Large Language Models (LLMs) such as GPT-4, Grok and Claude have revealed striking behaviors that seem to emerge as these models grow in scale. Certain abilities – from arithmetic and translation to common-sense reasoning – appear suddenly when the model’s size or training reaches a critical threshold, rather than improving smoothly from smaller models. This phenomenon has puzzled researchers, as it suggests qualitative shifts in behavior akin to phase transitions in physical systems. To shed light on these observations, we can turn to Hermann Haken’s synergetics, an interdisciplinary theory of how patterns and order emerge in complex systems. Synergetics provides conceptual tools – order parameters, the slaving principle, bifurcations, and self-organization – that can help us interpret LLM behavior in a new light.
Synergetics was originally developed to explain how coherent structure arises in systems ranging from lasers and fluids to biological organisms. It views a large system of many interacting parts as capable of spontaneously organizing into ordered patterns when driven beyond a critical point. In this article, we draw parallels between synergetics and modern LLMs. We will use synergetic concepts to qualitatively explain real phenomena in LLMs: the emergence of new capabilities at scale, the power-law scaling laws that govern performance, sudden “bifurcation-like” transitions in behavior, low-dimensional structures in high-dimensional neural networks, and the hierarchical organization of information across neural network layers. Our goal is to develop an intuitive, conceptual bridge between Haken’s physics-inspired framework and the observed behavior of today’s large neural networks – without using heavy mathematics. By doing so, we aim to provide both general scientific readers and machine learning researchers with a fresh perspective on why LLMs behave as they do, grounded in well-established principles of self-organizing systems.
Synergetics in a Nutshell: Order from Chaos
Synergetics, as formulated by Hermann Haken, is the science of self-organization – how order spontaneously arises in large systems of interacting parts. Classic examples include the formation of a laser beam out of random light emission, or the emergence of convection cells in a heated fluid. In synergetics:
- An open system with many nonlinear interacting subunits can organize itself into a coherent pattern when driven far from equilibrium by some external energy or input. In other words, if the conditions (the control parameters) are right, the system “chooses” an ordered state out of many possibilities.
- A central concept is the order parameter. This is a variable (or a few variables) that describes the macroscopic, collective behavior of the system. Near the onset of order, typically only a few modes or degrees of freedom become unstable and grow – these define the order parameters (for example, the amplitude of a laser’s dominant light wave, or the degree of alignment of spins in a magnet).
- Haken’s slaving principle states that once these slow, collective modes (the order parameters) emerge, they enslave the remaining microscopic degrees of freedom. The myriad of other possible micro-variations become slaved to the global pattern: they adjust rapidly to whatever the order parameter dictates, instead of evolving independently. This leads to a dramatic reduction in the effective degrees of freedom of the system as it becomes ordered. In essence, the macro-level pattern calls the shots, and the lower-level components fall in line.
- Self-organization often involves bifurcations or instabilities: as a control parameter is smoothly varied, the system can reach a critical threshold where the previous state becomes unstable and a new stable state (with a new order parameter) appears. This is a qualitative change in behavior – for example, a fluid suddenly forming convection rolls at a critical temperature difference, or a laser suddenly beginning to emit coherent light at a threshold pump power. Beyond the threshold, the order parameter grows from zero to a finite value, indicating the onset of a new collective regime.
- Importantly, the details of each microscopic interaction often don’t matter for the large-scale pattern – the system exhibits universal behaviors largely determined by the order parameters and symmetry, not by every tiny detail. This is why synergetics can draw analogies between, say, a laser and a chemical reaction: the mathematics of their self-organization can be similar even if the components differ.
To make this concrete, consider Haken’s favorite example: the laser. Below the threshold, each atom in the laser medium emits light independently and incoherently – just random, uncorrelated photon emissions (analogous to noise). Above the threshold, a single frequency mode of light suddenly dominates: all the atoms’ emissions lock in phase to produce a coherent laser beam. The amplitude of this coherent light mode is an order parameter – it was zero when the light was just noise, and it becomes nonzero above threshold. That collective light field then slaves the atoms’ behavior, forcing their individual emissions to stay in sync. In short, a whole new level of order emerges: the system went from chaos to an organized pattern (a beam of laser light) once the critical point was passed.
