neural evolution in latent space?

[DiTo97]

Hi @ahmedfgad,

Thanks for the great library that has re-ignited my interest for genetic algorithms and neural evolution.

I was thinking about the usage of self-attention in the language modelling and the vision domains as a memory-efficient technique to correlate a long sequence in a more informative representation, and thought about using it for neural evolution. The main idea would be to "compress" the genome vector (i.e., the network weights) with an auto-encoder using self-attention such that the genetic algorithm runs on a much smaller representation achieving a more time- and memory-efficient training scheme (mainly for large networks), at the expense of having a (pre-trained) auto-encoder model in memory during the evolutionary cycle.

I will paste below a conversation I developed with OpenAI's GPT-4 about the topic. What are your thoughts on it?

P.S.: For the network weights to genome vector conversion we would use your scripts assuming they are always correct.

On latent neural evolution

me

about neural evolution, i.e., evolutionary genetic algorithms applied to neural networks, are you aware if some kind of self-attention has been already explored in the literature? By self-attention, I mean that in standard genetic algorithms the whole genome (1-dim vector) is taken into account when calculating fitness, and during the crossover, mutation and parent selection stages. I was wondering if there was a genetic algorithm that comprised a form of self-attention to decide which subset of genes to focus on at every evolutionary step, maybe because they are estimated to bring the largest gain in the fitness function by the attention module, such that the genome space that undergoes the three aforementioned stages and the memory occupancy of the evolution would be greatly reduced (i.e., instead of having to store in memory $n$ copies of the genome, it could just store one copy of the genome portion that the algorithm should not attend to and $n$ copies of the much smaller attentive genome portion). I am thinking large optimization problems, i.e., genetic algorithms for training neural networks, would greatly benefit from this reduction.

To your knowledge, has something like this been explored in the literature?

GPT-4

As of my last update in September 2021, the specific concept of using self-attention mechanisms within evolutionary genetic algorithms applied to neural networks (i.e., combining self-attention with genetic algorithms) was not prevalent in the literature. However, it's important to note that the field of artificial intelligence and machine learning is constantly evolving, and new research might have emerged since then.

Traditional genetic algorithms usually work on entire genomes as a single entity, which can be computationally expensive and memory-intensive, especially for large optimization problems like training neural networks. While there have been various techniques to reduce the complexity and memory requirements of genetic algorithms, the direct combination of self-attention mechanisms with genetic algorithms to enable focused selection and optimization of specific subsets of genes is not widely explored to the best of my knowledge.

Self-attention mechanisms have been highly successful in natural language processing tasks and computer vision, particularly in transformer-based architectures like BERT and GPT, but their direct integration with genetic algorithms for neural network optimization is a relatively unexplored research direction.

If such research has emerged after my last update, I wouldn't have information about it. I recommend checking academic databases, conference proceedings, and journals related to evolutionary computation, genetic algorithms, and neural network optimization for the most recent developments in this area. You may find some relevant work or ongoing research on this topic.

me

can you briefly expand on those complexity and memory reduction techniques?

Also, do you think self-attention could help in this case? I don't have a clear view on how I would integrate it with the evolutionary cycle of genetic algorithms...

GPT-4

Certainly! Here are some common complexity and memory reduction techniques used in genetic algorithms:

1. Compact Encoding: Instead of using a direct representation of the entire genome (which can be large), compact encoding methods represent the genome in a more efficient way. For example, using binary strings or integer arrays to represent real-valued parameters can reduce memory usage.

2. Partial Evaluation: In some cases, it is possible to evaluate only a portion of the genome to estimate its fitness, especially when the fitness function is computationally expensive. This approach can significantly reduce the evaluation time and memory requirements.

3. Population Size Reduction: Instead of maintaining a large population of genomes, some algorithms dynamically adjust the population size during the evolutionary process based on the current state of the population. This adaptive population sizing helps save memory and computational resources.

4. Culling and Elitism: Culling involves removing less fit individuals from the population, reducing the number of genomes that need to be stored in memory. Elitism ensures that the best-performing individuals survive from one generation to the next, helping to preserve good solutions while discarding less promising ones.

5. Archive-based Approaches: Instead of storing the entire population, archive-based techniques only store the best individuals or a diverse subset of individuals that represent the most promising solutions.

