Execution-Grounded Training Signals

• Execution-Grounded Training Signals are defined as feedback directly derived from execution traces, enabling immediate local parameter updates.
• They utilize methodologies such as DRTP and IPA-GNN to couple training with real execution outcomes, improving hardware efficiency and systematic generalization.
• These signals offer tradeoffs like reduced memory overhead and bypass of update locking, while sometimes incurring a slight accuracy drop compared to full backpropagation.

Execution-grounded training signals are forms of supervision or feedback derived from real-time interaction, direct action outcomes, or actual execution traces within a learning system. These approaches diverge from traditional training paradigms by coupling model updates to the observable effects of execution—whether in neural networks, reinforcement learning agents, code synthesis models, or interactive systems. Execution grounding enables immediate and often local update mechanisms, improves hardware efficiency, and can contribute to systematic generalization across modalities and tasks.

1. Fundamental Principles and Definitions

Execution-grounded training signals are defined by the property that parameter updates are driven by feedback emergent at the point of execution, rather than by backpropagated gradients or post hoc global error signals. This feedback may be derived from target projections, observed action outcomes, code execution traces, system-level reward decoding, or runtime state transitions. Paradigmatic examples encompass:

• DRTP: Direct random target projection signals for layerwise feedforward updates utilizing the target label as the "error sign" (Frenkel et al., 2019).
• IPA-GNN: Soft attention over the control-flow graph to dynamically route execution signals during program interpretation (Bieber et al., 2020).
• IGL: Decoding latent reward signals from multidimensional feedback vectors in interactive agents (Xie et al., 2021).
• Execution-based reward assignment: Training agents with supervision coupled to observable success within an executable environment (Zhuo et al., 25 Aug 2025).
• Execution-guided code synthesis: Code generation using runtime trace feedback to steer candidate completions (Lavon et al., 12 Jun 2025).

Key mathematical objects include locally constructed modulatory signals, dynamic projections (with random or adapted matrices), and proxy objectives that tie decoded feedback to policy improvement (see the objective $\mathcal{L}(\pi,\psi)$ in (Xie et al., 2021)).

2. Algorithmic Frameworks and Mathematical Formulation

A prominent realization is in DRTP, wherein each hidden layer receives a training signal formed by a fixed random matrix $B_k$ acting on the one-hot label vector $y^*$. The updates are immediate and local:

$$W_k \leftarrow W_k + \eta \Big( \left(B_k^T y^*\right) \odot f_k'(z_k) \Big) y_{k-1}^T$$

$$b_k \leftarrow b_k + \eta \Big( \left(B_k^T y^*\right) \odot f_k'(z_k) \Big)$$

This construction eliminates dependence on symmetric weights and deferred updates, yielding highly hardware-efficient learning suitable for edge applications. The algorithm proceeds strictly in the feedforward direction.

In execution-guided code generation (EG-CFG (Lavon et al., 12 Jun 2025)), the model samples beam candidates for code continuation, executes those candidates against test cases, and integrates execution traces into the next-token prediction via classifier-free guidance:

$$\log M_{\mathrm{CFG}}(w_i \mid p_{\mathrm{sol}}, p_{\mathrm{dyn}}) = \log M(w_i \mid p_{\mathrm{sol}}) + \gamma \left(\log M(w_i \mid p_{\mathrm{dyn}}) - \log M(w_i \mid p_{\mathrm{sol}})\right)$$

A range of modalities—including plan generation with segmentation mask grounding (Gondola (Chen et al., 12 Jun 2025)), and agent reward learning from executable trajectory validation (CTF-Dojo (Zhuo et al., 25 Aug 2025))—further demonstrate that execution-grounded signals are agnostic to input type, supporting text, code, vision, and action domains.

3. Biological and Hardware Motivation

Execution-grounded training rules often address biological and hardware constraints ignored by canonical backpropagation. Standard BP suffers from:

• Weight transport: The need for symmetric weights in forward and backward passes.
• Update locking: The requirement to store intermediate activations until a backward pass completes.
• High memory bandwidth and buffering overhead.

DRTP replaces the backward path entirely; fixed random feedback projections allow immediate local updates post-forward computation. This yields strong gains in energy and area efficiency, especially in hardware-constrained environments:

Feature	Backpropagation	DRTP
Symmetry required	Yes	No
Local updates	No	Yes
Memory overhead	High	Low

In biological modeling (see (Hanut et al., 27 Feb 2025)), low-dimensional feedback signals exhibit greater plausibility; learning is driven by compressed task-relevant channels, matching the dimensionality of biological output spaces.

4. Generalization and Systematic Transfer

Execution-grounded training signals often confer enhanced generalization. IPA-GNN (Bieber et al., 2020) demonstrates that tying model updates to execution steps along the control flow enables transfer to programs with greater complexity than seen during training. The architecture’s attentional mechanism guides branch decisions dynamically, allowing systematic short-circuiting (e.g., ignoring redundant loop bodies):

• On full program execution tasks, IPA-GNN achieves 62.1% accuracy vs. 32.0% for line-by-line RNNs.
• In length generalization, baseline performance drops but execution-grounded models maintain robust accuracy.

Compositional lexicon learning with executable semantic programs (G2L2 (Mao et al., 2022)) similarly illustrates that explicitly grounded signals can drive generalization in visual reasoning (CLEVR) and language navigation (SCAN), outperforming end-to-end neural methods and supporting transparent interpretation of learned concepts.

5. Tradeoffs and Limitations

The precision of execution-grounded feedback varies by algorithm. Methods relying only on target projections (DRTP) experience a modest accuracy degradation compared to full error backpropagation, due to loss of magnitude information. However, this cost is offset by hardware benefits and resilience to noisy or partial observability.

In reinforcement learning with hybrid communication (MARO (Santos et al., 2022)), agents trained with robust predictive models handle missing information gracefully; execution-grounded loss terms ensure controllers generalize to variable operational conditions, but accuracy may plateau at sub-optimal levels when the execution signal’s informativeness is low.

6. Applications and Extensions

Execution-grounded training signals have found applications across numerous domains:

• Hardware-efficient neural learning for adaptive sensors and edge devices (Frenkel et al., 2019).
• Robust program execution modeling for static analysis, program synthesis, and code reasoning (Bieber et al., 2020, Jung et al., 12 Jun 2025, Lavon et al., 12 Jun 2025).
• Continual instruction generation in collaborative agent–human settings, with reward decoded from follow-on execution (Kojima et al., 2021).
• Robotic planning with multi-view visual grounding in long-horizon manipulation tasks (Chen et al., 12 Jun 2025).
• Cybersecurity and vulnerability discovery in interactive containerized environments (CTF-Dojo), where only execution-validated trajectories are used for model improvement (Zhuo et al., 25 Aug 2025).

A plausible implication is that execution-grounded signals will be increasingly adopted where real-time feedback, adaptability, and cross-modal generalization are required. Future work will likely integrate reinforcement learning with intermediate execution signals, further democratizing agent training in specialized domains.