arXiv subjects
Publications and source records attributed to Zihan Zhang.
We give a deterministic polynomial-time list-decoding algorithm for Reed-Solomon codes over prime fields that approaches list-decoding capacity for every evaluation set and every constant rate.
We give new explicit constructions of several fundamental objects in linear-algebraic pseudorandomness and combinatorics, including lossless rank extractors, weak subspace designs, and strong $s$-blocking sets over finite fields. Our focus is on the small-field regime, where the field size depends only on a secondary parameter (such as the rank or codimension) and is independent of the ambient dimension. This regime is central to several applications, yet remains poorly understood from the perspective of explicit constructions. In this setting, we obtain the first explicit constructions of lossless rank extractors and weak subspace designs for $r\ll k$, where $r$ denotes the rank (or codimension), over finite fields $\mathbb{F}_q$ with $q \ge \mathrm{poly}(r)$ and $q$ non-prime, with near-optimal parameters. For other finite fields, including prime fields and small fields, we obtain weaker but still improved bounds. As a consequence, we construct explicit strong $s$-blocking sets in $\mathrm{PG}(k-1,q)$ of size $O(s(k-s)q^s)$ for all sufficiently large non-prime fields $q \ge \mathrm{poly}(s)$, matching the best known non-explicit bounds up to constant factors. This significantly improves the previous best bound $2^{O(s^2 \log s)} q^s k$ of Bishnoi and Tomon (Combinatorica, 2026), which requires $q \ge 2^{Ω(s)}$. Our approach is primarily algebraic, combining techniques from function fields and polynomial identity testing. In addition, we develop a complementary Fourier-analytic framework based on $\varepsilon$-biased sets, which yields improved explicit constructions of strong $s$-blocking sets over small fields.
A Federated Learning (FL) system collaboratively trains neural networks across devices and a server but is limited by significant on-device computation costs. Split Federated Learning (SFL) systems mitigate this by offloading a block of layers of the network from the device to a server. However, in doing so, it introduces large communication overheads due to frequent exchanges of intermediate activations and gradients between devices and the server and reduces model accuracy for non-IID data. We propose Ampere, a novel collaborative training system that simultaneously minimizes on-device computation and device-server communication while improving model accuracy. Unlike SFL, which uses a global loss by iterative end-to-end training, Ampere develops unidirectional inter-block training to sequentially train the device and server blocks with a local loss, eliminating the transfer of gradients. A lightweight auxiliary network generation method decouples training between the device and server, reducing frequent intermediate exchanges to a single transfer, which significantly reduces the communication overhead. Ampere mitigates the impact of data heterogeneity by consolidating activations generated by the trained device block to train the server block, in contrast to SFL, which trains on device-specific, non-IID activations. Extensive experiments on multiple CNNs and Transformers show that, compared to state-of-the-art SFL baseline systems, Ampere (i) improves model accuracy by up to 11.70 percentage points while training up to 18.6x faster, (ii) incurs up to 911x lower device-server communication overhead and up to 14.5x lower on-device computation, and (iii) reduces standard deviation of accuracy by 71.13% for various non-IID degrees highlighting superior performance when faced with heterogeneous data. Ampere is available from https://github.com/blessonvar/Ampere.
Full-duplex voice assistants must continuously listen while speaking, handling user interruptions under low-latency and resource-constrained streaming conditions. Existing end-to-end full-duplex models can compromise reasoning-related capabilities after speech-domain adaptation, whereas cascaded pipelines introduce extra inference overhead and handcrafted control logic. We propose TurnFSM, an LLM-based state prediction framework that internalizes turn control as explicit finite-state transitions, unifying streaming semantic VAD and utterance-level rejection. TurnFSM decomposes submission and rejection into a serial decision process, reducing multi-task interference while maintaining performance comparable to single-task models. We further introduce a first-order state transition mechanism that enforces the dependency on only the previous state during training, enabling compact inference with the standard causal mask and original LLM positional encoding while avoiding historical state-token accumulation and unnecessary step-by-step state generation. Experimental results show that TurnFSM consistently outperforms the binary-head baseline and remains competitive with task-specific models.