With these concepts in mind – order parameters, slaving of components, bifurcation thresholds, and self-organization – let’s turn to large language models. An LLM, like a brain or a laser, is a complex system: it consists of many simple nonlinear elements (artificial neurons in a neural network) interacting and adapting through training. We will see that as LLMs scale up or undergo training, they too exhibit emergent order and collective behavior strikingly reminiscent of synergetic systems.
Emergent Abilities as Bifurcations in Model Scale
One of the most intriguing observations about modern LLMs is the emergence of new capabilities at certain scales. For example, DeepSeek R1 (with 671 billion parameters) demonstrated a surprising ability to perform tasks via few-shot prompting – something smaller models could not do. Researchers have systematically found tasks (from arithmetic to symbolic reasoning to translation) where model performance remains near chance for smaller models, then jumps to a high level once the model exceeds a certain size or training compute budget. These sudden jumps are emergent abilities. In synergetic terms, we can think of model scale (number of parameters or amount of training) as a control parameter. As we dial this parameter up, the LLM undergoes a phase transition in its behavior: a new “ordered” behavior (a new capability) appears abruptly at a critical point.
Analogy: It is as if an LLM is water being cooled – for a long time it remains liquid (no new capability), but at 0 °C it crystallizes into ice (a new structured capability appears). Just as water’s properties change qualitatively at the freezing point, an LLM’s performance on certain tasks changes qualitatively when it crosses a threshold in model size or training. Below the threshold, it essentially lacks the skill (performance near zero, akin to random guessing); above the threshold, it demonstrates the skill with confidence (performance leaps to a high level above chance). This qualitative shift is the hallmark of a bifurcation-like transition. Indeed, researchers explicitly note that these emergent behaviors “cannot be predicted by extrapolating” the smooth performance gains of smaller models – instead, “performance is near-random until a certain critical threshold… after which it increases to substantially above random”, a change “known as a phase transition” in complex systems.
For instance, one study observed a sudden jump in translation quality (measured by BLEU score) for French-to-English once a model reached a certain scale, whereas smaller models showed only poor performance. Another famous example is arithmetic: models below a certain size are basically guessing on multi-digit multiplication, but beyond a threshold (around tens of billions of parameters), accuracy leaps upward dramatically. In a survey of emergent abilities, many tasks showed “abrupt, non-linear performance jumps at specific model scales” – behavior highly reminiscent of how, say, a magnet’s magnetization jumps from zero to finite at the Curie temperature. The emergence looks like a new order parameter turning on in the system – a new global mode of behavior (such as “being able to do arithmetic reasoning”) that was absent before. We can say that this capability was latent and unstable in smaller models but becomes stable and dominant once the model is large enough (analogous to an unstable mode becoming an active order parameter after a bifurcation).
It’s important to note that not every aspect of LLM performance is discontinuous. In fact, neural scaling laws show that overall performance (e.g. the model’s average loss or perplexity on language modeling) improves smoothly as a power-law as models get bigger and are trained on more data. Over many orders of magnitude of scale, larger models steadily get better in a predictable way. This is akin to the “continuous” parameters in physics that change gradually (like the decreasing noise in a laser as you approach threshold). However, these smooth gains sometimes conceal sharp transitions on specific tasks. If we use a fine-grained metric or zoom in on a particular capability, we discover the leaps. Synergetics offers an explanation: a system can have an overarching smooth trend (e.g. decreasing energy or loss), yet still undergo phase transitions where the qualitative state shifts. The smooth background improvement is like steadily cooling water, and the emergent ability is like the sudden freezing.
In summary, the concept of a critical threshold and phase transition in synergetics maps well to emergent abilities in LLMs. The model’s scale or training acts as a control parameter. Once it passes a critical value, a new “collective mode” of behavior materializes that was not present (or was negligible) before. This analogy not only helps describe what we see, but also frames a question: why does a particular ability become viable only at large scale? Synergetics would suggest that below threshold the would-be order parameter is suppressed (perhaps drowned in “noise” or competing factors), but above threshold it can overcome damping and self-amplify. Some recent theories indeed propose that emergent abilities arise from the resolution of competition between different learned “circuits” in the network – for example, a trade-off between rote memorization and generalization that only tips in favor of generalization (a new skill) when the model is sufficiently large. This is analogous to how, in a phase transition, two phases compete and one wins out beyond the critical point.
