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Contextual Feedback Loops: Amplifying Deep Reasoning with Iterative Top-Down Feedback

Jacob Fein-Ashley, Rajgopal Kannan, Viktor Prasanna

TL;DR

Contextual Feedback Loops (CFLs) introduce a lightweight top-down feedback mechanism that re-injects a compact context vector, derived from the network's own output, into earlier layers to iteratively refine representations. The approach unifies feed-forward inference with multi-step feedback via per-layer adapters and a low-rank projector, achieving accuracy gains on ImageNet-1k, PG-19 language modeling, and Long Range Arena with modest overhead, and is theoretically grounded under contractive assumptions via Banach's fixed-point theorem. A single refinement ($T=1$) offers the best accuracy/efficiency trade-off across domains, while deeper unrolling provides diminishing returns, suggesting CFL as a scalable, broadly applicable mechanism for context-aware deep learning.

Abstract

Conventional deep networks rely on one-way backpropagation that overlooks reconciling high-level predictions with lower-level representations. We propose \emph{Contextual Feedback Loops} (CFLs), a lightweight mechanism that re-injects top-down context into earlier layers for iterative refinement. Concretely, CFLs map the network's prediction to a compact \emph{context vector}, which is fused back into each layer via gating adapters. Unrolled over multiple feedback steps, CFLs unify feed-forward and feedback-driven inference, letting top-level outputs continually refine lower-level features. Despite minimal overhead, CFLs yield consistent gains on tasks including CIFAR-10, ImageNet-1k, SpeechCommands, and GLUE SST-2. Moreover, by a Banach Fixed Point argument under mild Lipschitz conditions, these updates converge stably. Overall, CFLs show that even modest top-down feedback can substantially improve deep models, aligning with cognitive theories of iterative perception.

Contextual Feedback Loops: Amplifying Deep Reasoning with Iterative Top-Down Feedback

TL;DR

Contextual Feedback Loops (CFLs) introduce a lightweight top-down feedback mechanism that re-injects a compact context vector, derived from the network's own output, into earlier layers to iteratively refine representations. The approach unifies feed-forward inference with multi-step feedback via per-layer adapters and a low-rank projector, achieving accuracy gains on ImageNet-1k, PG-19 language modeling, and Long Range Arena with modest overhead, and is theoretically grounded under contractive assumptions via Banach's fixed-point theorem. A single refinement () offers the best accuracy/efficiency trade-off across domains, while deeper unrolling provides diminishing returns, suggesting CFL as a scalable, broadly applicable mechanism for context-aware deep learning.

Abstract

Conventional deep networks rely on one-way backpropagation that overlooks reconciling high-level predictions with lower-level representations. We propose \emph{Contextual Feedback Loops} (CFLs), a lightweight mechanism that re-injects top-down context into earlier layers for iterative refinement. Concretely, CFLs map the network's prediction to a compact \emph{context vector}, which is fused back into each layer via gating adapters. Unrolled over multiple feedback steps, CFLs unify feed-forward and feedback-driven inference, letting top-level outputs continually refine lower-level features. Despite minimal overhead, CFLs yield consistent gains on tasks including CIFAR-10, ImageNet-1k, SpeechCommands, and GLUE SST-2. Moreover, by a Banach Fixed Point argument under mild Lipschitz conditions, these updates converge stably. Overall, CFLs show that even modest top-down feedback can substantially improve deep models, aligning with cognitive theories of iterative perception.

Paper Structure

This paper contains 55 sections, 1 theorem, 23 equations, 3 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Predictive Coding and Neurocognitive Insights.
  4. Recurrent and Feedback Connections in Deep Models.
  5. Iterative Inference and Refinement.
  6. Cognitive and Generative Feedback Mechanisms.
  7. Summary.
  8. Method: Contextual Feedback Loops (CFL)
  9. Base Network
  10. Feedback Pathway and Context Vector
  11. Iterative Refinement Procedure
  12. Low-Rank Projector
  13. Merging Feedback Adapters
  14. Shared Core and Per-Layer Bias.
  15. Low-Rank Merge Variant.
  16. ...and 40 more sections

Key Result

Theorem 1

Suppose each component function in $\Phi$ (i.e., each $\psi^{(l)}$, $g$, and $f^{(L+1)}$) is Lipschitz continuous and that their combined Lipschitz constants (when composed) can be made strictly less than 1. Formally, assume there exists a norm $\|\cdot\|$ and a constant $L < 1$ such that Then the sequence $\mathbf{S}_{\tau+1} = \Phi(\mathbf{S}_\tau)$ converges to a unique fixed point $\mathbf{S}

Figures (3)

  • Figure 1: Iterative Refinement Visualization. Attention maps at refinement steps ($T=0$ to $T=3$) clearly illustrate how CFLs progressively focus attention on critical features, thereby enhancing alignment between internal representations and input signals.
  • Figure 2: Overview of the CFL Framework. The network first runs a forward pass from input $\mathbf{x}$ through layers $f^{(1)}\to f^{(L)}$, then $f^{(L+1)}$ produces an initial output $\mathbf{y}^{(0)}$. In the top--down pathway (dotted box), $\mathbf{y}^{(\tau)}$ is mapped via $g(\cdot)$ to a compact context vector $\mathbf{z}^{(\tau)}$, which is injected back into each layer through feedback adapters$\psi^{(l)}$. These adapters refine hidden states $\mathbf{h}^{(l)}_{\tau+1}$ by combining local activations with global context. After $T$ refinements, the model outputs $\mathbf{y}^{(T)}$.
  • Figure 3: End-to-end latency of ViT and CFL-ViT at different model scales. Measurements were taken on an NVIDIA A100 (batch size $8$, mixed precision). Moving from $T{=}0$ (standard ViT) to $T{=}1$ leaves latency essentially unchanged, while deeper unrolling incurs an approximately constant multiple per extra iteration.

Theorems & Definitions (2)

  • Theorem 1: Contractive Convergence of CFL
  • proof : Proof