State-Aware Feedforward Model

• State-aware feedforward models are neural architectures that explicitly incorporate historical, contextual, or latent state information into a purely feedforward framework.
• They employ mechanisms such as memory blocks in FSMNs, observer-based estimators, and physics-guided layers to improve performance across sequence learning, control, quantum photonics, and computer vision.
• Their design enables efficient, parallelizable training with back-propagation-only methods, offering enhanced stability, reduced latency, and improved parameter efficiency.

A state-aware feedforward model refers broadly to any neural or algorithmic architecture that implements a purely feedforward computation, but where the transformation at each step depends explicitly on a summary of system or sequence “state”—that is, it incorporates historical, contextual, or latent information in a non-recurrent, causal, or parallelizable fashion. This paradigm is foundational across several areas: sequential learning (e.g., Feedforward Sequential Memory Networks), control (observer–feedforward architecture, physics-guided neural feedforward control), quantum photonics protocols (adaptive feedforward in multi-photon conversion), and robust computer vision (semantic-aware state-space models). State-aware feedforward models unify the state-handling power of feedback-based systems with the stability, efficiency, and simplicity of explicit feedforward computation.

1. Fundamental Principles and Definitions

State-awareness in the feedforward context entails augmenting the computations of a system—not by recurrence or feedback loops, but by explicit mechanisms that aggregate, summarize, or inject state information. The core distinguishing features are:

• Explicit state representation: Contextual or historical data (past activations, disturbance estimates, semantic groupings, etc.) are formed into a state vector, which conditions the feedforward computation.
• Feedforward propagation: All computations are acyclic; state information is summarized or aggregated without the implicit recurrence of traditional RNNs or the feedback of observers in classical control.
• Learnable state-handling mechanisms: Memory blocks, state-space filters, or parallel observers admit parameterization and are jointly optimized with the primary feedforward weights.

In neural sequence modeling, state-aware feedforward models (notably FSMN) endow ordinary FNNs with learnable FIR-like filters over a context window, obviating the need for recurrence for long-term dependency modeling (Zhang et al., 2015, Zhang et al., 2015).

In control, state-aware feedforward takes the form of engineered architectures where feedforward terms—driven by observer estimates or explicit state regressor constructions—robustly reject disturbances or track references, often by leveraging parallel RNNs for observer roles and static, low-dimensional networks for policy mapping (Zhang et al., 2023, Bolderman et al., 2022, Bolderman et al., 2023).

State-awareness also extends to adaptive quantum state engineering, as in feedforward-enhanced photon subtraction protocols, and to semantic-driven enhancement modules in vision, which aggregate and propagate feature information conditioned on both estimated degradation and semantic state (Švarc et al., 2020, Wu et al., 5 Aug 2025).

2. Architectures and Mathematical Formulations

Feedforward Sequential Memory Networks (FSMN)

FSMN architectures augment each hidden layer of a standard deep FNN with a "memory block"—a finite impulse response (FIR) filter over the layer’s own past activations. The memory output at layer $\ell$ and time $t$ is:

• Scalar FSMN (sFSMN):

$$\tilde h_t^{\ell} = \sum_{i=0}^N a_i^{\ell} \cdot h_{t-i}^{\ell}$$

with $a_i^{\ell}$ shared across dimensions.

• Vectorized FSMN (vFSMN):

$$\tilde h_t^{\ell} = \sum_{i=0}^N a_i^{\ell} \odot h_{t-i}^{\ell}$$

with learnable $a_i^{\ell} \in \mathbb{R}^{D_\ell}$.

The memory-augmented hidden vector is then passed to the next feedforward layer. Alternatives exist, such as attention-parameterized taps and bidirectional extensions with both look-back and look-ahead taps (Zhang et al., 2015, Zhang et al., 2015).

State-Aware Feedforward in Control: Structured Observer–Controller Decomposition

The state-aware feedforward model for policy learning decomposes as follows (Zhang et al., 2023):

• RNN observers: $$\hat x_t = \phi_o(\hat x_{t-1}, u_{t-1}, y_{t-1}, d_{t-1})$$
• Feedforward paths: Both reference $r_t$ and estimated disturbance $\hat x_t^d$ (from a parallel RNN) are injected directly into the (typically shallow) feedback/feedforward controller:

$u_t = \pi(\hat x_t, r_t, \hat x^d_t)$

This decoupling matches classical observer-based control, with modern extensions for nonlinear or partially observable systems.