From a practical standpoint, this synergy view means that building larger models isn’t just incremental – it can unlock fundamentally new regimes of behavior. Just as one might need to reach a certain temperature to get a laser or a superconducting state, one might need a certain model size to get high-quality reasoning or abstraction. In the next sections, we delve deeper into synergetic ideas of order parameters and slaving, to see how an LLM’s behavior might be dominated by only a few effective degrees of freedom despite its enormous complexity.
Order Parameters and Low-Dimensional Structure in LLMs
An LLM like GPT-4o has on the order of 1012 parameters and processes information in thousands of dimensions (hidden neuron activations, embedding vectors, etc.). Yet, researchers have been finding that the actual effective dimensionality of certain neural network behaviors is much lower. This resonates strongly with the synergetic idea that a few order parameters capture the macroscopic state, while many microscopic degrees of freedom are redundant or “slaved.” How can we identify possible order parameters in an LLM? Let’s consider a few perspectives:
- Global representation of context: When an LLM reads a prompt, it transforms it into an internal vector representation (for example, the hidden state of the model at the final layer). This vector condenses the information from all the words in the prompt into a single abstract representation. We might think of this as an order parameter of the prompt-processing system – a collective variable summarizing the state of the input. It has a determined value for that prompt and will largely dictate the model’s next output. In a sense, the entire swarm of neurons’ activities is distilled into this vector, which then “enslaves” the word prediction that follows. If the model’s response can be changed in predictable ways by manipulating just one or two aspects of this vector (say, one direction corresponds to formality of tone, another to topic), those aspects act like order parameters for the style or high-level content of the response. Indeed, anecdotal evidence from model probing has found single directions in the latent space corresponding to broad attributes (for example, a “sentiment neuron” was once discovered that largely governed whether a generated movie review was positive or negative). Such findings hint that the model internally might use a few summary features to control global aspects of the output – much as an order parameter controls the overall pattern of a system.
- Low-dimensional manifolds in weight space: Even though the weight matrices of a network are huge, their effective rank or the spectrum of significant directions can be small. Empirical studies have shown that, after training, neural networks often have weight matrices or gradients with a characteristic “bulk and outliers” spectrum. For instance, when examining the Hessian matrix of the training loss (which is a measure of how sensitive the loss is to changes in different parameter directions), researchers found that most eigenvalues are near zero (a large bulk), but a few eigenvalues are much larger, sticking out as outliers. Notably, the number of large outlier eigenvalues has been observed to often match the number of classes or tasks the network is trained on. This means effectively only a small number of directions in the high-dimensional parameter space really matter for the network’s learned function – those are the stiff directions where changing parameters makes a big difference in output, whereas moving in the other many directions has negligible effect (they’re “flat” dimensions). In one study, it was noted that the gradients during training lie mostly in the subspace spanned by those top Hessian eigenvectors – the gradient descent updates happen in a very low-dimensional subspace of the full parameter space. Moreover, this subspace (the top eigen-directions) “emerges early in training and remains well preserved” as training progresses. All of this is a strong parallel to the idea of order parameters enslaving fast modes: the few large-eigenvalue directions are like the unstable modes that drive the dynamics (order parameters), and the numerous small-eigenvalue directions correspond to stable modes that quickly relax and have little influence (slaved variables). The network swiftly suppresses or neutralizes changes along those trivial directions, while the important directions govern the outcome.
- Neural collapse and feature simplification: In supervised deep learning (e.g. image classification networks), an intriguing phenomenon called “neural collapse” has been observed at the final layer. As the network trains to classify, the internal features for each class cluster together, and those cluster means arrange themselves in a simple symmetric configuration (like the corners of a simplex). The last-layer classifier basically aligns with these means. In effect, even if the network had hundreds of neurons in the penultimate layer, by the end, all images of “cat” might end up on one direction, all images of “dog” on another, etc., with only a small number of unique directions equal to the number of classes. This is a dramatic reduction of dimensionality – the network has self-organized such that the variability within a class is collapsed. This again is the emergence of a few collective variables (one per class, perhaps) out of many degrees of freedom. While LLMs deal with continuous language rather than discrete classes, similar compression of information likely occurs for certain structured tasks or concepts. The network may effectively use a limited basis of conceptual vectors to represent a vast variety of inputs.
