Self-Organizing Intelligent Matter:  A blueprint for an AI generating algorithm
Authors: Karol Gregor
Frederic Besse
Venue:  (2021)
Keywords: Artificial Life
AI Generating Algorithms

Abstract: We propose an artificial life framework aimed at facilitating the emergence of intelligent organisms. In this framework there is no explicit notion of an agent: instead there is an environment made of atomic elements. These elements contain neural operations and interact through exchanges of information and through physics-like rules contained in the environment. We discuss how an evolutionary process can lead to the emergence of different organisms made of many such atomic elements which can coexist and thrive in the environment. We discuss how this forms the basis of a general AI generating algorithm. We provide a simplified implementation of such system and discuss what advances need to be made to scale it up further.

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SELF-ORGANIZING INTELLIGENT MATTER: BLUEPRINT FOR AN AI GENERATING ALGORITHM
A
Anonymous authors Paper under double-blind review
ABSTRACT
We propose artificial life framework aimed at facilitating the emergence of intelligent organisms. In this framework there is no explicit notion an agent: instead there is environment made of atomic elements. These elements con- tain neural operations and interact through exchanges of information and through physics-like rules contained in the environment. We discuss how an evolution- ary process can lead to the emergence of different organisms made of many such atomic elements which can coexist and thrive in the environment. We discuss how this forms the basis of a general AI generating algorithm. We provide simplified implementation of such system and discuss what advances need be made scale it up further.
INTRODUCTION
An AI generating algorithm (Clune 2019) is a computational system that runs by itself without outside interventions and after certain amount of time generates intelligence (though the general idea much older than this reference). Evolution on earth is the only known successful system thus far that we know of. In this paper we propose computational framework, and argue why it might constitute such general algorithm, while being computationally tractable on current or near future hardware.
Building such system successfully will take many iterations and require a number of advances. What hope to provide however, is general procedure, where better and better systems arise as result of improving the elements of the system and of experimentation rather than a fundamentally new algorithm. As example, had such procedure for supervised learning since the 1980's neural networks trained by back-propagation and stochastic gradient descent. To reach the current impres- sive performance, it required number of clever improvements, such rectified non-linearities, convolutions, batch normalization, attention, residual connections and better optimizers, but the overall algorithm hasn't changed.
1.1 EVOLUTION
Evolution is the primary process by which our algorithm operates. We describe it here.
In machine learning, the word evolution is typically used to describe variations of the following process (Back 1996). We have a number of individuals and an objective to optimize. We evaluate the individuals, select the ones with good values of the objective, and mutate them to produce the next generation. Over time, individuals that are better at optimizing the objective appear. The use of the word evolution in this context is perhaps unfortunate, as this process is quite unlike the evolution observed in nature (Stanley et al. 2017). The clearest difference we can see is in the outcome. The former results in small variation of final individuals that are the best the objective. The latter results in coexistence of huge variation of individuals with different behaviors it is open-ended.
Let us therefore discuss the basic operation of natural evolution. We have an environment built out of elements (atoms) that organized into bigger units such as individual bacteria animals or groups of these. Those classes of units that propagate (Joyce 1994h into the future (e.g. replicate will discuss this in moment) keep existing, while those that don't 't propagate cease exist. There is no objective based on which units are selected for propagation. Different collections of units find different means of propagating.

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An important mechanism for the coexistence of a large number of different solutions is niche con- struction (NicheConstruction 2020). Different collections of individuals modify or form the envi- romment for one another. For example bacterium consumes food and excretes waste products, which modifies the local environment, being either food or toxic substance for other bacteria. An- other example is prey forming food source for predator. These systems are self balancing, for example too many predators means they can't 't find food and die off, and vice versa. This means that the coexistence of multiple solutions present (and evolving). Collections of individuals in such systems have different means of propagating, rather then being selected by a global objective.
The lack of objective we believe, as argued in (Stanley & Lehman 2015), is critical and fundamen- tal to open-ended creation and coexistence of diversity and runs counter to most developments in machine learning. Conversely, a presence of an objective in a system likely leads to collapse of diversity. To see that attempting to create an objective is problematic, let us therefore try to suggest one and see what the problems would be. One of the clearest objectives one might propose to re- ward an individual for reproduction. However, a predator might then simply kill its offspring which would increase its chance of making another one. We could try to tweak or find other objectives, but this might lead to unwanted and unforeseen behaviours similar to the one described above. There are other issues. We don't 't actually make copies of ourselves, but instead mix genes from individuals (sexual reproduction), which we need to select. What do actually want reward? In addition, most of the time, propagation of species depends on individuals working together in a group, often sacrificing some members for the good of the group. What is then a real reproducing unit? This is the reason why the word "propagate" (Joyce, 1994) is more appropriate than "reproduce". What really happens is that those classes of groups of elements that are set "a certain way" propagate and those that are not, don't. Note that this does not contradict the evolution of an intrinsic reward which is an evolved means of finding a good policy during the lifetime of given individual.
Another example of evolutionary process is our society. People don't 't have children in proportion to some objective the society has set, or there isn't just one job or hobby that we all converge on and that is the "best". People engage in large number of jobs and hobbies. At the same time, memes, values, work practices, company structures and many other emergent concepts propagate. All these things cocxist, both cooperating and competing.
