Existing coded-computing designs do not explicitly exploit the intrinsic structure of the input data. In communication systems, statistical structure and redundancy are often removed through source coding (or compression) before channel coding is applied. This principle, however, does not transfer directly to coded computation. In many computational tasks, particularly in machine learning, the structure of the data is precisely what the computation seeks to exploit to infer outputs or learn meaningful patterns. Consequently, coded-computing schemes should preserve and leverage this structure in their code design, rather than ignoring or eliminating it through source coding. This observation motivates a different perspective on code construction. In many channel-coding schemes, such as Reed-Solomon codes, coded symbols are generated by evaluating a low-dimensional algebraic representation at selected points. In contrast, many high-dimensional datasets naturally concentrate near low-dimensional manifolds. In this paper, we exploit this intrinsic geometry by designing coded samples that follow the natural manifold of the data, rather than imposing an artificial low-dimensional structure unrelated to the data distribution. Inspired by graph-based manifold learning, we propose a manifold-aware encoding strategy for general coded computing (GCC). Experiments on neural network inference and high-dimensional polynomial evaluation demonstrate that the proposed strategy consistently and significantly reduces the mean squared recovery error under straggling compared with standard GCC.
Dataset distillation, a training-aware data compression technique, has recently attracted increasing attention as an effective tool for mitigating costs of optimization and data storage. However, progress remains largely empirical. Mechanisms underlying the extraction of task-relevant information from the training process and the efficient encoding of such information into synthetic data points remain elusive. In this paper, we theoretically analyze practical algorithms of dataset distillation applied to the gradient-based training of two-layer neural networks with width L. By focusing on a non-linear task structure called multi-index model, we prove that the low-dimensional structure of the problem is efficiently encoded into the resulting distilled data. This dataset reproduces a model with high generalization ability for a required memory complexity of \tildeΘ$$(r^2d+L), where d and r are the input and intrinsic dimensions of the task. To the best of our knowledge, this is one of the first theoretical works that include a specific task structure, leverage its intrinsic dimensionality to quantify the compression rate and study dataset distillation implemented solely via gradient-based algorithms.
Network failures are among the most frequent hardware faults in large-scale GPU clusters and a leading cause of training-job interruptions. Modern collective communication libraries such as NCCL mitigate network failures by rerouting traffic through surviving NICs on the same server, trading reduced inter-node bandwidth for uninterrupted training. However, the degraded server remains on the critical path of the standard ring algorithm, slowing the entire collective. We present the first information-theoretic lower bound on AllReduce completion time under asymmetric network bandwidth and show that when the straggler retains at least half of its original bandwidth, the unavoidable overhead relative to the fault-free optimum is only O(1/p) for p GPUs. We then design OptCC, a four-stage pipelined AllReduce algorithm that approaches this lower bound. Experiments on SimAI confirm that OptCC closes the gap left by existing fault-tolerant schemes: under practical network failures with up to 50% bandwidth loss, OptCC completes AllReduce within 2-6% of NCCL's fault-free ring performance, whereas the state-of-the-art incurs up to 57% overhead.
Classical coding-theoretic guarantees often rely on trust assumptions, such as requiring sufficiently many honest nodes compared with adversarial ones. These assumptions are difficult to enforce in open decentralized systems where participants are not centrally certified. At the same time, such environments often contain incentive mechanisms: participants may be rewarded only when their submitted data are accepted and the system remains functional. This changes the role of an adversary. Rather than acting as a pure saboteur, a strategic adversary may submit data that are consistent enough to be accepted while still degrading the quality of the final estimate. The game-of-coding framework models this strategic interaction between a data collector (DC) and an adversary. Existing works on the game of coding mostly consider the complete-information case, where the DC knows how the adversary trades off acceptance and estimation error. In this paper, we study an incomplete-information version of the game of coding in which the DC, acting as a Stackelberg leader, does not know the adversary's utility trade-off and must learn through repeated interaction. Prior work on the unknown-adversary setting considered an explore-then-commit objective, where only the final selected acceptance rule is evaluated. In contrast, we study the full learning trajectory: every acceptance rule used during the algorithm is executed and contributes to performance. We propose an algorithm that refines its search around promising acceptance rules, prove that it achieves sublinear cumulative regret, and evaluate its performance through numerical experiments.
Hanzaleh Akbari Nodehi, Parsa Moradi, Mohammad Ali Maddah-Ali