# Interpreting intermediate convolutional layers of generative CNNs trained on waveforms

arXiv: https://arxiv.org/abs/2104.09489 · HTML: https://mlsanity.com/paper/2104.09489/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 65 references that are in the map.
- First posted on arXiv 19 Apr 2021.

## Builds on (most cited first, 30 of 31)

- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets](https://mlsanity.com/paper/1606.03657/) (2016)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Understanding the Role of Individual Units in a Deep Neural Network](https://mlsanity.com/paper/2009.05041/) (2020)
- [Adversarial Audio Synthesis](https://mlsanity.com/paper/1802.04208/) (2018)
- [Unsupervised speech representation learning using WaveNet autoencoders](https://mlsanity.com/paper/1901.08810/) (2019)
- [Vector-Quantized Autoregressive Predictive Coding](https://mlsanity.com/paper/2005.08392/) (2020)
- [Deep Voice 3: Scaling Text-to-Speech with Convolutional Sequence Learning](https://mlsanity.com/paper/1710.07654/) (2017)
- [Vector-quantized neural networks for acoustic unit discovery in the ZeroSpeech 2020 challenge](https://mlsanity.com/paper/2005.09409/) (2020)
- [On the Quantitative Analysis of Decoder-Based Generative Models](https://mlsanity.com/paper/1611.04273/) (2016)
- [The Zero Resource Speech Challenge 2020: Discovering discrete subword and word units](https://mlsanity.com/paper/2010.05967/) (2020)
- [Audio Word2Vec: Unsupervised Learning of Audio Segment Representations using Sequence-to-sequence Autoencoder](https://mlsanity.com/paper/1603.00982/) (2016)
- [Truly unsupervised acoustic word embeddings using weak top-down constraints in encoder-decoder models](https://mlsanity.com/paper/1811.00403/) (2018)
- [Interpretable Convolutional Filters with SincNet](https://mlsanity.com/paper/1811.09725/) (2018)
- [Unsupervised acoustic unit discovery for speech synthesis using discrete latent-variable neural networks](https://mlsanity.com/paper/1904.07556/) (2019)
- [Towards Visually Grounded Sub-Word Speech Unit Discovery](https://mlsanity.com/paper/1902.08213/) (2019)
- [CiwGAN and fiwGAN: Encoding information in acoustic data to model lexical learning with Generative Adversarial Networks](https://mlsanity.com/paper/2006.02951/) (2020)
- [Inductive biases, pretraining and fine-tuning jointly account for brain responses to speech](https://mlsanity.com/paper/2103.01032/) (2021)
- [Generative Adversarial Phonology: Modeling unsupervised phonetic and phonological learning with neural networks](https://mlsanity.com/paper/2006.03965/) (2020)
- [End-to-End Speech Recognition From the Raw Waveform](https://mlsanity.com/paper/1806.07098/) (2018)
- [Estimating Phoneme Class Conditional Probabilities from Raw Speech Signal using Convolutional Neural Networks](https://mlsanity.com/paper/1304.1018/) (2013)
- [Identity-Based Patterns in Deep Convolutional Networks: Generative Adversarial Phonology and Reduplication](https://mlsanity.com/paper/2009.06110/) (2020)
- [Unsupervised Acoustic Unit Representation Learning for Voice Conversion using WaveNet Auto-encoders](https://mlsanity.com/paper/2008.06892/) (2020)
- [Local and non-local dependency learning and emergence of rule-like representations in speech data by Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/2009.12711/) (2020)
- [Generalizing Outside the Training Set: When Can Neural Networks Learn Identity Effects?](https://mlsanity.com/paper/2005.04330/) (2020)
- [Visualizing Deep Neural Networks for Speech Recognition with Learned Topographic Filter Maps](https://mlsanity.com/paper/1912.04067/) (2019)

## Built on by (most cited first, 6 of 6)

- [Basic syntax from speech: Spontaneous concatenation in unsupervised deep neural networks](https://mlsanity.com/paper/2305.01626/) (2023)
- [Approaching an unknown communication system by latent space exploration and causal inference](https://mlsanity.com/paper/2303.10931/) (2023)
- [Exploring How Generative Adversarial Networks Learn Phonological Representations](https://mlsanity.com/paper/2305.12501/) (2023)
- [Unsupervised Learning and Representation of Mandarin Tonal Categories by a Generative CNN](https://mlsanity.com/paper/2509.17859/) (2025)
- [Deciphering Assamese Vowel Harmony with Featural InfoWaveGAN](https://mlsanity.com/paper/2407.06547/) (2024)
- [Structural Bottlenecks on Frequency Representation in End-to-End Audio Models](https://mlsanity.com/paper/2607.08545/) (2026)

## Abstract (arXiv)

This paper presents a technique to interpret and visualize intermediate layers in generative CNNs trained on raw speech data in an unsupervised manner. We argue that averaging over feature maps after ReLU activation in each transpose convolutional layer yields interpretable time-series data. This technique allows for acoustic analysis of intermediate layers that parallels the acoustic analysis of human speech data: we can extract F0, intensity, duration, formants, and other acoustic properties from intermediate layers in order to test where and how CNNs encode various types of information. We further combine this technique with linear interpolation of a model's latent space to show a causal relationship between individual variables in the latent space and activations in a model's intermediate convolutional layers. In particular, observing the causal effect between linear interpolation and the resulting changes in intermediate layers can reveal how individual latent variables get transformed into spikes in activation in intermediate layers. We train and probe internal representations of two models -- a bare WaveGAN architecture and a ciwGAN extension which forces the Generator to output informative data and results in the emergence of linguistically meaningful representations. Interpretation and visualization is performed for three basic acoustic properties of speech: periodic vibration (corresponding to vowels), aperiodic noise vibration (corresponding to fricatives), and silence (corresponding to stops). The proposal also allows testing of higher-level morphophonological alternations such as reduplication (copying). In short, using the proposed technique, we can analyze how linguistically meaningful units in speech get encoded in each convolutional layer of a generative neural network.