Shida Wang

Shida Wang, Beichen Xue

State-space models have gained popularity in sequence modelling due to their simple and efficient network structures. However, the absence of nonlinear activation along the temporal direction limits the model's capacity. In this paper, we prove that stacking state-space models with layer-wise nonlinear activation is sufficient to approximate any continuous sequence-to-sequence relationship. Our findings demonstrate that the addition of layer-wise nonlinear activation enhances the model's capacity to learn complex sequence patterns. Meanwhile, it can be seen both theoretically and empirically that the state-space models do not fundamentally resolve the issue of exponential decaying memory. Theoretical results are justified by numerical verifications.

Shida Wang, Qianxiao Li

In this paper, we investigate the long-term memory learning capabilities of state-space models (SSMs) from the perspective of parameterization. We prove that state-space models without any reparameterization exhibit a memory limitation similar to that of traditional RNNs: the target relationships that can be stably approximated by state-space models must have an exponential decaying memory. Our analysis identifies this "curse of memory" as a result of the recurrent weights converging to a stability boundary, suggesting that a reparameterization technique can be effective. To this end, we introduce a class of reparameterization techniques for SSMs that effectively lift its memory limitations. Besides improving approximation capabilities, we further illustrate that a principled choice of reparameterization scheme can also enhance optimization stability. We validate our findings using synthetic datasets, language models and image classifications.

Shida Wang, Chaohu Liu, Yubo Wang et al.

Large language models represent significant investments in computation, data, and engineering expertise, making them extraordinarily valuable intellectual assets. Nevertheless, these AI assets remain vulnerable to unauthorized redistribution and commercial exploitation through fine-tuning or black-box deployment. Current fingerprinting approaches face a fundamental trade-off: intrinsic methods require full parameter access, while backdoor-based techniques employ statistically anomalous triggers easily detected and filtered by adversaries. To address these limitations, we introduce FPEdit, a novel framework that leverages knowledge editing to inject semantically coherent natural language fingerprints through sparse, targeted modifications to model weights. Our approach introduces Promote-Suppress Value Vector Optimization, which simultaneously enhances target token likelihood while suppressing competing tokens, ensuring robust fingerprint integration without degrading core model functionality. Extensive experiments show that FPEdit achieves 95-100% fingerprint retention under both full-parameter fine-tuning and parameter-efficient adaptation, while preserving performance on downstream benchmarks. Moreover, FPEdit remains robust under quantization, pruning, and stochastic decoding, and can embed 10 fingerprint pairs into LLaMA2-7B in under 2 minutes using less than 30 GB of GPU memory, which represents a substantial reduction in resource requirements. These advances establish FPEdit as the first fingerprinting approach to simultaneously achieve robustness against adaptation, resistance to detection, and preservation of model utility, thereby providing a minimally invasive solution for reliable provenance verification of large language models in adversarial deployment scenarios.

Shida Wang

In this paper, we investigate the length-extension of state-space models (SSMs) in language modeling. Length extension involves training models on short sequences and testing them on longer ones. We show that state-space models trained with zero hidden states initialization have difficulty doing length extension. We explain this difficulty by pointing out the length extension is equivalent to polynomial extrapolation. Based on the theory, we propose a simple yet effective method - changing the hidden states initialization scheme - to improve the length extension. Moreover, our method shows that using long training sequence length is beneficial but not necessary to length extension. Changing the hidden state initialization enables the efficient training of long-memory model with a smaller training context length.