1.2 PRINCIPLES
The field of artificial life aims at producing life and an evolutionary process inside a computer
[Langton] 1997 Ray 1991; Lenski et al. [2033] Sims 1994 Yaeger et al. 2011 Gras et al., 2009 Soros & Stanley 2014), see (Aguilar et al. 2014 for a review. In seminal work on Tierra (Ray 1991). Thomas Ray created an artificial life system in the substrate of assembly instructions in computer memory. The set of instructions is executed by number of heads and one organism corresponds to one head. The system was initialized by a handcrafted sequence of instructions that when executed, will copy itself to another part of the memory. The executions undergo mutations. Some of these result in organisms that are unable to replicate, while some others get better it. Some organisms find ways to use other organisms copying mechanism to copy, forming parasites. Then resistance to parasites evolves, and hyper-parasitee phenomenons of sociality and cheating are observed.
This process eventually peters out, and the quest ever since has been to create a system that is truly open-ended, where complexity keeps increasing without bounds (Standish) 2003). A number of principles that characterize and open-ended process has been proposed (Soros & Stanley 2014] Taylor et al.] 2016) Here we select two that that we find the most important (points 2 and 3) and introduce two new ones (points and 4).
There should be built in notion of an individual and no built in operation for reproduction of an individual. Instead, these should be an emergent properties of collections of units, composing new collections of units or themselves.
The evolution of new (here emergent) individuals should create novel opportunities for the survival of others (Soros& & Stanley 2014).
The potential size and complexity of the individuals phenotypes should be (in principle) unbounded (Soros& & Stanley 2014).
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To tractably obtain intelligent agents, fundamental neural operations should be basic build- ing blocks of the environment.
The first property is absent in majority of works artificial life, except few that review later below. However, this property quite close to being true in Tierra and Avida (Lenski et al. 2003). A given individual (organism), consisting of sequence of instructions, actually has to construct new one (create the new sequence of instructions). Then however, a new agent is declared, a new head is allocated for it, and there is distinction in operations within and outside of/hetween the individuals. Properties two and three should really be consequences of property one, which we will see once we describe the system in section Property four is introduced for tractability and again will become clearer below.
There are other approaches that studied diversity in evolution. To prevent collapse of diversity in objective based evolution, ideas such map elites (Mouret & Clune| 2015) or quality diversity (Pugh jet al. 2016) have been proposed, that explicitly try to keep diverse set of solutions. These assume a small handcrafted space of variables that define what individuals are different. However, given such space, they show that searching for space of diverse solutions, leads to a better result on the final objective than optimizing the objective directly, as the search process is able to step through solutions that are not obviously directly on the path aimed at the objective. To remove an objective, (Soros & Stanley, 2014 2014 Brant & Stanley, 2017) propose to give every organism a chance reproduce but do so if it satisfies a minimal criterion, such as sufficient amount of energy. In the latter, they consider the next generation if there solvers solving it and a solver is propagated if there are mazes it can solve. This results in a coexistence of many solutions in the population. The system however behaves somewhat like random walk through solvable mazes and it would be good to find system with a stronger selection pressure.
set of mazes and their solvers. A maze is propagated
Another approach create an open ended system to co-evolve one agent that designs an en- vironment (sets the layout of things and such) and another one that tries to solve it (Wang et al., 2020 Racaniere et al. 2019). The former maintains a collection of anviromment-agent pairs, and a new such pair is allocated if it is sufficiently far from the pairs in the collection according to a pre-specified objective that does not depend on the details of the environment (but on the ability of agents to solve the environment).
In the system that we propose that there is no special agent designing the environment -theee is actually no concept of agent, and instead there is only an environment where agent-like organisms can emerge and reshape the environment from within. There neither is any explicit minimal criterion for an organism since there is explicit operation of copy of individual, but such criterion will appear for any emergent individual.
PROPOSED SYSTEM
The real world is built out of elementary particles that interact and compose bigger entities. Our proposed environment (an aspiring Al generating algorithm) is as follows. The environment is built out of elements, but much coarser scale. Each element contains neural operation. This can be for example matrix multiplication, an outer product, or more likely a sequence of such operators comprising a mini neural network. The elements interact with each other through some form of underlying rules, a type of physics, and through a direct communication of neural states.
There can be various implementations of this system. In section 3 we provide a grid-world im- plementation with basic elements lying on a grid, communicating with propagating signals or via an attention mechanism and with underlying physics implementing energy and chemical-lic ex- changes. Another example could be elements forming rigid pieces in three dimensional space that can be attached using joints, that contain the neural operations, interacting through exchange of sig- nals with nearby attached pieces and that set the torques the joints. There could be several types of elements in the system, and not all need to have neural networks inside.
In section 3 we provide grid world implementation that highlights number of important prop- erties. Along the way we discuss what advances need to be made to make this system powerful. However, the potential of the proposed system is unbounded and here some of the features that this system supports. Larger units composed of several elements can be formed either by physical attachment (like a robot) or simply as a set of units that decide to communicate and form whole.
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There is no limit to the potential size of these units. These units can propagate in number of ways they can grow by taking over other elements in the environment (a colony), they can replicate by assembling copies moving appropriate collected elements to place (e.g. robot assembling copy itself from pieces), or self-assemble, or they can produce whole different units that either im- plement specialized functions (a useful machine) units that are even better than their predecessors. The latter likely requires intelligence.