Physics-Guided Neural Feedforward (PGNN)

In precision mechatronics, state-aware PGNN feedforward controllers structurally combine parametric physics-based layers and neural network residuals:

$$u_\mathrm{ff}(k;\theta)=f_\mathrm{phy}(\phi(k);\theta_\mathrm{phy})+f_\mathrm{nn}(T(\phi(k));\theta_\mathrm{nn})$$

where $\phi(k)$ collects state features (positions, velocities, etc.), $T$ extracts or composites relevant components, and $f_\mathrm{phy}$ encodes first-principles dynamics. Joint training with explicit regularization preserves the fidelity of the physics parameters while endowing the controller with nonlinear correction capacity (Bolderman et al., 2022, Bolderman et al., 2023).

Context-Selective State Space Models

Recent advances in sequence modeling, such as the COFFEE architecture, parameterize state-update gating by accumulated state rather than just input, yielding time-varying SSMs where selectivity is expressed as a function of the prior state vector:

$$\Delta_t^{(i)} = \sigma(w_D^{(i)} \odot s_{t-1}^{(i)})$$

This gating modulates the recurrent linear operator, enabling history-dependent adaptation while preserving parallel feedforward solvability (Zattra et al., 15 Oct 2025).

Semantic-Aware State-Space Models in Multiview Vision

For robust feedforward 3D reconstruction under degrading conditions, multi-view features and compact degradation codes are input to semantic-aware state-space modules. These modules aggregate features across both spatial and view axes, with parameters adaptively modulated by degradation embeddings, and tokens reordered based on semantic clustering (Wu et al., 5 Aug 2025).

3. Training, Optimization, and Stability

All state-aware feedforward models share crucial software and hardware advantages:

• Back-propagation-only training: No need for back-propagation through time (BPTT); the explicit state summarization, whether via memory blocks, observer outputs, or state-space stacking, is deterministic with bounded dependency on prior inputs, permitting trivially parallel backward passes.
• Efficient matrix operations: In FSMNs, the contextual summation—expressed as banded matrix multiplication—maps naturally to highly optimized GPU kernels (Zhang et al., 2015).
• Stability properties: State-aware controllers (e.g., PGNNs) can be guaranteed input-to-state stable (ISS) under sufficient Lipschitz and structural constraints. Regularized joint identification and Lipschitz-based matrix inequalities (see Equation 4 in (Bolderman et al., 2023)) play a critical role in ensuring real-world robustness.
• Parameter efficiency: Structured observer–controller models reduce parameter count by decomposing estimation and control, leading to reduced search spaces and more interpretable learned policies (Zhang et al., 2023). COFFEE and related context-selective SSMs dramatically reduce gating parameter overhead without sacrificing expressivity (Zattra et al., 15 Oct 2025).

4. Key Applications and Empirical Outcomes

State-aware feedforward models are empirically validated across domains:

• Speech and language modeling: FSMNs (in both scalar and vectorized/bidirectional forms) achieve WER and PPL superior or comparable to LSTM/BLSTM while requiring far less training time (per-epoch training for bidirectional vFSMN on Switchboard: 7.1 h/epoch vs. 22.6 for BLSTM) (Zhang et al., 2015).
• Reinforcement learning and control: Structured observer-chain policies converge 5–10× faster and exhibit superior disturbance rejection compared to unstructured RNN baselines. In nonlinear tank cascade control, disturbance-dedicated feedforward structure achieves rapid disturbance settling with minimal overshoot (Zhang et al., 2023).
• Precision feedforward motion control: PGNN-based controllers reduce tracking MAE by more than 2× compared to physics-only baselines, with superior extrapolation and guaranteed ISS (Bolderman et al., 2022, Bolderman et al., 2023).
• Photonic quantum state engineering: State-aware feedforward tuning of optical elements (e.g., beam-splitter transmission) as a function of previous measurement outcomes yields a provable increase in conversion probability for target Fock states, outperforming any non-adaptive protocol (Švarc et al., 2020).
• Long-context visual scene understanding: In 3DGS, semantic-aware feedforward enhancement modules recover robust reconstructions under severe degradations without requiring retraining of the main backbone (Wu et al., 5 Aug 2025).
• Sequence learning: State-feedback gating (COFFEE) delivers near-perfect accuracy with orders of magnitude fewer parameters and samples compared to previous gating paradigms, especially on synthetic induction and image tasks (Zattra et al., 15 Oct 2025).

