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SymKL: A Unified Representation-Space Measure of Signal Degradation

Dhananjaya Jayasundara, Sudarshan Rajagopalan, Vishal M. Patel

arXiv:2610.39403v1cs.CVcs.AI

TL;DR

Existing full-reference degradation measures rely on modality-specific representations and criteria. SymKL compares a pristine reference and degraded signal through the Fisher information of a shared implicit neural representation; experiments show it tracks degradation across images, audio, and 3D signals, including regimes where conventional measures become less informative.

  • Problem

    Existing degradation measures use modality-specific representations and similarity criteria, limiting a unified approach across signal modalities.

    Source: Introduction · p. 1

  • Method

    SymKL compares reference and degraded signals using a common Fisher representation derived from a frozen implicit neural representation.

    Source: Introduction · p. 2, Conclusion · p. 7

  • Results

    Across images, audio, and 3D signals, SymKL tracks degradation severity and remains discriminative where conventional measures become less informative.

    Source: Introduction · p. 2, Conclusion · p. 7

  • Takeaways & Limitations

    SymKL applies unchanged across modalities and extends full-reference degradation measurement to signals without established measures.

    Source: Conclusion · p. 7

    SymKL is not a perceptual quality metric and does not aim to approximate human visual or auditory judgments.

    Source: Introduction · p. 2

Abstract

from arXiv · show

Quantifying degradation between a pristine signal and its degraded observation is fundamental to signal processing, yet existing full-reference measures are inherently modality-specific. We introduce SymKL, a unified full-reference degradation measure based on implicit neural representations (INRs). An INR is fitted once to the pristine reference and characterized by its diagonal Fisher information, which captures the local information geometry of the learned representation. Evaluating the Fisher information with the pristine reference and a degraded observation yields two parameter-sensitivity profiles whose symmetric KL divergence defines the degradation score. The proposed formulation requires only the reference and degraded observation, without knowledge of the corruption process or degradation severity, making it applicable across images, audio, and 3D data. We further derive an exact closed-form expression for the diagonal Fisher of SIREN, enabling efficient computation. Experiments on image, speech, and volumetric 3D benchmarks demonstrate that SymKL accurately tracks degradation severity, remains monotonic where conventional metrics saturate or fail, and provides a unified modality-agnostic measure of signal degradation. Code will be made publicly available after the review process.

Introduction

Existing degradation measures use modality-specific representations and can lose sensitivity as distortion grows. SymKL uses a frozen INR’s Fisher information to compare pristine and degraded signals, with efficient SIREN computation and evaluation across modalities.

Introduction

  • Across modalities, established measures use different representations and criteria, and some become less informative as degradation increases.On KADID-10k, a fivefold increase in displaced patches changes CLIP similarity by less than 1%, from 0.998 to 0.990, despite substantially greater visual distortion.Source: Introduction · pp. 1–2
  • A reference INR is fitted once and frozen; Fisher profiles evaluated on pristine and degraded observations define the representation-space discrepancy.The Fisher is used because mean gradients vanish near a fitted solution, while the Hessian can be computationally prohibitive.Source: Introduction · p. 2
  • An exact closed-form diagonal Fisher for SIREN reduces computation to efficient matrix operations, while a hypernetwork with first-order MAML rapidly produces accurate reference representations.The amortized framework uses only a small number of optimization steps.Source: Introduction · p. 2
  • A physically grounded protocol compares measures against continuously varying distortion severity; experiments across images, audio, occupancy fields, and medical imaging find SymKL tracks severity and remains discriminative where conventional measures become less informative.The paper also reports that SymKL substantially outperforms alternative weight-space characterizations.Source: Introduction · p. 2
  • SymKL is not a perceptual quality metric; it measures how degradation alters a learned representation and applies where perceptual judgments are ill-defined, unavailable, or not the primary objective.The stated examples include volumetric representations, occupancy fields, medical imaging, and scientific measurements.Source: Introduction · p. 2
  • SymKL characterizes degradation through changes in parameter sensitivities rather than observation-space discrepancies, using a shared INR representation.The paper presents this as a modality-agnostic measure based on INR information geometry.Source: Introduction · p. 2

Method

SymKL fits and freezes a reference INR, then compares its parameter-sensitivity profiles for pristine and degraded signals using symmetric KL divergence. The method includes amortized reference fitting for images, exact diagonal Fisher computation for SIREN, and a physically grounded protocol for evaluating metric sensitivity.