From the synergetics perspective, we would say the LLM exhibits “an enormous reduction of degrees of freedom” once it’s organized. The pattern of activity (or the function it computes) can be described by a few dominant modes – its order parameters. The rest of the degrees (neurons or weights) either coordinate to support those modes or fluctuate around them without contributing to the large-scale behavior. In Haken’s words, the system’s macro-state is governed by only a few collective variables, and this is largely independent of the microscopic details. This might explain why different LLMs trained on similar data (even by different teams) end up with broadly similar capabilities: the specific weight values can differ, but as long as they span essentially the same crucial feature subspace (the same order parameters), their high-level behavior will be alike.
One striking piece of evidence for this in neural networks is the observation that a network’s performance can often be preserved even if you randomize a large fraction of its weights, as long as you keep the important weight subspace. For example, one can prune or compress networks heavily or even project the gradients to a smaller subspace without too much loss in performance, implying that not all weights carry independent information – many are redundant or “enslaved” to the important ones. All these findings align with the idea that what an LLM learns is not a billion separate facts, but rather a structured, low-dimensional representation of the world encoded in a very high-dimensional system. The magic of the training process is that it finds those few needles (order parameters) in the haystack of possibilities.
The Slaving Principle: How Few Features Guide Many Neurons
We’ve hinted at the slaving principle in the above discussion, but let’s explicitly connect it to LLMs. In synergetics, once an order parameter emerges, it enslaves the fast variables – meaning the whole system’s detailed components now quickly adjust to support the global pattern, rather than evolving on their own agenda. How does this manifest in a large language model?
Think of the billions of individual neuron activations and attention heads in a transformer model at any given time. When the model is processing an input (say a paragraph of text), each layer’s neurons interact and pass information. By the final layer, the model produces a probability distribution for the next word. Now, not every neuron is equally important in determining that output – often, a few latent features will dominate the decision. For example, perhaps one dimension strongly indicates the topic is “sports” vs “politics”, another dimension indicates the sentence is a question needing a question-mark, etc. These high-level features constrain what the next word can logically be. Once those features are set, the vast majority of neurons are just filling in details (adjusting slight nuances of phrasing, etc.). In effect, the microscopic activity of countless neurons is enslaved to the high-level intent and context captured by those crucial features.
Hermann Haken explicitly drew an analogy in the context of biological brains: “the brain is conceived as a self-organizing system operating close to instabilities where its activities are governed by collective variables, the order parameters, that enslave the individual parts, i.e., the neurons”. We can borrow that description almost directly for an artificial neural network: a trained LLM can be seen as operating in a poised regime where a few collective modes (learned features) govern the activity of all the neurons. The individual artificial “neurons” in the network fire in synchrony to realize the directive of those order parameters.
During training, the slaving principle is apparent in how quickly the “unimportant” directions in weight space settle down. As mentioned, the gradient descent updates concentrate in a low-dimensional subspace. One can imagine that early in training, the model discovers a few key patterns (e.g. how to represent basic syntax or common words) – those are like nascent order parameters. Subsequent training then largely tweaks those patterns and brings other weights in line with them, rather than creating completely independent new patterns. The fast degrees of freedom (many weights) relax under the influence of the learned features. This is analogous to how, in a laser above threshold, the microscopic fluctuations (individual atomic emissions) quickly damp out except in directions that reinforce the coherent field. In an LLM, once a pattern of solving a certain linguistic task is established, additional training examples mostly serve to reinforce that pattern and align other parameters to it, rather than invent a wholly new solution.
