Learnable sparse retrieval (LSR) models encode texts into high-dimensional sparse representations, supporting token-level expansion beyond the original text and addressing the vocabulary mismatch problem in traditional bag-of-words retrieval. However, in the absence of representation-level supervision, these representations usually overemphasize irrelevant tokens while neglecting truly relevant ones. We term this phenomenon the Representation Hallucination problem in LSR models, a critical bottleneck impeding accurate retrieval. To address this challenge, we introduce SiRe, a self-improving training framework for sparse retrieval that integrates two core strategies: Heuristic Representation Refinement and Representation-Focused Learning. Specifically, SiRe first identifies and corrects representation hallucinations in the outputs of the current LSR model using heuristic methods. The resulting representations serve as the primary supervision signals, guiding a pretrained language model (e.g., BERT) to mitigate the problem directly at the representation level. This process can be iterated, enabling progressive model improvement. Extensive experiments on both in-domain and out-domain benchmarks show that SiRe produces higher-quality sparse representations, significantly enhancing retrieval performance over strong baselines.