2.1 CAPACITY FOR INTELLIGENCE.
In this subsection we discuss why the computational system just proposed has the capacity to repre- sent general intelligence. We provide two arguments. First, any neural algorithm in machine learning that we have created, and likely create in the future, can be written as a sequence of operations, such as additions, matrix multiplications, outer products and non-linearities, operating on states which are tensors. An example is the sequence resulting from the forward, backward, and optimizer op- erations of a neural network. Auto ML Zero (Real et al.) 2020) realized this, and directly searched for the sequence of such operators along with connectivity to states on which they operate and was able to learn basic neural algorithms. Since these operators are fundamental building elements of our environment, and these elements can be made to communicate with arbitrary connectivity, all neural algorithms can be implemented in our system as well.
Second, the human brain is capable of general intelligence, and its computation closely resembles an online recurrent network (not trained by back-propagation time). That is, it can be approximated by function F that updates neural and synaptic values online h2, W, F(h--1, W,-1 22, v) where h2 is a cell state of neuron i and Wij is the state of the synapse connecting neurons i and j. is input and represent hyper-parameters such as connectivity, coefficients, and nonlinearities. To represent actual neural computations well enough (note that we are not interested in faithful representation but something with similar algorithm and computational power) we likely need to represent fú2 and Wy by small vectors, as suggested in (Gregor 2020 Bertens & Lee 2019). These computations are local and therefore to search for them, we need to search for relatively simple functions (with few hyperparameters). We can search for them automatically, as in Auto ML zero or other neural architecture search works (Zoph & Le 2016 Pham et al.. 2018 Liu et al. 2018 Elsken et al., 2018). The important point to remember from this, is that there likely exists an online neural update, of power at least as large as that of the human brain, on system of a similar size in terms of computational capacity. We could implement the computation of given element of the environment by a layer of such neurons. During the run of the environment, other elements can set well h, W of given element. Those groups that have elements with the right settings of these parameters, for example v's that implement a good learning algorithm (the update of W), should enable better propagation of this group compared to others.
the
2.2 AGENT HYPOTHESIS.
In our system there is separation between agent and environment (AgentHyypothesis 2020) there is only an environment. The elements themselves may or may not form units of evolution (Smith] 1986 Szathmáry et al., 2005)- entities that multiply, show heredity and where the heredity is not exact. In the former case, they could move autonomously, collect energy and replicate, and form bigger aggregates or replicating organisms because that provides an advantage. However, we propose to aim for the latter, where certain minimal number of simpler cooperating units are need to propagate themselves.
There is a large amount of works that are related in one way or another to self oraaiiaganiztiion, and we can only review certain ones most relevant to our paper. The study of origins of life aims to understand how life evolved from non-living things. At some point in time in early earth, there were only simple combinations of elements: atoms combined into simple molecules, and at later time, there was the last universal common ancestor (Theobald (0100) of all current life, which was already a rather complex organism containing core structures of bacteria. There are theories of how life emerged in the period in between, such as catolyat system enclosed in membrane (Gánti, 2003) or a self-replicating molecule (Joyce 2002). As model of later, (Virgo et al.] 2012) consider physical system of shapes and succeed at finding length chains that replicate. However, they
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find that the shapes have to have a very specific features, arguing that such shapes unlikely to emerge spontaneously from chemistry, and are therefore this process isn't 't a likely origin of life.
Simple substrates to study artificial life are cellular automata and related particle systems. (Gardner 1970 Chan 2020; Schhmickl et al. 2016 Sayama 2009; Ventrella 2020 Nichele et 2017). cells on grid and in the later they have real valued coordinates and move. Their behavior is governed by simple rules that update their state based on their previous state and that of near neighbours. replication, variation and heredity. This has proven quite difficult and while simple self replicating structures have been found, they don't t satisfy these criteria of life. is then especially difficult to imagine how to obtain an intelligent life from such simple rules in a tractable fashion. The proposal we put forward in this paper, is to use general neural networks of section 2. as the key parts of the elements, which can together form large neural networks, but with comparatively much fewer elements than basic cellular automata/particle systems. This is the reason for the word "intelligent" in the title of the paper. In addition, obtaining complex behavior should be much easier that tweaking cellular automata rules since we are starting with good learners- knowing the current capabilities of reinforcement learning agents, which we can
In the former, elements
goal is to find a set of rules that give rise to life, exhibiting
jump-start the system.
Cellular automata can be implemented using convolutional neural networks (Wulff' & Hertz, 1993, Gilpin 2019). In study of morphogenesis (self-assembly of given object/patterm), (Mordvintsey et al.) 2020) trained a convolutional neural network that respects the structure of cellular automata produce a given pattern starting with single cell or number of other patterns. Similar approach was pursued using compositional pattern producing networks (Nichele et al. 2017). These works however are not studying evolution.
