Large language models solve hard problems through intermediate computations across multi-step reasoning. Traditional chain-of-thought encodes these computations as tokens. Recent continuous and recurrent methods instead move partial computations into fixed-dimensional latent states, where a single thought can superpose multiple alternatives. This raises a fundamental design question:what should continuous thoughts preserve as reasoning proceeds? An intuitive approach discards past computations and keeps only the current reasoning frontier. Storing more items seems to dilute states and waste limited representational capacity. We show this intuition can be incorrect. Under identical downstream computations, cumulative superposition retaining full reasoning history can require lower representational dimensions than frontier-only superposition holding only current alternatives. At fixed hidden width, this advantage allows latent reasoners to retain more valid evidence, distinguish more plausible downstream outcomes, and delay the point where compressed states turn unreliable. This counter-intuitive effect emerges because informative historical components coherently reinforce each other, while unrelated alternatives bring random interference. This perspective also answers a practical design question: how should models weight memories accumulated inside latent states when their future use is unknown? Across reusable weighted superpositions, prioritizing a small set of recent or salient items produces weakly-represented memories that bottleneck subsequent attention. Uniform cumulative weighting avoids this flaw, and we prove it is minimax-optimal for robust future reasoning. Our results turn superposition from an observed latent-space effect into a design principle: balanced cumulative memory lets a fixed representational budget support more reliable, reusable computations.
Semantic communication (SemCom) and task-oriented communication (TOC) can reduce wireless resource consumption by focusing on transmitting semantic or task-relevant information instead of raw messages. In practice, a main challenge is to make transmitting information robust to channel noise and fading while keeping it compact. Existing learning-based transceivers often improve reliability by using larger encoders or higher-dimensional channel features, which increase computation complexity and channel uses. Therefore, optimized system design needs explicit rate control to balance performance and transmitting resources e.g., bandwidth and power. For this purpose, we propose a manifold-constrained hyper-connection (mHC) coding scheme with an entropy bottleneck (EB) for resource-efficient SemCom and TOC over wireless channels. Instead of using a single residual path of existing encoders, the proposed mHC-based semantic encoder applies multiple residual streams and constrains their interaction by doubly stochastic (DS) mixing matrices. The new structure improves representation diversity and training stability with negligible parameter and floating-point overhead. The EB quantizes the channel features and estimates the entropy-coded rate, enabling end-to-end rate--distortion/task optimization under bandwidth and transmit-power constraints. We further show that DS-constrained stream mixing does not increase the differential entropy of the transmitted features. This implies no increase in the ideal EB coding length. Experiments on SemCom and TOC under additive white Gaussian noise (AWGN), Rayleigh fading, Rician fading, and imperfect channel state information (CSI) show that the proposed scheme improves semantic/task performance, communication robustness, and convergence stability over residual and unconstrained HC baselines, while requiring no additional channel uses.
Jingwen Fu, Ming Xiao· 0 citations
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