During inference (text generation), we also see slaving in effect. Consider that an LLM often produces very coherent and contextually consistent text. This means all the neurons across all layers are working in concert to maintain a single narrative or line of reasoning. If the model has determined (via its order parameters) that the user’s prompt is, say, a question about physics, then as it generates the answer, thousands of activations will align to ensure the answer stays on-topic and uses factual, scientific language. It’s not the case that half the neurons are trying to veer off-topic – they have been effectively enslaved to the overarching context. If a rogue activation pattern deviates (analogous to a fluctuation), the network’s dynamics quickly suppress it or ignore it, because it doesn’t align with the strong context signals. In technical terms, the attention mechanism and residual connections in a transformer facilitate this – they allow salient information (like the order-parameter-like context vectors) to propagate and dominate the computations, while subdominant signals get overwritten or muted.
Another way slaving shows up is in the speed of adaptation: when you prompt an LLM with a new context, the lower-level neurons (like earlier layers that detect word patterns) adjust their firing almost immediately to conform to the demands of that context. They are not carrying on with some autonomous behavior; they are driven by the input and the higher-layer representations that are being formed. This is analogous to how, in a synergetic system, lower-level variables adiabatically follow the slowly changing order parameters. The lower layers in a neural network are often said to extract “surface features” (like words or syntax) which are then organized by higher layers into semantic or abstract features. Once the higher layers settle on a semantic interpretation, the lower layers’ role is essentially to support that – they funnel up the relevant details and ignore irrelevant ones. The enslavement here is the fact that the activity of earlier neurons is largely determined by the requirements of the later neurons (which carry the global meaning). In physics language, the high-level pattern imposes boundary conditions on the micro-level dynamics.
To put it succinctly: In an LLM, the whole network dances to the tune of a few key melodies (features). Those melodies are the order parameters – perhaps an internal notion of topic, intent, sentiment, etc. – and once they start playing, every neuron synchronizes to keep the output coherent. Just as a conductor sets the tempo and the orchestra members follow, the order parameters conduct and the neurons follow. Empirical evidence for this in language models can be subtle, but it appears in phenomena like coherence over long text generation. Despite the many opportunities for divergence in a long generated paragraph, the model often maintains consistency (staying on topic, preserving character personalities in a story, etc.), suggesting a persistent guiding variable (like “what is the story about”) that enslaves the local word-by-word choices. Without such an implicit global variable, the output would wander aimlessly.
Thus, Haken’s slaving principle offers a satisfying explanation for why large neural networks don’t collapse into gibberish despite their complexity: once the model commits to a high-level pattern, everything else in the network is constrained by that commitment. And this happens not by explicit programmer design, but as an emergent property from training: the network learns to organize itself in this hierarchical, coordinated way because that’s the structure present in language data (language has topics and contexts, which impose constraints on word choice).
Hierarchical Self-Organization Across Layers
Modern LLMs (especially transformer-based models) are typically organized into layers – each layer processes the data and passes it to the next. Interestingly, even though all layers in a transformer have the same basic structure, they end up specializing in different aspects of the task. In BERT and similar models, it has been observed that “surface features [like word morphology] are captured in lower layers, syntactic features in middle layers, and semantic features in higher layers.” In large GPT-style models, a similar hierarchy is often noted: early layers focus on short-range patterns (e.g. spelling, local grammar), middle layers on longer-range syntax and coreference, and later layers on high-level semantics and world knowledge. This layered specialization emerges without being explicitly hard-coded; it is discovered by the model during training. We can view this as a form of self-organized hierarchy, where each layer corresponds to a different scale or level of description of the data – very much in line with synergetic thinking.
Haken’s synergetics was not limited to just one level of order; in complex systems, you often get hierarchies of order parameters. For instance, in the brain, one might identify order parameters at the level of local neural assemblies and also at the level of large brain regions – a nested hierarchy of collective variables. Similarly, in an LLM, we can think of order parameters at each layer: each layer’s outputs can be seen as order parameters for the layer below (since they constrain the lower layer’s activity via the residual or feedback connections), and as micro-variables for the layer above (which will treat them collectively to form its own higher-order features). In other words, layer L sees the emergent patterns of layer L-1 as its “microscopic” inputs and then finds a higher-order pattern spanning several of those. This builds a hierarchy of patterns-of-patterns, very reminiscent of how nature often has structures within structures.