Preliminaries: signals as coordinate networks

  • Signals across images, waveforms, and volumes are represented as coordinate-to-value functions using SIREN networks, with modality-dependent frequency scales but an unchanged degradation measure.The signal dimensions and channels cover images, waveforms, and occupancy or signed-distance volumes.Source: Preliminaries: signals as coordinate… · p. 2

Amortized reference fitting for images

  • For images, a hypernetwork predicts target SIREN parameters from the reference, providing an initialization that reduces the optimization needed to fit its representation.It is pretrained on MS-COCO and LSDIR, then fine-tuned with first-order MAML so predictions can adapt in a small number of reconstruction steps.Source: Amortized reference fitting for images · pp. 2–3

Fisher profiles of a frozen representation

  • The reference INR is frozen, and diagonal empirical Fisher profiles measure the average squared sensitivity of its parameters to the pristine or degraded signal.Squared gradients preserve coordinate-wise contributions that can cancel in the mean gradient.Source: Fisher profiles of a frozen… · p. 3

The degradation measure

  • SymKL compares the reference and degraded signals’ Fisher profiles with a symmetric KL divergence, producing a nonnegative score that is zero only when the profiles match.Larger values indicate greater reorganization of the parameter-sensitivity structure, and the formulation applies unchanged across modalities.Source: The degradation measure · p. 4

Exact closed-form Fisher for SIREN

  • For SIREN, the diagonal Fisher can be computed exactly with one forward pass, one backward pass, and one matrix multiplication per layer, avoiding per-coordinate parameter gradients.This factorization makes an otherwise memory- and time-intensive computation practical.Source: Exact closed-form Fisher for SIREN · p. 4

Physically grounded sensitivity protocol

  • The evaluation protocol compares metrics by relative score change per relative change in physical distortion, after mapping metrics to nonnegative ratio-scale degradation values.It excludes steps near zero degradation and evaluates non-monotonic distortion sequences as separate monotonic branches.Source: Physically grounded sensitivity protocol · p. 4

Experiments

Across image, occupancy-field, and audio benchmarks, SymKL responds strongly to increasing degradation. It is monotonic on the tested image sequences and remains well separated across progressively degraded occupancy fields, while showing the highest relative sensitivity across tested audio degradations.

Experiments

  • The evaluation compares SymKL with modality-specific measures on RGB images, occupancy fields, audio, and medical imaging.The supplied results describe image, occupancy-field, and audio comparisons; medical-imaging experiments are reported in supplementary material.Source: Experiments · p. 4

Images

  • For the image weight-space comparison, Fisher cosine measures cosine distance between reference and degraded Fisher profiles, whereas Fisher relative ℓ2 also captures changes in their overall magnitude.The other tested alternatives use mean-gradient vectors or first-step Adam updates from the same frozen reference parameters.Source: Images · p. 5
  • SymKL has the highest relative sensitivity across representative KADID-10k distortions, outperforming image-domain and frozen-INR weight-space baselines.The comparison uses mean relative sensitivity, with higher values indicating better performance.Source: Images · p. 5, Table 1 · p. 6
  • On color-block and quantization sequences, SymKL increases monotonically while several image-quality metrics respond non-monotonically.The sequences increase degradation through more color blocks and fewer quantization levels.Source: Images · p. 5, Table 2 · p. 6, Figure 3 · p. 6

