It’s been a while…

I probably could have kept this post for myself, since the main reason I’m writing this is to force myself to better formalize and structure these ideas. But I also wouldn’t mind discussing these topics with other people. ;)

This will be a look at generative models for music from the perspective of a deep learning researcher. In particular, I will be taking the standpoint that such models should aim to possess some sort of creativity: Producing truly novel and “interesting” artifacts. To put it another way: They should model the process, not the data. I realize that many of the aspects I bring up are already being considered and actively researched in other communities (e.g. computational creativity). However, my main goal is to bring up specifically why some of the current research directions in deep generative modeling are (IMHO) misguided and why resources might be better spent on other problems.1

Copying Is Not Creativity

Generative modeling may be summarized as: Given a set (or more generally, a domain) of data x, build a model of the probability distribution p(x). In fact, most “modern” deep generative modeling frameworks (such as GANs or VAEs)2 do not actually represent this distribution, focusing instead on producing samples from p(x). The implications of this (e.g. preventing many potential applications of a generative model, such as inpainting or density estimation), while certainly important, are not the topic of this discussion. Instead, I want to focus on the case where generating outputs is all we care about.

While such models are mostly built and tested in the image domain (especially faces), attempts at creating music “from nothing” are becoming more ambitious (e.g. Music Transformer, Musenet, or most recently Jukebox). These models are certainly great accomplishments of engineering, since musical data (especially on the raw audio level) is very high-dimensional with dependencies across multiple (and very long) time spans. But what is their value, really? No matter how many layers the model has, how many units per layer, or which fancy connection schemes and training tricks are used – at the end of the day, the model will capture statistical relations between data points, because that’s what we ask it to do. Better models and/or smart conditioning on factors such as musical style, composers, lyrics etc. may mask this somewhat, but it doesn’t change the fundamental nature of these models – produce things that are like the things they have seen (or rather, been shown) before. 3 The inadequacy of this approach will be discussed further in the following sections, where I will sometimes refer to such models as copy models (please take this as somewhat tongue-in-cheek).

Please note: I am aware that there are contexts/applications where training a generative model to “copy” a distribution is actually the goal, and there is nothing wrong with that. However, models like the ones mentioned above are usually presented “as is”, with their ability to generate an endless stream of music as the main selling point. Interestingly, they are often explicitly advertised as generating music “in a certain style”, which IMHO masks their limitations somewhat by pretending that generating hours of Mozart-like music (for example) is the whole point. Of course, there is some value here – namely, exploring/showcasing model architectures that are capable of the kind of long-term structure needed to produce music. I’m certainly not proposing to get rid of deep models altogether – their incredible expressiveness should be leveraged. But I believe that at some point, the relentless scaling-up should be stopped, or at least halted for a bit, and the insights be applied to more creative approaches to making music.

As an approach radically different from copy models, it might be possible to start generating artifacts (e.g. pieces of music) without any reference data whatsoever. This will likely result in pieces that seem very alien to us, since they are not at all grounded in our own experience. Still, I believe it could be interesting to see where, for example, purely information-theoretical approaches could take us. That is, art should be predictable (so it is “understandable”), but not too predictable, since that would be boring/not stimulating. The process could additionally be equipped with simple sensory priors (e.g. related to harmony) to make the results more familiar. Such models could be used to investigate many interesting questions, for example: Under which models/assumptions is human-like music possible to evolve? When adding more assumptions, does it eventually become inevitable? Speaking of evolution…

There Is No Goal

Given a fixed data distribution for training, a generative model will be “done” eventually. That is, it will have converged to the “best” achievable state given the architecture, data, learning goals, training procedure etc. If we then start sampling thousands upon thousands of outputs (compositions) from the model, these will all come from the exact same (albeit possibly extremely complex) distribution. Diversity can be achieved by using conditional distributions instead, but these will still be stationary.

It should be clear that this is not a reasonable model of any creative process, nor will it ever create something truly novel. On the contrary, such a process should be non-stationary, that is, always evolving. New genres develop, old ones fall out of favor. Ideas are iterated upon. New technology becomes available, fundamentally disrupting the “generative distribution”. Such things should (in my opinion) be much more interesting to model and explore than a literal jukebox.