Finally, there is a body of work on swarm systems and self-assembling robots. The former studies how can swarms of robots coordinate their behavior to accomplish tasks such as disaster relief or to study an emergent swarm behavior. The later, which is the closest in some ways to out proposal, studies how robots can self-assemble from smaller pieces. In (Weel et al. 2014), they consider a single type of (simulated) robot piece from which varying bodies are assembled through a process of evolution. There are some differences from what we propose: There is an explicit notion of an individual that is constructed in central birthing facility according to an evolved template, an individual has a central brain (rather than composed one), and individuals replicate if they meet after certain minimal distance from the birthing facility. While they do indeed aim for objective free evolution, the individuals do tend be selected based on how quickly they can get certain distance from the birthing area. Finally, in (Mathews al., 2017) they use physical cylindrical robots on a table, that can attach and detach to accomplish a task. When they attach, their controllers form one nervous system, where one chosen unit acts as brain and the rest the body. The controllers are implemented using a specific logic rather than neural networks. In our case we propose to use general learner neural networks, that can combine form a bigger computational system (assembling a brain), that can in principle program newly added units (as we propose in section below) and that undergo objective free evolution.
GRID VERSION OF SIM AND GENERAL PROPERTIES.
This section introduces an instance of the self-organizing intelligent matter (SIM). It also serves as a discussion of various points relating to SIM and gives more reasons of why we believe it can form an AI generating algorithm.
As discussed in subsection 2.2 there is no built-in notion of an agent and there really is just an environment. Seeing that, it feels unnatural to implement the system on two different platforms as is commonly the case one for the physical part- such as a physics simulator, and one for the neural part- a neural network framework such as TensorFlow, Py Torch or Jax. Instead, we propose to make such system in single platform. Because would like to produce intelligent behavior, need to run neural networks efficiently, and therefore the system needs to be implemented on one of the latter platforms. Because of its fiexibility, we choose Jax.
Jax operates on tensors, which we use to store elements. The elements need to interact and have the ability to form flexible aggregates of arbitrary size (property 3, subsection 1.2 We first focus on
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neural operations and describe the ideal system: the aspire for. We then talk about the steps we took towards implementing that system.
3.1 THE IDEAL SYSTEM
In our system, we place a neural network at every point of an m x m grid (m up to 400 in our experiments), but in general, a different and flexible connectivity can be used. The ideal system would use the networks described in subsection 2.1 since, as we argued, they are likely able to compose general learners. At every point in time such network updates activations, weights and possibly hyperparameters hr, Wt, 1z = Fh W 1.)) Each network outputs a number of "actions" that affect other elements the cells of the grid. One fundamental action a network can take is to set the values of h. W, v of neighbouring cells. This action can be executed if certain conditions satisfied, such as the cell having enough energy the energy concept and its updates in our system are described later (this is a minimal criterion for an element, not an emergent individual). What does such action allow? We give few examples.
The first example is to copy u with a noise, set W's and h's to some random variables and keep v constant through the lifetime of any cell. This corresponds creating new mini- brain (consisting of one cell) that has very similar structure to the source and is untrained- in other words, a replication operation, but without replicating the learned content similar to way children are created.
The second example is to copy all the variables, with some noise. This creates copy with the same knowledge as the original cell.
The third example somewhere in between, transferring some knowledge and not other.
The fourth example is to have a joint set of weights for an aggregate of cells, and select out those which are used in a given copy, analogous cell differentiation animal bodies or bee specialization in a colony of bees.
The fifth example is setting the parameters (or some of them) something quite different programming them that causes new aggregates of cells to perform useful functions for the original such as collecting energy in effect creating useful machines for the original aggregate.
In the final example, again, the new cells are programmed, but this time with the goal of creating new aggregates that are better than the original. The aggregates can be thought of as both organisms and machines there is no distinction between the two our envi- ronment. Here, machines create better machines by both designing better brains and better bodies. Such process requires intelligence, which is exactly what we are aiming for. We believe there will be point in time in the evolution of the environment when this will hap- pen, creating a self reinforcing loop of improving intelligence. Having neural operations as the fundamental elements of the environment is the reason that makes believe that such state can be achieved in computationally tractable fashion in this type of system.
3.2 OUR PROPOSED STEPS TOWARDS THAT SYSTEM
Let us come back to describing the system we built. Since more powerful algorithms are not yet available, we use standard recurrent neural networks. We cannot use reinforcement learning to train these networks in direct way RL is an algorithm for optimizing an objective, which we fundamentally don't have here. We could try evolving such objective and such approach might be tractable. Instead we resort to what is usually done these situations simply evolve weights. We use the standard tanh recurrent network and the operation of setting the weight matrices and biases of new cell is simply copy with mutation. Alternative representation that common are compositional pattern producing networks (Stanley 2007).
The neurons, and all the other variables mentioned below (such as energy and chemicals), are placed on an m dimensional grid, with m up 400, Figure comprising up to 160k networks. The second action that a network can output is to move to a neighbouring cell, which will swap the content of this cell with the new (we experiment with allowing and disallowing this action).

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Elements are layed out on grid with the following layers
Actions:
Transfer energy
Transfer chemical
Make Enzyme
Set neurons state of neighbor cell (e.g. copy weights + noise)
Neurons Energy Chemicals Enzymes
Transfers:
Two cells create pull/ush
+
cell
cell2
cell3
Resulting flow: U1-U2
Figure 1: Diagram of the grid version of the system.
