SSM

SSM is a class of architectures that process sequences in a linear recurrent manner, with representatives such as Mamba and Mamba-2.

State space models represented by Mamba compress historical information by maintaining a fixed-size hidden state, with both time and space complexity of O(1) during inference.

The SSM framework consists of three frameworks: Spring, SpringMVC, and MyBatis.

SSMs have a linear time complexity advantage in processing long sequences, whereas the attention computation complexity of standard Transformers is quadratic with respect to sequence length.

Standard self-attention has a computational complexity of O(n²); SSA reduces complexity by having each token attend only to the most relevant subset, theoretically compressible to O(n·log n) or even O(n) level.

SpringBoot simplifies the XML configuration work of SSM through its Auto-Configuration and Starter dependency mechanisms.

The prerequisite knowledge needed to study this hands-on project includes: proficient Spring/SSM engineering skills, database experience, Redis-related knowledge, and a proficient command of LangChain4j.

The continuous form of a state space model is h'(t) = A·h(t) + B·x(t), with output y(t) = C·h(t) + D·x(t); after discretization it processes a sequence of length n with O(n) complexity.

Mamba2 is a sequence modeling architecture based on the state space model (SSM), which binds the SSM state dimension to the input channels and rewrites the per-timestep serial recurrence into matrix multiplication form, allowing parallel computation using GPU Tensor Cores.

Whether SSMs can fully match Transformers on tasks such as language modeling, reasoning, and retrieval remains a focus of debate in academia and industry.

SSM 的代价是状态容量有限，对需要精确检索远距离细节的任务表现弱于注意力机制。

SSM 通过随时间演化的隐藏状态 h_t = A·h_{t-1} + B·x_t 压缩历史信息，输出由 h_t 线性映射得到，单步解码计算量与序列长度无关，显存占用恒定。

在自回归解码中，注意力层通常缓存所有历史 token 的 Key 和 Value（KV Cache），显存随序列长度线性增长，但每步只需追加、无需重算；SSM 层则只保留固定大小的状态。

混合模型通过在少量注意力层之间穿插状态空间模型（SSM）层，在保持长上下文能力的同时降低计算开销，正成为大语言模型架构演进的重要方向。

在混合架构中，SSM 层与注意力层交替出现时，模型需要在层之间传递和恢复状态，频繁的状态存取会带来额外开销，在长序列生成场景下会制约解码吞吐量。

Hybrid architecture typically refers to a design approach that combines the Transformer's attention mechanism with state space models (SSMs, such as Mamba).

LFM draws in its architecture from aspects of State Space Models (SSM) and liquid networks, aiming to reduce computational complexity when processing long sequences.

The mathematical roots of SSMs come from linear time-invariant systems in control theory, using matrices A, B, and C to describe how inputs update the hidden state and how the hidden state maps to outputs.

State Space Models (SSMs) pull the direction back toward fixed-size recurrent memory, but use a different state structure and update rules.

Land surface forecasting systems based on Mamba-series structured state space models absorb non-stationary confounding events into the state transition matrix, leading to persistent prediction bias.