaling: matching semantically similar features across layers, and compressing large feature circuits into interpretable supernodes. This paper argues both are the same underlying problem, estimating semantic distances between SAE features that sit on different activation manifolds. Its representation treats each feature not as a single decoder vector but as an activation-weighted distribution over the hidden states expressing it, projects those distributions into a shared reference space, and compares them with Wasserstein distance. The representation is proved invariant to activation rescaling and stable under perturbation, and recovers true matches under finite-sample margin conditions. Empirically it outperformed decoder-vector and LLM-based baselines and captured subtle functional distinctions between related features, and it compressed large feature circuits into interpretable supernodes automatically. The limitation is that this is interpretability tooling: the paper demonstrates better feature matching and circuit compression, not that downstream interpretability claims become more accurate.
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