It is difficult implement rigid bodies on grid in Jax. To allow coordinated movements of larger units, we the neurons communicate. For example they can communicate all the cells belonging to given group to move. One way communicate is via local attention mechanism, where given cell can read values of the h of a cell in its neighborhood. This would also allow an aggregate of cells to implement deep neural network, having different units representing different layers of deep network. single pass through such network takes a number of world updates. In our case opt for simpler communication mechanism, because locally connected computation which local attention would utilize is not available in Jax. We create four signal layers that move in four directions (right, up, left, down). Each cell writes h into all the layers, which then move and each cell can then read the content of all four signal layers.
Next we introduce a type of physics into the system, other than motion. We consider fields of energy and fields of ne types of chemicals CI...., Cn, with typically 4 - 9, at every location of the grid. A given cell can pull or push all these quantities in each of the four directions, which costs it energy proportional to the push or pull. Neighbouring cells can "fight" for these quantities, and if an energy of a cell falls below threshold, the cell is declared dead and its weights are set to zero. The cell also produces enzymes Zi..., Zn. that control the reactions in the respective order (e.g. Za controlling C2- - C3). that cost energy to make and that sum to at most one. A given reaction releases energy equal to C,Z, except the last reaction which releases zero energy. As an example, to maximize energy, the cell should have one enzyme, say Zz. pull chemical C2 from outside (assuming some other cell is producing it), convert it C3 and excrete it to another cell. The cell also has a maximum lifetime and therefore it has to do something non-trivial (at least produce energy and copy) to propagate its information. If the population of live elements is below 10% we reawaken new ones with random weights. We also note that in our implementation, the elements themselves form autonomous units capable of self-replication, however, as discussed in section 2.2 in an ideal system they wouldn't.
There are two other variations that we experimented with. First we wanted know how simple can one make the system and still observe and interesting behavior. We created pure energy system, where instead of having chemicals, energy increases every location up to some threshold. In the second system we experimented with different implementation. Instead of having a network at every point of the grid, we consider π (1600) elements on m X m (200 200) grid that can move around. This time we used attention mechanism for communication within some distance between elements. We again only had a background energy, and the elements don't 't die or need anything for them to be "alive". They could just "sit around" (as atoms can). However, those that active, can acquire energy by moving (energy gets automatically absorbed) and copy their weight onto others that have lower energy. Those that do that will be the ones that propagate and overtake the system.

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4 EXPERIMENTS
We run the system explained in the previous section. More detailed explanation and the settings of hyper-parameters are in the Appendix. The code will be released in near future. What we observe is an exciting diversity among series of runs, with snapshots shown in the Figure 2 This is best It also shows the run of the system from the the start, showing
viewed in accompanying video | competition among various classes of elements.
Mym
37-
1.-
12--
DAS
Figure 2: Results of runs. Top row. We selected three random weights and plotted them RGB channels. This way elements with similar weights will have similar colour and those with differ- ent weights will likely have different colour. Bottom row. First three chemicals plotting RGB channels. Discussion. We see lot of diversity in the runs. These are best viewed in accompanying video. We often see coexistence of two species seen in two different colours in the same region of space. We also see that the elements moved the chemicals around creating regions of high and low densities. In the top left square, we see that the region low density is occupied by different species than the region of high density First graph Fraction of elements alive as a function of time from the start of the run (random new weights with no evolution in this run only). We see oscillatory behavior resulting from dynamics of two species. Second graph Energy content of elements in pure energy system of moving elements that need no energy to survive. However, those elements that collect energy can copy weights onto those with less energy, and those that do that propagate.
Looking closely the Figure 2 top, we see in several regions stable coexistence of two species of elements, represented by dots of different color in the same region of long amount of time, as can seen from the videos, meaning they found way to coexist, creating niches for one another.
space. These persists for
Furthermore, looking at the Figure top left, we see a light yellow region, containing two species, and orange region containing different, third species. We see that the chemicals have been moved to sub-regions space, and that the the species of the orange region live a place with less chemical density. Thus the elements created niches by modifying density of chemicals in the environment. The challenge is not simply to be able to reproduce alone, but in the presence of others.
There other types of behaviour observe. In smaller system, where diffused the chemicals everywhere quickly, and turned off evolution for stability (weights are reset if density is less then 10%) observed oscillations in population of species, Figure 2 middle (and in the video) is reminiscent the Lotka- Voltera system, (Lotka 2002). The behavior in the pure energy grid system usually results in one species, but there are instances of two. This is similar for the version of neural elements not living in a grid, In Figure 2 right we see that in this system, despite not having any survival notion or an explicit selection for energy, the elements learn to collect energy, this allows them to copy their weights onto others, which causes them to propagate.
Videos: Best viewed by downloading (not viewing the site): |ttps//biitll/33n6MMCI (3.2Gb). Com- pressed version (more blurry): httss//yautuheeiijjhhW..
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5 DISCUSSION
In this paper we proposed a framework for achieving intelligence by evolutionary process in an environment that is built out of interacting elements implementing computationally efficient and general learning. Only time will tell whether this framework is capable of such a feat. There are some critical advances that need to be made, most notably, creating general neural updates that can be evolved, or otherwise designed. Other directions for development are way these elements interact, their embedding in a space and the underlying physics.