Concretely, I believe that concepts from research on open-endednessshould be very interesting to explore here. One example might be co-evolving generators along with “musical tastes” that can change over time. Speciation could lead to different genres existing in parallel. A minimal criterion approach could guarantee that only music that actually has listeners can thrive, while at the same time making sure that listeners like something instead of just rejecting everything for an easy “win”. Importantly, this allows for modeling the apparent subjectivity/taste that plays a big role in human appreciation of art, without relying on black-box conditioning procedures using opaque latent codes or similar approaches.

To expand upon the speculation on “ex nihilo” generative models at the end of the last section, it could be interesting to train a copy model to initialize an open-ended search process which is then perhaps guided by more general principles/priors. This would allow for exploring possible evolutions of existent musical genres.

The Right Level of Modeling

Generative modeling of music is usually done at one of two levels.

Symbolic

The first one is the symbolic level, where music is represented by MIDI, ABC notation, piano rolls or some other format. What is common to such representations is that they use (often discrete) “entities” encoding notes or note-like events in terms of important properties such as the pitch and length of a tone. Importantly, there is no direct relation to audio in these symbols – the sequences need to be interpreted first, e.g. by playing them on some instrument. This implies that the same MIDI sequence can sound vastly different when it is interpreted via two different instruments. This is arguably already a problem in itself, since widely used symbolic representations lack means of encoding many factors that are important in contemporary music (electronic music in particular).
In that regard, it is quite telling that many symbolic models are trained on classical (piano) music. Here, the instrument is known and fixed, and so it can be assumed that a “sensible” sequence of symbols will sound good.4

However, there is a second problem related to the interpretation of musical symbols, which is perhaps easier to miss. Namely, the symbols have absolutely no meaning by themselves. Previously I said that they usually encode factors such as the pitch or length of a tone – but the exact relationships are imposed by human interpretation. Take the typical western twelve-tone equal temperament (which MIDI note pitches are also commonly mapped to) as an example: Here, every twelve tones are one octave apart (i.e. they double in fundamental frequency). Seven tones (a fifth) are in a relation of 3:2, etc. Generally, every tone increases in frequency by about 6% compared to the next-lower one. Such intervals undoubtedly play an important role in human perception of music. But these relations are completely absent from a symbolic note representation. For a model training on such data, there might as well be five tones to an octave, or thirteen, or… The concept of intervals does not arise from symbolic data, and thus a model trained on such data cannot learn about it.

Then why do such models manage to produce data that sounds “good”, with harmonic intervals we find pleasing? This is simply because the models copy the data they receive during training. If the data tends to use certain intervals and avoid others, the model will do so, as well. The difference is that the training data was generated (i.e. the songs where composed) with a certain symbol-to-sound relationship in mind (e.g. twelve-tone equal temperament). However, this relationship is lost on the model, which merely copies what is has been taught without understanding the ultimate “meaning” (in terms of actual sound). In fact, this seems incredibly close to John Searle’s famous Chinese Room argument. Thus, unless one wants to view music generation as an exercise in pure symbol manipulation, the symbolic level seems unfit for any kind of music generation that is not content with merely copying existing data, although possible remedies could be to use more expressive symbols that relate more closely to the audio level (e.g. using frequencies instead of note numbers), or equip the model with strong priors informed by this relationship.

Waveform

Aside from the symbolic level, it is also possible to directly generate data on the audio (waveform) level.5 However, this approach has so far been lagging behind symbolic models in terms of structure, coherence and audio quality. Some models were developed on the single-note level (e.g. GANSynth), with a focus on quality. While such models are interesting for creative applications in human-in-the-loop scenarios (e.g. sound design), they are obviously not capable of producing interesting musical sequences. Still, there have been examples of modeling sequences in the waveform domain with some success (e.g.DAA).