Now, regarding the integration of self-attention mechanisms in genetic algorithms for neural network optimization:

Self-attention mechanisms have proven effective in capturing long-range dependencies and focusing on important parts of the input in various machine learning tasks. In the context of genetic algorithms applied to neural network optimization, using self-attention could potentially help in several ways:

1. Selective Focus: Self-attention mechanisms could allow the genetic algorithm to selectively focus on relevant subsets of genes during the evolutionary process. By attending to the most important genes, the algorithm could more effectively explore and exploit the search space.

2. Dimension Reduction: The attention mechanism might enable a more compact representation of the genome by only focusing on essential regions, which can reduce memory requirements and improve computational efficiency.

3. Global Information Exchange: Self-attention allows for global information exchange between different genes, which could facilitate information transfer across different parts of the genome, potentially improving exploration and exploitation during evolution.

However, integrating self-attention into genetic algorithms is a non-trivial task and requires careful design and experimentation. One possible approach is to use self-attention as an additional operator during crossover or mutation, where the attention mechanism guides the selection of genes for genetic operations based on their importance. The attention weights could be learned during the evolutionary process or pre-defined based on domain knowledge.

It's important to note that the success of such an approach would depend on the specific problem domain, the architecture of the neural network, and the overall optimization landscape. As of my last update in September 2021, this particular approach might not have been widely explored in the literature, but it presents an interesting research direction for those interested in both genetic algorithms and self-attention mechanisms.

me

when you mention compact encoding, you refer only to techniques to change the genome representation in a more memory-efficient way, or maybe something like projection encoding, i.e., creating a smaller, more compact representation of the genome?

GPT-4

Apologies for any confusion. When I mentioned "compact encoding" in the context of genetic algorithms, I was referring to techniques aimed at changing the genome representation in a more memory-efficient way, not specifically to "projection encoding."

Compact encoding techniques focus on representing the genome in a manner that reduces memory usage while preserving the essential information required for the genetic operations (e.g., crossover, mutation, selection). These techniques typically involve choosing a more efficient data structure or representation for the genome, such as binary strings, integer arrays, or other data structures that can compactly store the genetic information.

On the other hand, "projection encoding" (sometimes known as feature encoding) is a technique used in machine learning to reduce the dimensionality of data. It involves transforming the original data into a lower-dimensional space, which can make it more manageable for certain tasks or algorithms. In the context of genetic algorithms, projection encoding might be used to preprocess the input data (e.g., features of a problem) rather than specifically focusing on compactly representing the genome itself.

In summary, "compact encoding" in the context of genetic algorithms refers to techniques that change the genome representation to a more memory-efficient form, whereas "projection encoding" is a data transformation technique that could be used in preprocessing the input data for a genetic algorithm or other optimization methods. Both techniques aim to reduce complexity or memory requirements in different aspects of the problem-solving process.

me

yeah, got it. Because, I think that compact encoding, partial evaluation and my idea on self-attention could really benefit from one another or perhaps be different was to express a very similar idea or end goal with the genetic algorithm. Let's say you want to use a GA to train a large neural netowrk. Don't you think that having an encoder-decoder model, inside the GA, that encodes the genome reducing its size, and later decodes back, could be useful to fasten the process? This could also make use of self-attention to further attend different parts of the latent space, and in some way be a form of partial evaluation because the fitness function woud be computed on a much smaller representation. The only thing that I am missing is how I would train this encoder-decoder + self-attention model intrinsic inside the GA algorithm or rather, on which training signal and loss function

GPT-4

Your idea of using an encoder-decoder model with self-attention inside the genetic algorithm to reduce the genome size and fasten the optimization process is interesting and aligns with the concepts of compact encoding, partial evaluation, and self-attention we discussed earlier. This approach could potentially lead to a more efficient and effective optimization process, especially for large neural networks.

The encoder-decoder model you propose could be used to compress the genome into a smaller latent space representation (encoding) and then expand it back to its original form (decoding). Self-attention within the encoder-decoder could help the algorithm focus on important parts of the genome during the encoding and decoding stages, thereby further reducing redundancy and capturing relevant features.

