π€ AI Summary
This work investigates the fundamental performance limits of remote inference under unreliable communication links and resource-constrained, error-prone receiver-side computation units. By modeling fragile computational components as memoryless noisy channels and introducing a βcommit/no-bypassβ receiver closure framework, the study formulates notions of cuts and serial cuts within the internal computation graph of the receiver. It reveals that the first-order performance loss of hard-separated architectures stems from the closure assumption rather than computational unreliability per se. Leveraging information-theoretic converse arguments, a soft-path budgeting mechanism, and achievability constructions under protected closures, the paper establishes a general min-cut-based converse bound. Under soft-visibility conditions, this bound reduces to a single-bottleneck form, and task-to-task direct connectivity along with serial hard separation is shown to be achievable under strongly protected closures.
π Abstract
Classical information theory typically assumes reliable receiver-side processing. We study remote inference when communication is noisy and the receiver itself is built from unreliable components under a finite redundancy budget. Under a committed/no-bypass receiver closure, task-relevant information can affect the final estimate only by passing through a budgeted collection of vulnerable primitives unless an explicit protected bypass is modeled. Modeling each vulnerable primitive as a memoryless noisy channel yields a baseline supply--demand converse: the task-relevant information needed to attain a target distortion cannot exceed the smaller of the total information supplied by the communication channel and the total information supplied by the vulnerable compute budget. Our main converse shows that committed intermediate interfaces create additional first-order serial cuts and receiver-internal computation-graph cuts, captured in general by a receiver-internal compute min-cut converse. In particular, the twofold loss in the symmetric two-stage hard-separation special case is not inherent to unreliable receiver computation but induced by hard-separation under the committed/no-bypass closure. This extra first-order tax is therefore closure-dependent rather than universal. On the converse side, if downstream modules retain soft visibility to the raw channel output, the converse reduces to the single-bottleneck supply, up to any explicitly reserved soft-path budget. Under a separate stronger protected-support closure with reliable decoder and control support, we establish achievability results for task-direct and serial hard-separation constructions. For the fully noisy-logic regime, we obtain only a conservative depth-dependent converse, and matched achievability remains open.