Audio Processing Graphs

• Audio processing graphs are defined as directed acyclic graphs that represent audio modules (e.g., EQs, compressors, reverb) and enable precise signal routing and parameter control.
• They support both differentiable and black-box computations, allowing end-to-end gradient optimization and robust plugin integration through advanced training strategies.
• Graph topology search and pruning techniques efficiently reduce processor count while maintaining high-quality audio mixes, as evidenced by substantial speedups and minimal perceptual loss.

Audio processing graphs provide a rigorous, modular framework for representing, optimizing, and modeling the complex signal flows characteristic of modern sound engineering and machine listening. In contemporary research, these graphs underpin domains ranging from differentiable mixing console search, black-box plugin automation, and DAW-driven data synthesis to harmonic feature extraction, signal compression, and audio-visual reasoning. The graph abstraction, typically as a directed acyclic graph (DAG), enables precise formalization of signal routing, parameterization, differentiable computation, and data-driven inference. This article surveys the definitions, computational methodologies, core representations, optimization strategies, and applications of audio processing graphs, synthesizing methodologies and metrics from leading research efforts.

1. Formal Definitions and Core Structure

Audio processing graphs are typically formalized as directed acyclic graphs $G = (V, E)$, where each node $v_i \in V$ represents either an audio processing block (e.g., equalizer, compressor, reverb, noise gate, delay, stereo imager, gain/pan) or an auxiliary operation (input, mix/sum, subgrouping, output). Edges $E$ represent unidirectional signal flow between nodes, including channel-specific routing or sidechain connections (Lee et al., 2024, Yang et al., 14 Jul 2025, Lee et al., 2023, Braun, 2021).

Each processor node $v_i$ is associated with a real-valued parameter vector $p_i \in \mathbb{R}^{d_i}$ and a “dry/wet” scalar weight $w_i \in [0, 1]$, controlling the blend between the processed (wet) and bypassed (dry) signal: $y_i = w_i\,f_i(u_i;\,p_i) + (1-w_i)\,u_i$ where $u_i$ is the node input, typically the sum of predecessor outputs. Auxiliary nodes enable topological operations such as multitrack input, mixing (subgroup aggregation), and global summation for mixdown (Lee et al., 2024, Lee et al., 19 Sep 2025).

For time–frequency representations, graph structures also appear in the construction of transform bases (e.g., spectral visibility graphs (Yela et al., 2019), graph-based transforms for compression (Farzaneh et al., 2019)) and in the representation of analysis-synthesis pipelines (Wedekind et al., 2019).

2. Differentiable and Black-box Graph Computation

There is a divergence between fully differentiable architectures and black-box plugin systems:

• Differentiable Audio Graphs: All processor implementations are differentiable (e.g., FIR-based EQs, IIR compressor envelopes, STFT-based reverbs, etc.), supporting end-to-end gradient-based optimization. The node outputs form a global computational graph, enabling joint optimization over parameters and structure by backpropagation (Lee et al., 2024, Lee et al., 19 Sep 2025, Lee et al., 2024).
• Black-box/Plugin Frameworks: Third-party plugin layers are treated as stateful, non-differentiable black boxes. Training with such graphs requires stochastic gradient estimators (e.g., simultaneous perturbation stochastic approximation, SPSA), employing parallel evaluations of plugins under varying parameterizations to estimate gradients for upstream controller networks (Ramírez et al., 2021).

Batch processing and hardware acceleration are central for scalability. Modern implementations (e.g., GRAFX) exploit source-level, node-level, and graph-level batching, partitioning nodes by type and dependency order. This yields substantial speedups (6×–8× on typical GPU hardware) compared to single-node sequential evaluation (Lee et al., 2024).

3. Graph Topology Search and Pruning Algorithms

Graph topology is typically overparameterized at initialization (all processor types per track and subgroup), and pruned using explicit audio similarity constraints:

1. Overcomplete Console Initialization: A canonical sequence of processors is applied to all dry inputs and subgroups, producing a full mixing console [Eq→Comp→Gate→Imager→Gain/Pan→Delay→Reverb].
2. Parameter Optimization: The full graph is trained to match a reference mix under an objective combining multi-resolution spectral loss ($L_a$), gain staging penalties ($L_g$), and an $L_1$ dry/wet sparsity term ($L_p$):

$$L(P, w) = L_a(\hat y, y) + \alpha_g L_g(P) + \alpha_p L_p(w)$$

1. Structured Pruning: Nodes (processors) are pruned if their removal does not increase the loss by more than a small tolerance $\tau$. Strategies include brute-force single-node, dry/wet-guided ranking (removal by small $w_i$), and hybrid alternation (Lee et al., 2024, Lee et al., 19 Sep 2025).
2. Alternating Prune and Fine-tune: After each accepted prune, the remaining graph undergoes short fine-tuning to recover any performance loss. This process is iterated until convergence (no further acceptable prunes), yielding a sparse, task-specific graph (Lee et al., 2024, Lee et al., 19 Sep 2025).

This strategy is effective for real-world multitrack mixes: empirical results indicate ≈67% of processors can be eliminated (final ≈2.3 processors/chain), while maintaining Δloss ≈ 0.013 in MRSTFT metric and perceptual quality (MUSHRA tests) within <1 MUSHRA point of unpruned graphs (Lee et al., 2024). Similar findings are corroborated in complementary studies focused on efficient GPU batched graph evaluation (Lee et al., 2024).