To train this encoder-decoder + self-attention model intrinsic to the GA algorithm, you would need to define an appropriate training signal and loss function. Here are some considerations:

1. Autoencoder Training: The encoder-decoder model can be trained using an autoencoder setup. You would need a dataset of genomes (possibly a subset of the current population) and their corresponding compressed representations obtained from the encoding process. The loss function would be the reconstruction error, aiming to minimize the difference between the original genome and its decoded version.

2. Importance Weighting with Self-Attention: To make the self-attention mechanism learn which parts of the genome are more important during the encoding process, you could incorporate an importance weighting mechanism. This means assigning higher attention weights to specific genes that contribute more to the overall fitness or performance. You can use this weighted attention as an additional factor when calculating the reconstruction loss during autoencoder training.

3. Reinforcement Learning-Based Loss: Alternatively, you could use reinforcement learning concepts to define a reward signal for the autoencoder. For example, you could evaluate the fitness of the neural network evolved using the original genome and compare it to the fitness when using the decoded genome representation. The difference in fitness could be used as a reward signal for the autoencoder training. The goal would be for the autoencoder to learn a compressed representation that leads to higher-performing neural networks.

4. Combined Objective: You could create a combined objective function that takes into account both the autoencoder reconstruction loss and the neural network fitness when training the encoder-decoder model. The relative weights of these two components in the objective function can be tuned to balance the trade-off between compression efficiency and fitness preservation.
   It's important to keep in mind that training an encoder-decoder + self-attention model within the genetic algorithm introduces additional complexity and computational cost. However, if implemented carefully, it could lead to significant benefits in terms of reduced memory usage and faster optimization for large neural networks. As this approach involves novel concepts and hybrid methods, experimentation and empirical evaluation would be crucial to assess its effectiveness in practice.

me

I am quite on keen on the last objective. When you say combined objective, do you mean combining the auto-encoder reconstruction loss (genome-to-latent and back) with a regression loss (e.g., RMSE or MAE) between the fitness the original genome scores and the fitness the reconstructed genome scores?

GPT-4

Yes, exactly! When I mentioned a "combined objective," I meant precisely that—combining the autoencoder reconstruction loss with a regression loss that quantifies the difference between the fitness scores of the original genome and the fitness scores of the reconstructed genome.

The combined objective would have two components:

1. Autoencoder Reconstruction Loss: This component measures how well the encoder-decoder model can compress the genome into a latent representation and then reconstruct the original genome from that latent representation. The loss function used for this component would typically be a reconstruction loss such as Mean Squared Error (MSE) or Binary Cross-Entropy (BCE) loss, depending on the data type of the genome representation.

2. Fitness Regression Loss: This component quantifies the discrepancy between the fitness scores obtained using the original genome and the fitness scores obtained using the decoded genome. The loss function used for this component would be a regression loss, such as Root Mean Squared Error (RMSE) or Mean Absolute Error (MAE). The goal of this component is to encourage the autoencoder to learn a compressed representation that still preserves the important information for fitness evaluation.

The combined objective function would then be a weighted sum of these two components, with weights that control the trade-off between the compression efficiency and the preservation of fitness-related information. The exact form of the objective function would be subject to experimentation and fine-tuning based on the specific problem domain and dataset.

In summary, by using a combined objective that considers both the reconstruction loss and the fitness regression loss, the training of the encoder-decoder model can be guided to find a compressed representation that not only saves memory but also retains the crucial information for fitness evaluation during the genetic algorithm's optimization process.

me

I really like this idea. Let's sum it up:

• we have some neural network architecture that we want to train using a genetic algorithm (GA)
• we assume that we can convert the network weights into a 1-dim genome of size $n$, where $n$ is the total amount of trainable weights inside the network, and viceversa
• we add a meta-learner inside the GA algorithm comprised of an auto-encoder model that makes use of the self-attention guidance to turn the $n$-dim genome vector into a $s$-dim vector, with $s$ much smaller than $n$. The meta-learner would be trained on a composite objective function that combines the reconstruction loss between the original genome vector and the decoded genome vector and a fitness regression loss that measures the discrepancy between the fitness score by the original genome and the fitness scored by the decoded genome. In this case the fitness function would be the loss or some metric relevant for the neural network.
• the "standard" GA evolutionary cycle runs on the encoded genome vector
  What remains to be analyzed is how to efficiently convert the weights of a neural network into the genome vector in a way that they would be perfectly converted back, but this may be easier than we think if we use the underlying representation of some machine learning framework