Occupancy Fields

  • Across Gaussian blur, erosion, and resolution reduction, SymKL has the highest sensitivity among the tested occupancy-field metrics.The comparison includes Chamfer distance, F-score, and volumetric IoU.Source: Occupancy Fields · p. 5, Figure 4 · p. 7
  • Under increasing occupancy-field downsampling, all metrics preserve degradation ordering, but conventional metrics attenuate while SymKL maintains clear separation between levels.The accompanying figure shows fine geometric details disappearing while overall structure is preserved.Source: Occupancy Fields · p. 5, Table 3 · p. 7, Figure 5 · p. 7

Audio

  • Across six audio degradation types, SymKL has the highest sensitivity, with the largest gains for spectral notching, clipping, and µ-law companding.It also attains the highest sensitivity for additive Gaussian noise, sample dropout, and high-pass filtering.Source: Audio · pp. 6–7

Additional Results

Supplementary material broadens the evaluation with additional quantitative comparisons, extended visualizations, and medical-imaging experiments.

Additional Results

  • Supplementary material adds quantitative comparisons, extended qualitative visualizations, and experiments on medical imaging datasets.These materials broaden the evaluation across signal modalities.Source: Additional Results · p. 7

Conclusion

SymKL measures degradation by comparing the Fisher information profiles of a pristine signal and its degraded observation through a frozen INR. Across images, audio, and 3D occupancy fields, it tracks degradation severity even where conventional measures saturate or lose monotonicity.

Conclusion

  • SymKL compares pristine and degraded signals through a common Fisher representation derived from a frozen INR, rather than modality-specific representations.The measure depends on the reference representation and reconstruction objective, not the corruption process or its severity.Source: Conclusion · p. 7
  • Across images, audio, and 3D occupancy fields, SymKL tracks degradation severity while remaining monotonic and discriminative where conventional measures saturate or violate monotonicity.The framework also naturally extends to signals without an established full-reference measure.Source: Conclusion · p. 7
  • An exact closed-form expression for the diagonal Fisher of SIREN enables efficient computation of SymKL.The paper suggests learned representations' information geometry as a substrate for signal analysis across modalities.Source: Conclusion · p. 7

Related Works

The related work positions SymKL as using an INR to analyze degradation, rather than reconstruct signals, learn embeddings, or compare tasks. It also describes an approach to efficient INR fitting using a hypernetwork and meta-learning.

Implicit neural representations

  • Unlike prior INR work focused on reconstruction, compression, or downstream tasks, this paper analyzes the learned INR as a shared substrate for cross-modal degradation measurement.INRs model signals as continuous functions mapping spatial or temporal coordinates to signal values.Source: Related Works · p. 10

Learning in the weight space of neural representations

  • Unlike weight-space methods that learn embeddings for tasks such as classification or retrieval, SymKL uses one reference INR's Fisher profile to measure degradation.The cited examples include Functa [Dupont et al. 2022a] and inr2vec [De Luigi et al. 2023].Source: Related Works · p. 10

Fisher information as a descriptor of neural representations

  • Unlike Task2Vec, which compares tasks using Fisher vectors from an adapted probe network, this work compares pristine and degraded evaluations of a fixed INR.The network parameters remain unchanged; the target signal used for evaluation changes the Fisher profiles.Source: Related Works · p. 10
  • An exact closed-form diagonal Fisher for SIREN eliminates expensive per-sample gradient computations required by conventional Fisher estimation.The paper applies parameter sensitivity within a single signal rather than comparing datasets or learning tasks.Source: Related Works · p. 10

Efficient INR fitting

  • A DINOv2-conditioned hypernetwork predicts SIREN weights, and first-order MAML meta-training makes them high-quality initializations for test-time refinement.This combines hypernetwork prediction with meta-learning to address the cost of independently fitting an INR for each signal.Source: Related Works · p. 10

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