4. Dataset Generation, Inference, and Neural Graph Prediction

Large-scale, labeled datasets of audio processing graphs and corresponding rendered audio are critical for learning-based inference. Two dominant approaches have emerged:

• Synthetic Differentiable Pipelines: Entire graph/parameter search is performed over differentiable consoles with open implementations; pruning yields ground-truth (sparse) graph-labels for supervised graph neural network (GNN) or transformer-based models. Downstream systems are trained to predict either processor selection (which blocks to keep), parameter values (EQ bands, compressor thresholds, etc.), or both, from dry-input features. End-to-end audio loss or parameter regression losses enable joint training (Lee et al., 2024, Lee et al., 19 Sep 2025, Lee et al., 2023).
• DAW-Driven, Plugin-Powered Data Pipelines: Platforms such as WildFX (Yang et al., 14 Jul 2025) use real DAWs (e.g., REAPER via Docker, Wine, yabridge), scripting APIs (reapy), and rapid layer-based scheduling to record audio outputs and extract full graphs involving arbitrary commercial plugins (VST/VST3/CLAP/LV2). Graphs include edge attributes (e.g., main vs. sidechain, splitters) and full parameter domain metadata (YAML/JSON schema). Autoencoding/decoding neural models achieve competitive edge and node error rates on blind-graph estimation from mixed audio (Yang et al., 14 Jul 2025).

Such datasets support not only direct parameter regression and topology recovery but also enable research into architecture search, meta-learning, and protocol translation between differentiable and plugin-based DSP ecosystems (Yang et al., 14 Jul 2025, Lee et al., 2023).

5. Graph-Based Feature Representations in Audio Analysis

Beyond signal-routing DAGs, audio processing graphs have been utilized in the extraction of robust audio features and improved transform coding:

• Spectral Visibility Graphs: The spectral visibility graph (SVG) transforms each spectral frame into a graph whose node degrees capture harmonic structure while being invariant to vertical (broadband noise) shifts, enabling improved similarity search and cover detection under noise (Yela et al., 2019). These graph-derived features yield up to ≈50% relative improvement in mean reciprocal rank (MRR) in noisy harmonic matching over magnitude spectra.
• Graph-Based Transforms for Compression: Interpreting each audio frame as a graph, where nodes are samples and edges connect first or second neighbors, the eigenbasis of the Laplacian enables sparsity-promoting transforms exceeding classic DCT/WHT in PSNR and ERP at comparable compression ratios. Tables from (Farzaneh et al., 2019) show that GT-I achieves PSNR ≈42.6 dB at CR 2:1 and ERP ≈99.4%, outperforming fast Walsh-Hadamard by large margins.

These methods quantitatively demonstrate the value of graph-based descriptors and transforms in audio, distinct from signal-routing graphs used in mixing/modeling (Yela et al., 2019, Farzaneh et al., 2019).

6. Integration with Machine Learning and GNNs

Audio processing graphs intersect with graph neural networks both as (a) inputs—encoding either graph-structured audio features or signal paths for end-to-end learning—and (b) outputs, where the aim is graph topology or parameter recovery:

• Neural networks are trained to map input features to processor selection masks, graph edges, and parameterizations, either directly in the feature domain or using autoregressive tokenized graph decoders (Lee et al., 2024, Lee et al., 2023).
• Dense graph representations (e.g., GRAFXTensor format) enable batched GNN ingestion and parallel evaluation, facilitating gradient-based learning over large-scale graph datasets (Lee et al., 2024).
• Applications extend beyond mixing to include scene-graph-driven audio-visual source separation, where node/edge attributes and adjacency quantify both semantic and spatial relationships, processed via graph attention and edge-conv layers (Chatterjee et al., 2022).

A plausible implication is an emerging convergence: audio processing graphs provide a scalable, interpretable interface between rule-based DSP, modern ML, and applied AI for sound.

7. Metrics, Benchmarks, and Practical Considerations

Comprehensive evaluation combines objective and subjective measures:

• Losses: Multi-resolution STFT (MRSTFT), gain-staging penalties, $L_1$ sparsity, multi-scale spectral loss (MSS), cosine/MFCC distance.
• Metrics: Mean reciprocal rank (MRR) for similarity, node/edge error rates for topology recovery, invalid-graph rate, node-type intersection-over-union (IoU), perceptual scores (MUSHRA panel).
• Performance: Speedups via batched and schedule-optimized execution (6–8×) (Lee et al., 2024), parallel DAW rendering (WildFX: 12–15 s/project on 64-core servers (Yang et al., 14 Jul 2025)).
• Perceptual integrity: Experiments show that aggressive pruning (≈2/3 processors removed, $\tau \leq 0.01$) yields mixes subjectively indistinguishable from reference consoles, while maintaining low MRSTFT and consistent MIR features (Lee et al., 2024, Lee et al., 19 Sep 2025).

A plausible implication is that, with careful design, audio processing graphs support both industrial-scale data generation and fine-grained interpretability with negligible quality loss.

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In summary, audio processing graphs offer a principled, scalable model for representing, optimizing, and learning complex audio workflows. They underpin practical mixing-console automation, plugin-driven dataset generation, feature extraction, transform coding, and the development of interpretable end-to-end machine learning architectures for audio. The formal abstraction of audio as a DAG of parameterized processors, equipped with advanced optimization and learning methods, constitutes a foundational paradigm for modern computational auditory signal processing and music engineering (Lee et al., 2024, Lee et al., 19 Sep 2025, Lee et al., 2024, Yang et al., 14 Jul 2025, Lee et al., 2023, Chatterjee et al., 2022, Yela et al., 2019, Farzaneh et al., 2019, Braun, 2021, Ramírez et al., 2021).