We have created version of this system, that we believe has all the necessary components, or would have if we had more powerful learning updates. could form a starting point for the devel- opments outlined in the previous paragraph. We summarize the core properties of this system that are general to all instances of SIM. There are elements containing neural networks. These elements interact and communicate, forming larger units, in effect implementing larger networks. There is no objective based on which anything is selected. Instead, those compositions of units that find ways to propagate, will. There is distinction between organisms and machines. 'hhe elements can write into other clements, they can do this by copying, or they can write other information to build machines that are useful for their creators or they can create whole new autonomous machines. The machines can create both new "bodies" functional compositions utilizing physics, and new brains creating better algorithms than themselves.
A very intriguing question is what is the necessary physics needed for explosion of diversity and rise of intelligence. In the real world, the elements are elementary particles such as quarks and electrons. The former combine into protons and neutrons (there are few other particles such as photons), these combine into atoms. Few core atoms, primarily carbon, hydrogen, oxygen, nitrogen and phosphorus, form wide diversity of molecules in the form of proteins and other types of molecules, eventually building cells as a basic units life. What are the core rules that could give rise to complex life in the system propose, where fundamental units themselves can already exhibit complex interaction and behavior? Does one need to introduce a complex chemistry or classical physics? An intriguing possibility, that would like explore in the future is whether any built in complexity is even necessary? What we have the brain elements and only a basic rule that of energy? Will natural selection, with such general learners, progressively construct more and more complex structures that outsmart one another? These are some of the exciting questions we plan to study in the future.
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A APPENDIX
A.1 DETAILED DESCRIPTION OF THE SYSTEM.
We describe the system grid implementation in detail here. We consider grid of sizes varying from 100 100 to 400 x 400. At every location of the grid we have the following variables: Energy (real scalar), chemicals (ne real scalars, typically 4, but up to 9), enzymes (n. real scalars). We also have signals carrying information about various variables as we describe below. Finally, we have recurrent neural network variables (we describe the network next): hidden layer activations of

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Under review as a conference paper at ICLR 2021
size ny, (typically 16), input to hidden weights, hidden to hidden weights, hidden biases, hidden to actions weights and action biases.
Next, describe the neural network operations. At every point in time, except special times de- scribed below, we apply a classic recurrent neural network update to activations while keeping the weights fixed: h4 = tanh(W,, + Wi,h + by)) âz Wah, + das where W"s weights, h are activations and are variables from which actions are computed (as described below). In the above formula we dropped the time index from W's as they weren't 't updated at this time. The W's were updated at the following times: If one cell (grid element) took a specific action (copy + mutate) aimed at neighbour cell, if it had sufficient energy threshold) and if the neighbour cell was empty meaning having zero energy the weights and biases got copied with added noise to the other cell.
As mentioned in the text, we use this update because we haven't yet discovered a good forms of general update. In sections 2.1, 3.1 we propose that such update would take the form h,, We, 14 = F(h W 14-1) where ue are the hyperparameters of the update rules. The simplest analogue to the previous paragraph would be that at every point in time except the same special times, h, W's are updated (so the network can learn = update weights) while u's are fixed. Finally, during the special times, u are not merely copied, but the network can generate new u's in the neighbour cell, as well as h and W, allowing the originator cell to program the new one.
Next let us describe the energy chergycchemical dynamics within the cell. Energy is scalar that is bound between 0 and some max value. The chemicals transform in directions Z; + Z(i+1)modn i = 1,...,,A ne in proportion the amount of enzymes C₁ respectively and all the reactions release fixed amount of energy except for i = ne which does not release any. The released energy is added to the energy of the cell. If energy falls below threshold (by mechanisms described next), the weights and activations are erased set to zero We also use maximum lifetime of a cell after which the weights and activations are erased. The amount of enzyme as well as flows of quantities between the cells is controlled by the cell's actions which we describe next.
The cell has the following actions. 1. Copy action: from we extract five components and take softmax to decide where and if to copy (0 - do not copy. 1-4 copy to one of the four directions). If a copy is successful, fixed energy (tending to be large) is removed from the cell. 2. Move action: This is optional. If enabled, it has the same logic, but this time, the full content of the two cells (originator and target) swapped. 3. Energy flow: The four values determine the proportion of energy the cells want to suck from each neighbour The cost of such action is proportional to the push. The resulting flow between two cells is obtained by subtracting the values of actions from the two cells, allowing two cells to fight or cooperate in moving the energy. 4. Chemical flow: The same logic but for each chemical. There are 4n, values, one for each chemical and direction. 5. Enzyme production: n. actions that create each enzyme. The total amount of enzyme is normalized to be at most one. There are two extra features. The energy is normally protected from falling below a threshold (protecting the cell from accidentally killing itself). The exception is that if the energy pull from the neighbour is sufficiently large, it will pull all the energy and kill the other cell (erase its weights and activations).
push to the neighbour (positive
negative).
Finally there are signals. The cells need to know about what is happening at the other cells and to communicate to form larger aggregates and networks. We implemented the following communica- tion. There are four information grids one moving in each of the four directions. At every point in time, each grid moves in its direction. In addition, part of activations as well as energy, chemicals and enzymes overwrite to information grids for those cell for which energy is above threshold. The neural network input is formed by concatenating the four information grids at a given location.