5. Variants, Extensions, and Limitations

Architectural innovations extend core state-aware feedforward mechanisms:

• Attention-based FSMNs: Substituting fixed taps with contextually learned weights, further increasing temporal flexibility (Zhang et al., 2015).
• Parallel observer-chains and structured policy heads: Used in nonlinear or partially observable environments, allowing decoupling and specialization of estimation and control (Zhang et al., 2023).
• Analytical and gradient-based inversion for feedforward control: Analytical inversion leverages invertible physics terms for latency minimization, while gradient-based numerical inversion generalizes to more complex or non-invertible settings (Bolderman et al., 2022).
• Semantic-guided token routing in state-space models: Enables robust cross-view information propagation in vision under challenging conditions (Wu et al., 5 Aug 2025).

Principal limitations are:

• Fixed memory horizon: FSMN's fixed FIR order bounds effective history length, whereas RNNs possess infinite impulse response capacity. However, high-order FIR can approximate stable IIR arbitrarily well (Zhang et al., 2015).
• State representation quality: The practical effectiveness of state-aware variants relies on the sufficiency of the state summarization mechanism (e.g., observer RNN, degradation encoder); model misspecification can limit performance.
• Computation vs. latency trade-offs: Analytical inversion achieves minimal latency but only if the NN residual is suitably architected (Bolderman et al., 2022).

6. Design Guidelines and Practical Recommendations

Empirical and theoretical studies recommend the following:

• Maximal use of prior structure: Decompose observer, feedforward, and feedback pathways whenever possible, to reduce sample complexity and improve interpretability (Zhang et al., 2023).
• Regularization and parameterization discipline: Jointly train state-aware, physics-guided architectures with explicit regularization to preserve the fidelity and interpretability of physical layers while enabling robust nonlinear compensation (Bolderman et al., 2023).
• Parallelizable implementations: Prefer designs where feedforward computation is cast as parallel prefix or scan operations, exploiting modern hardware for speed and stability (FSMN, COFFEE) (Zhang et al., 2015, Zattra et al., 15 Oct 2025).
• Stateful context in gating and aggregation: Make the gating or selection operations sensitive to accumulated context or semantic cues (“state feedback gating”) to permit history-dependent adaptation beyond input-driven selection (Zattra et al., 15 Oct 2025, Wu et al., 5 Aug 2025).
• Plug-and-play enhancements: Isolate state-aware boosters (e.g., MV-SSEM) so robustness can be retrofitted into existing pipelines without disrupting primary system weights (Wu et al., 5 Aug 2025).

7. Cross-Domain Impact and Outlook

The state-aware feedforward paradigm provides a unifying abstraction for context-sensitive processing in acyclic architectures. It scales across perception, control, communication, quantum information, and sequence learning:

• Modeling long-term dependencies: Unifies FIR-based feedforward models (FSMN), context-selective SSMs (COFFEE), and semantic enhancement modules for efficient long-context integration.
• Control and robotics: Enables sample-efficient, interpretable, and robust trajectory or disturbance rejection using explicit separation of estimation, feedback, and feedforward paths—beneficial for real-time, safety-critical settings.
• Quantum systems engineering: Supports adaptive feedback policies in non-unitary state transformation protocols where classical feedforward control directly leverages measurement history (Švarc et al., 2020).
• Vision under non-idealities: Incorporates high-dimensional context summaries (e.g., degradation codes, semantic clusters) to condition enhancement or inference in the context of adverse real-world inputs (Wu et al., 5 Aug 2025).
• Theoretical convergence and stability: When deployed with proper regularization, guarantees of input-to-state stability are tractable, particularly for control systems modeled via PGNNs with bounded Lipschitz constants (Bolderman et al., 2023).

A plausible implication is continued cross-fertilization between control-theoretic approaches, neural sequence modeling, and structured vision pipelines, with state-aware feedforward models acting as a foundational building block for efficient, scalable, and interpretable context handling.