Recently, OpenAI released their Jukebox model, which scaled up waveform generative models to levels far beyond what has been seen before. The fact that a single model can produce samples of such variety, conditioned on styles and even on lyrics, is astounding. However, there are still some issues with generating at the audio level:

  1. Fundamentally, the model still tries to copy the training data.
  2. The symbolic level is completely removed. Personally, I don’t think this is the right approach, either. It means that the model has to essentially discover concepts such as note events, tempo, rhythm etc. on its own. In a sense, it is lacking knowledge of how to make sounds, i.e. what instruments are there and how can they be played. Note that this is likely alleviated by using models such as VQ-VAEs which at least enforce some kind of discrete representation in the hidden space, but these are not necessarily connected to useful/interpretable musical concepts (certainly not when the model is initialized).
  3. As it stands, most waveform generative approaches lack priors regarding the kind of data they produce, i.e. oscillating waveforms. This means that not only does the model have to learn what useful “sound sources” would be (see above), it also needs to learn how sound itself “works”, that is, to create oscillations at certain frequencies. This causes waveform models to produce audible artifacts as they struggle to adhere to clean oscillations. A possible remedy for this are approaches like DDSP.

Hybrids

It may be possible to combine symbolic and waveform approaches to achieve the best of both worlds. Essentially, this means using a symbolic-level model to produce sequences of symbols, and then a waveform model that translates those symbols into sound. This preserves many advantages of symbolic models (e.g. explicit, interpretable representations and specific ways of making sound) while also allowing the model to “connect” with the domain we eventually care about (audio).

While this sounds good in theory, there are of course problems with this approach, too. The main one is probably how to formulate a joint model for symbols and sound. A major obstacle here is that it is not possible to backpropagate through discrete symbols. Since most symbolic models output soft probability distributions over symbols, this is not a problem in the pure setting. But a joint model would probably not be able to work with such soft outputs, since it would be like “pressing every piano key a little bit, but one more than the others”. Still, there are workarounds for this issue, such as vector quantization with straight through estimators – or dropping gradient-based methods entirely and using alternatives like reinforcement learning or evolutionary computing instead.

Besides this problem at the symbolic level, there is also one in the symbol-to-audio pipeline: This generator needs to be differentiable, too. This means we cannot simply train a symbolic model with a “real” piano (samples), since the instrument cannot be backpropagated through. Alternatively, using standard neural network architectures (e.g. Wavenet) can lead to artifacts and/or slow generation as discussed before. Personally, I am really interested in approaches like DDSP that preserve differentiability while incorporating a sensible inductive bias for audio, leading to much better quality with simpler models.

A possible hybrid approach could go like this:

  1. Train a DDSP model on instrument samples, say, a piano.
  2. Train a symbolic model, but not on a symbolic loss; instead, use the trained DDSP network to turn the symbols into audio and compute a loss (or some other target function) on the audio level. Gradients can be backpropagated through the DDSP model, which should not (need to) be trained anymore, and then through the symbolic model – assuming the problem of non-differentiable discrete symbols (i.e. the transition between the two levels) can be solved somehow.

Perception

Colton argues that a creative system needs to have three distinct properties:

  1. Imagination, or the ability to create novel artifacts. Models that learn and sample from p(x) arguably have this to an extent, in that they can draw samples that have never been seen before. On the other hand, as argued above, these models cannot move beyond p(x) and are thus unlikely to produce something truly novel.
  2. Skill, or the ability to create quality artifacts. I would argue that this is the only property that standard data-driven generative models fulfill – given that they have enough capacity and are well-trained, outputs can be quite impressive.
  3. Appreciation, or the ability to judge the novelty an quality of their own creations.

Heath & Ventura argue that this third point is a key component that is lacking in many generative systems. We can find analogues, however, in some modeling frameworks: (Variational) Autoencoders have an inference network (encoder) that can process data, which would include its own outputs. However, it is not clear how one would connect this to “appreciation”, since the main point of the encoder usually is to simply map the data to a lower-dimensional representation. Still, perhaps it could be easier to work in this space than in the data space directly.

On the other hand, autoregressive models as well as flow-based models (which generalize the former) can explicitly compute probabilities for a given data point, which might be taken as a proxy for “quality”. A model could use this to reject bad samples (e.g. that resulted from an unfortunate random draw) on its own. This is troublesome, however, since it is not clear a priori what a “high” probability is, and accordingly what kind of score one should strive for. This is particularly true in the (common) case where the data is treated as continuous, and the probabilities computed are actually densities. Also, this approach seems inappropriate for judging novelty – truly novel work would likely receive a low probability and thus be difficult to differentiate from work that is simply low-quality, which would also receive a low score.