Finally each run of the system was run on single GPU, and the largest system size 400 x 400 at n4 = 16 (160000 networks) was determined by the largest size we could fit into GPU memory.
12


Reviews:
[{"review_id": "luPF-nIPNsP", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 1, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper describes a framework for artificial life, where basic building blocks are artificial neural networks (ANN) elements (matrix multiplication, and other linear algebra operations), intended to be open-ended and without any guiding objective. The authors emphasis that in their proposed approach there is no predefined distinction between environment and agents, as they attempt that the 'physics' of their proposed framework allow agents to emerge on their own. \n\nPros:\n- The paper is very well written. Language is clear at times, the paper is well organized and the there is no overuse of math notation.\n- The framework advanced by the authors seems solid enough to experiment on the emergence of life. \n- Results need to be further analyzed, but they are encouraging at this stage of the research.\n- Paper provides in-depth, or even philosophical, discussion relating topics such as emergence of life and current advances in computer science. It is very re-freshing to read a paper that is not only about surpassing other methods by a marginal score in benchmark datasets.\n\nCons:\n- Although the paper provides a thorough discussion on related work, it is surprising that it does not make more emphasis on results related to cellular automata. Conway's Game of life seems to comply with their main aim at developing an environment where no distinction between agents and environment is made, and where agents emerge on their own. It would be good if authors provide a bit of contrast discussion on this issue.\n- There are some strong claims across the paper or concepts being left without neither references or definitions. For example:\n1. In Sec. 2.1 authors introduce the concept of \"general intelligence\". What exactly does that mean?\n2. Also, in Sec. 2.1 authors claim that human brain computation closely resembles recurrent networks, but they do not provide a reference that backs such strong statement. Last time I check, there was little evidence that processes similar to backpropagation were happening in the brain, let a alone that artificial neurons models are now considered poor approximations of actual neurons.\n3. The whole idea that life is objective-less can be controversial. A recent hypothesis [1] actually suggests that the life's objective is to accelerate entropy, that is, that emergence of life-like molecular structures, and even evolution itself,  are only a consequence, or even a particular case, of second law of thermodynamics. Authors should be more careful when dealing with such motifs.\n\nReferences:\n1. England, J. L. (2013). Statistical physics of self-replication. The Journal of chemical physics, 139(12), 09B623_1.", "extra_scores": {}, "extra_text": {}}, {"review_id": "HoXRXlOMXG6", "reviewer": "AnonReviewer2", "summary": "", "questions": "", "limitations": "", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The work follows the idea of artificial life on a computer and proposes to use RNNs as building blocks with simple rules of exchanging information between those individual RNNs on a grid. \n\nThe main weakness of this submission is the lack of the mathematical formulation of the algorithm that is used for generating the complexity. There are only two formulas in the manuscript: sections 2.1 and 3.1, which basically say that the authors consider a general dynamical system in discrete time with many degrees of freedom. This is not sufficient to explain the mathematical procedure used to arrive at figure 2. \n\nThere are many non-linear dynamical systems that can generate complexity (some of them are mentioned in the manuscript). Typically, the larger the number of degrees of freedom is, the more complex behaviors one obtains. The authors consider an extreme case when the overall dynamical system is composed of a collection of RNNs, with synaptic weights learned using some learning rule (unspecified in the manuscript). It is not surprising that a non-linear system with so many degrees of freedom can produce complex behaviors. \n\nThe authors present beautiful pictures of weights produced by their system. However, I do not understand if the authors are claiming that their dynamical system is somehow more meaningful than other more traditional counterparts. If so, I would appreciate a mathematical definition of the system considered, and a justification of this claim.  Or maybe the authors are saying that the precise mathematical form of the update rules for h and W is not important (and that’s why they don’t write them down explicitly in the manuscript) because they belong to some universality class, which often happens in studies of non-linear systems. Then, it seems necessary to provide evidence for this claim.  \n\n——————————\n\nThank you for your response. I have read the revised paper and the discussion with other reviewers. While I still think that the overall problematic discussed in this paper is important, I am not satisfied with the revisions. I think the paper would benefit from more technical content and clear mathematical definitions of the procedures used. I have updated my score to a reject. \n", "extra_scores": {}, "extra_text": {}}, {"review_id": "GTgZkFG7gj-", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This is an interesting paper that proposes a particular Alife framework to study the question of how to create an AI-generated algorithm. In the proposed system, each cell in a 2D grid-like environment is controlled by a different neural network. As far as I understand it, these neural networks are randomly mutated without rewarding the overall system for any particular objective. The authors study some of the dynamics that emerge from this framework.\n\nWhile the main ideas in this paper are exciting (especially they idea that there is no direct concept of an agent),  it currently feels more like a workshop paper than a fully-fledged ICLR paper. Results are very preliminary, and while the emerging dynamics look interesting, the paper is missing a more systematic study of how different settings effect them. Additionally, I am slightly sceptical how these interesting patterns can lead to actual AI-generating algorithms. Without a task or some minimum criteria, what would drive the evolution of this system towards increasing complexity?\n\nIt would also be useful to further highlight the implications of this work for the larger ML and ICLR community. While certainly of interest to the Alife community, the potential importance of Alife domains for learning representations should be mentioned in more detail.