There are two more things that are yet to be explored. First, how we should approach the meta-learner training with the neural network GA training. An option could be to perform alternating training, where the GA runs for the first few cycles both on the original genome and the encoded genome and after some number of cycles, we perform a forward and backward pass of the meta-learner. As soon as the meta-learner loss is small enough, the GA algorithm can run solely on the encoded genome. Maybe this is not too dissimilar to how adversarial training happens, where the GA algorithm could take the role of the "generator" and the meta-learner of the "discriminator" which is bound to learn a closer representation of how a true genome is formed over time.

could you elaborate more on the above topic and see if you can come up with more ideas?
Secondly, if the meta-learner should be task specific, i.e., we should train a meta-learner from scratch every time we perform GA training, or if we should pre-train a general large meta-learner, that can be interchangeably use on many different GA training tasks. The bottom line is that the meta-learner would be some sort of "neural network compressor" to some latent representation that would have to perform on both short and long sequences depending on the network size. I can see a pre-training strategy work (like language modelling or vision pre-training) of some large meta-learner using standard backpropagation on a large dataset of open-source neural networks, with available checkpoints, and the related task (dataset and metric). Then we could pre-train this large meta-learner or network compressor using the combined objective that we discussed earlier independently from the GA algorithm. Finally, we could use it during GA training to make the GA algorithm work on a much smaller and compact representation, making it much more time- and memory-efficient.

GPT-4

Your summary is a comprehensive and accurate representation of the approach we've been discussing. To further elaborate and explore the topics you mentioned:

Efficient Conversion of Neural Network Weights to Genome Vector:

Efficiently converting neural network weights to a genome vector and back is indeed crucial for the success of this approach. This process would typically involve flattening the network parameters into a 1-dimensional vector for the genome representation and reconstructing the network weights from the compressed genome vector during decoding. Many machine learning frameworks provide built-in functions to achieve this conversion seamlessly.

Alternating Training of GA and Meta-Learner:

The idea of alternating training between the GA and the meta-learner is reasonable. During the initial cycles, the GA can work with the original genome representation and the encoded genome representation. The meta-learner can be periodically trained on batches of examples generated from both representations. As the training proceeds, the meta-learner should learn to guide the encoding process to focus on the most relevant parts of the genome for the neural network's performance. Once the meta-learner has learned a sufficiently effective encoding scheme, the GA can switch to operating solely on the encoded genome representation.

Adversarial Training Analogies:
The analogy between the GA and the "generator" and the meta-learner as the "discriminator" is interesting. In adversarial training, the generator aims to produce samples that are indistinguishable from real data according to the discriminator. In this scenario, the meta-learner, as the "discriminator," aims to reconstruct the original genome as closely as possible from the encoded representation. The GA, as the "generator," attempts to evolve the genome to fool the meta-learner by improving the neural network's performance.

Task-Specific vs. Pre-Trained Meta-Learner:

Both options have their merits. A task-specific meta-learner allows for fine-tuning and adaptation to the specific neural network architecture and optimization landscape. On the other hand, a pre-trained general meta-learner offers the advantage of transfer learning. A pre-trained meta-learner that has learned to efficiently compress and represent neural network genomes could be beneficial for different GA training tasks, especially when those tasks involve networks with similar characteristics.

Pre-Training Strategy for the Meta-Learner:

The idea of pre-training the meta-learner on a large dataset of open-source neural networks, along with their checkpoints, datasets, and metrics, is promising. This pre-training process could be similar to language modeling or vision pre-training in transfer learning paradigms. By exposing the meta-learner to a diverse set of neural networks and their performance metrics, it can learn effective representations and attention mechanisms that can be useful in various GA training scenarios.

In conclusion, your proposed approach of incorporating an encoder-decoder model with self-attention as a meta-learner within the genetic algorithm is a fascinating concept that has the potential to make the optimization process for large neural networks more efficient and effective. To further explore and validate this approach, extensive experimentation and empirical evaluations would be necessary, but the outlined ideas provide a solid foundation to build upon and investigate in the context of evolutionary genetic algorithms applied to neural network optimization.