Additionally, none of these models use their “self-judging” abilities to actually iterate and improve on their own outputs. This is fairly common in a creative process: Create something (perhaps only partially), judge which parts are good/bad and improve on the ones that are lacking. Here, I find self-attention approaches such as the transformer interesting: The model can essentially take multiple turns in creating something, looking at specific parts of its own output and use this information to iterate further. However, current transformer models usually do not produce actual outputs (in data space) at each layer; instead they compute on high-dimensional hidden representations and only produce an output at the very end.

Given our evolutionary history, I believe it’s safe to say that perception came first, and the ability and desire for creativity arose out of these capacities. At the same time, generative and perceptual processes could also be tightly interlinked inside a model, e.g. using a predictive coding framework. At this time, I don’t know enough about PC to really make a judgement (or go into more detail), however.

Intentionality

Likely the biggest challenge in modeling (human) creativity is that art is usually “about” something, meaning that it relates in some way to the artist’s own experience in the world. As such, properly approaching this subject seems to require solving strong AI. However, there may be ways to at least make steps towards a solution via simpler methods. One example could be multi-modal representations. As humans, we are able to connect and interrelate perceptions from different senses, e.g. vision, touch and hearing. We can also relate these perceptions to memories, abstract concepts, language etc. It seems obvious that such connections inform many creative artifacts. For example, program music provides a “soundtrack” that fits a story or series of events. Such music is neither creatable nor understandable without understanding language/stories (which in turn requires general world knowledge). On a more personal level, an artist may create a piece of music that somehow mirrors a specific experience, say, “lying at night at the shore of a calm mountain lake”.

Models that simply learn to approximate a given data distribution (limited to the modality of interest) clearly cannot make such connections.6 However, this could be different for a model that learns about audio and vision (for example) concurrently. As long as there is some connection between modalities, e.g. via a shared conceptual space (embeddings are an extremely popular method and could be a simple way of achieving this to a first approximation) it should be possible for the model to connect the visual concepts it is learning about with the audio dimension. This, like the other proposals in this text, is obviously an extremely rough sketch with many, many details to be considered – but this requires research, not blog posts.

Conclusion

To summarize:

  • Existing deep generative models mainly aim to copy a given data distribution. This condemns them to produce artifacts that are “like” the training data in that they simply follow learned statistical regularities. Data-free models could instead have the potential to discover truly “new” artifacts from more general principles.
  • Existing models learn a fixed distribution and generally do not evolve beyond this, making them “uncreative” by design. Methods from open-endedness research could result in models that continually push the boundaries of their own creations.
  • Symbolic models are too far removed from the modality of interest (audio) to be meaningful on their own. Pure waveform models ignore important inductive biases from how music and sound are created. Hybrid models seem the most promising, but there are obstacles regarding their implementation and training with current methods.
  • Perception, or the ability for appreciation, is an important aspect of creativity that is lacking in current models.
  • Intentionality is central to art and creativity, but is missing from current models; nor is it possible to achieve by modeling data distributions in a single modality.

Each of these points offers several directions for future research to explore. It is possible that none of these proposed methods/directions will result in anything comparable to copy models, in terms of surface-level quality, for a very long time. However, I believe it is important to break the mould of trying to make progress by throwing humongous amounts of compute at highly complex data distributions. Instead, generative music (at least for creative purposes) should start from first principles and accept that the results might be “lame” for a while. In the long term, this has the potential to teach us about music, about creativity in general, and about ourselves. Can Jukebox do that?

  1. Besides, including detailed reviews of CC literature would make this post excessively long. ↩

  2. Please note, I will not be providing citations for general deep learning concepts that I would believe practitioners to be familiar with, nor a few other things – I’m a bit lazy and this is not a publication. ↩

  3. To take a more extreme view: The only reason these models produce anything “new” is due to limited capacity and inherent stochasticity of the data. If they could literally copy everything perfectly, they would. ↩

  4. Another reason for the preference for such data sets is likely that they are widely available without copyright issues, which is a big problem with musical data. The fact that they use a single instrument also makes them much more straightforward to model. ↩

  5. We can also generate audio at the spectrogram level. This tends to be easier, but then the problem is how to invert the spectrograms to audio without loss of quality. ↩

  6. This would also include the creation of emotional music; this cannot be created without “knowledge” of emotions. Except, of course, if the model learns to copy a database of existing emotional music – the common approach. ↩