\n\nAdditionally, some related work on neural cellular automates is missing:\n- Growing Neural Cellular Automata, Mordvintsev et al.\n- CA-NEAT: Evolved Compositional Pattern Producing Networks for Cellular Automata Morphogenesis and Replication. Nichele et al\n\n[After rebuttal: Increased my score from 4 to 5. Still think the approach needs some more work to appeal to the broader ML community and in its current state would be best suited for a conference focused on Alife]\n", "extra_scores": {}, "extra_text": {}}, {"review_id": "Fcl-dEivMLy", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "\nThis paper discusses an artificial life approach to artificial intelligence, through 1) first discussing some general principles that may be useful in artificial life/chemistry systems from the perspective of open-endedness; 2) sketching an experimental system aiming to implement these principles and showing preliminary qualitative results. While the paper discusses a number of ideas that are highly relevant to AI and should be better known by the AI community, the paper has also some weaknesses and is not currently in a form that is ready for publication.\n\nStrengths:\n+ This paper's topic is a nice opportunity to enable the AI/ML community to know better about Alife approaches to artificial intelligence\n+ The particular topic of open-endedness is also highly relevant, including in the perspective taken in this paper where one aims to model complex dynamical systems that do not assume a pre-defined concept of agent/individuals. This is useful in helping researchers in the AI community to deconstruct some of the assumptions of the models they are working on\n\nWeaknesses:\n- The paper does not explain clearly the relevance of the Alife approach to AI, in particular it does not explain well the historical roots of this idea that could enlighten AI readers (e.g. discussing foundational work such as Brooks and Steels, 1995), and does not analyze what fundamental contributions where made in the past, and what were the limits.\n- Related to the point above, the paper does not position itself clearly in this vast literature: both the general/theoretical ideas and the experimental framework discussed overlap significantly with the large body of work in Alife. Clear statements of contributions would be useful.\n- It is not clear what is the concept of \"(general) intelligence\" considered here, and whether there is a real value/utility in using this word, as opposed to saying the family of systems discussed in the paper is for studying the \"self-organization and evolution of complex structures\". Formulating the general problematics around theoretical questions on the origins and evolution of complexity would also enable better linking with the literature in the sciences of complexity and theoretical biology, which is not sufficiently made in the current version of the paper.\n- It is not clear what is the logical rationale of the listing of principles considered in the paper: what is the scientific objective of this list of principles? how can one measure/evaluate their utility? where do they come from? Also, there seems to be some (at least apparent) inhomogeneity between them, e.g. point 1 says \"there should be no built in notion of an individual\", but point 2 says \"the evolution of new emergent individuals create novel opportunities...\" --> point 1 reads like an assumption while point 2 reads like a desirable emergent property.\n- The proposed SIM system lacks formal definition (e.g. precise pseudo-code enabling precise understanding and reproducibility)\n- While the paper aims for a general system with \"general neural network controllers inside much fewer elements\", in practice the system appears to have a lot of specific elements (e.g. physical/enzymatic systems) that are less generic than several recent work generalizing cellular automata as grids of neural networks with multiple kernels, e.g. Chan, 2020; Mordvintsev et al., 2020; Gilpin, 2019. Thus, it is not clear which properties are more general/differ/more useful than these other works\n- There is no proposed methodology for evaluating the success/failure/progress of the approach: e.g. how could one characterize the self-organized structures that are qualitatively observed in the preliminary runs presented in the paper? What are precisely the scientific questions addressed by experiments, and how can experiments answer them?\n\nI recommend the author(s) frame more precisely their work in terms of scientific objectives and links with the conceptual history of alife approaches to AI. The framing of the scientific objectives would benefit from a clear formulation of the scientific questions addressed, and a strategy for measuring progress towards answering them (in addition to the strategy for developing experimental tools presented in the paper, which requires more details to enable better understandability and reproducibility). \n\nReferences:\n\nBert Wang-Chak Chan. Lenia and expanded universe. arXiv preprint arXiv:2005.03742, 2020.\n\nBrooks, R. A., & Steels, L. (Eds.). (1995). The artificial life route to artificial intelligence: building embodied, situated agents. L. Erlbaum Associates.\n\nWilliam Gilpin. Cellular automata as convolutional neural networks. Physical Review E, 100\n(3):032402, 2019.\n\nAlexander Mordvintsev, Ettore Randazzo, Eyvind Niklasson, and Michael Levin. Growing neural cellular automata. Distill, 2020. doi: 10.23915/distill.00023. https://distill.pub/2020/growingca.", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper proposes a framework for artificial life. In the framework, there is no primitive agent construct, but rather a set of basic recurrent network components (such as linear algebra operations). The framework is open-ended and objective-less. The authors describe the emergence of different organisms out of these building blocks, illustrating the idea with a simplified implementation.

The paper is extremely original, at least in the context of the deep learning/ICLR community. At the same time, together with a majority of reviewers (mostly experts in relevant topics such as neuro-evolutionary methods and artificial life), I felt that this work is not ready to be presented at a major conference, for three main reasons. 1) It should make its links to the huge literature on artificial life outside the ICLR community clearer. 2) The empirical work is somewhat limited and 3) this is not counterbalanced by a clear theoretical roadmap.

I thus do not recommend acceptance, although I really hope the authors will present a more thoroughly worked out version of the paper soon.

Decision: Reject