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All chapters References

Part I · Foundations

  1. W01 Linear ODEs as state-space systems
  2. W02 Stability theory: Lyapunov, A-stability, BIBO
  3. W03 Linear algebra for sequence models: structured matrices and conditioning
  4. W04 Discretization theory: ZOH, bilinear, exponential families
  5. W05 Stability regions, Butcher tableau, and order conditions
  6. W06 Implicit methods, stiff systems, symplectic integration

Part II · SSM Core

  1. W07 HiPPO theory: orthogonal-basis projection operators
  2. W08 LTI SSMs: S4, S4D, S5 as discretized continuous systems
  3. W09 Selective SSMs: Mamba-1, Mamba-2, and the SSD framework
  4. W10 Mamba-3 and the exponential-trapezoidal integrator

Part III · Beyond SSMs

  1. W11 Linear attention and Hyena: long convolution and gated recurrence
  2. W12 Delta-rule lineage: DeltaNet, Gated DeltaNet, Kimi Linear
  3. W13 Exponential gates and matrix memory: xLSTM and RWKV-7

Part IV · Integration

  1. W14 Hybrid architectures and gating mechanisms
  2. W15 Counter-evidence and diagnostic tools: where SSMs fail
  3. W16 Empirical methodology: benchmark protocols and evaluation

Part V · Synthesis

  1. W17 Niche-pilot integration: from curriculum to research output
ssm-foundations A dynamical-systems lens on sequence-model architectures
All chapters References

Part I · Foundations

  1. W01 Linear ODEs as state-space systems
  2. W02 Stability theory: Lyapunov, A-stability, BIBO
  3. W03 Linear algebra for sequence models: structured matrices and conditioning
  4. W04 Discretization theory: ZOH, bilinear, exponential families
  5. W05 Stability regions, Butcher tableau, and order conditions
  6. W06 Implicit methods, stiff systems, symplectic integration

Part II · SSM Core

  1. W07 HiPPO theory: orthogonal-basis projection operators
  2. W08 LTI SSMs: S4, S4D, S5 as discretized continuous systems
  3. W09 Selective SSMs: Mamba-1, Mamba-2, and the SSD framework
  4. W10 Mamba-3 and the exponential-trapezoidal integrator

Part III · Beyond SSMs

  1. W11 Linear attention and Hyena: long convolution and gated recurrence
  2. W12 Delta-rule lineage: DeltaNet, Gated DeltaNet, Kimi Linear
  3. W13 Exponential gates and matrix memory: xLSTM and RWKV-7

Part IV · Integration

  1. W14 Hybrid architectures and gating mechanisms
  2. W15 Counter-evidence and diagnostic tools: where SSMs fail
  3. W16 Empirical methodology: benchmark protocols and evaluation

Part V · Synthesis

  1. W17 Niche-pilot integration: from curriculum to research output

ssm-foundations

17-chapter lens-led foundations book bridging numerical analysis and dynamical systems to modern sequence-model architectures (SSMs, Mamba, S4, Hyena, DeltaNet).

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