From the perspective of self-organization, each layer in the network self-organizes to produce a useful representation for the next layer. Early in training, the layers might be more or less interchangeable, but as training proceeds, a form of symmetry breaking occurs: the first few layers become different in function from the last few layers, despite being architecturally identical. This is analogous to how a uniform medium can spontaneously break symmetry and form a patterned state. For example, in a fluid that’s heated, initially all levels are the same, but after reaching the convection threshold, distinct layers of circulating fluid appear (hot rising, cool falling). In an LLM, after training, the “lower” part of the network consistently does something different (concrete pattern extraction) while the “upper” part does abstract integration. The training process provides the driving force (like heating the fluid) that induces this structured flow of information.
We can illustrate this with a concrete example from research: A recent analysis compared a smaller LLM (with 28 layers) to a much larger one (with 80 layers) in terms of what each layer encodes. In the smaller model, there was a clear progression – item-level facts (like whether a word is an animal or food) peaked in early layers, pairwise relations peaked in middle layers, and complex analogies peaked in somewhat later layers, then everything fed into a general understanding by the top. This matches the expected hierarchy (specific → general). In the larger 80-layer model, the researchers found an even more complex pattern: there were fluctuations where certain mid-layer groups would again become focused on intermediate relations after a period of more abstract processing, and adjacent layers would coordinate by alternating their focus. This suggests that at very large scales, the model may develop multiple hierarchical modules or repeating patterns of processing – an emergent architecture on its own. It’s as if the model had several “phases” of processing, perhaps analogous to multi-stage reasoning. This too can be seen as synergetic: sometimes large systems can have multiple pattern-forming instabilities and layered structures (like oscillatory patterns within patterns). The key point is that none of this hierarchy was predefined by programmers; it self-organized from the optimization process, reflecting the structure of language tasks.
From a synergetics viewpoint, we could say each layer’s emergent properties become the substrate for the next layer’s self-organization – a recursive application of order parameters enslaving the layer below. The entire deep network can be seen as a multilayer dynamical system, where each layer operates near an instability (sensitive to inputs) and generates an order parameter (its output features) that influences the next layer. If we imagine “zooming out,” we see coherent behavior at the scale of the whole network: an intelligent response to an input, which is built from these layer-wise transformations. The far-reaching macroscopic order is strikingly independent of microscopic details of any single neuron. For example, two different LLMs might have completely different internal weight values, but both organize into a similar hierarchical processing of language (because that’s the natural structure of the problem). This is analogous to how two samples of the same ferromagnetic material can have different micro arrangements of atoms but will exhibit the same magnetization vs. temperature behavior macroscopically.
Analogy: Consider a large company (the organization) trying to respond to a complex project. The process may self-organize hierarchically: individual workers handle simple tasks, team leaders synthesize those into sub-projects, and upper management integrates everything into the final product. Each level emerges to coordinate the level below it. If done well, the whole company produces a coherent result (like an LLM’s coherent answer). In this analogy, the company is not explicitly designed by an external hand to have, say, exactly three layers of hierarchy – it evolves that way for efficiency, and the exact number of middle managers might vary. What matters is the principle of hierarchical coordination. LLMs similarly developed an implicit chain-of-command among neurons across layers, through the guidance of the training data.
Toward a Synergetic Understanding of LLMs
By viewing large language models through the lens of synergetics, we gain a conceptual framework for understanding their remarkable behaviors. Emergent abilities in LLMs are not magical occurrences, but rather analogues of phase transitions, where a quantitative accumulation of scale leads to a qualitative leap in capability. The synergetic concepts of order parameters and enslavement help explain why a model with billions of parameters can act as if it has only a few degrees of freedom guiding it – because, in effect, it does: a few broad features or directions in activation space dominate its decisions, and the rest of the neurons rapidly fall in line to support those features. The self-organized hierarchical structure of LLMs, with different layers specializing in different aspects of language, mirrors the multi-scale organization seen in many complex systems, from the convection rolls of fluid dynamics to the functional layers of the human brain.
Crucially, this synergy-based viewpoint stays close to what we observe in current models, avoiding fanciful speculation. We did not invoke any mysterious new physics or claim LLMs achieve consciousness; we simply used a well-established theoretical language (originally developed for lasers and chemical reactions) to describe phenomena like scaling laws, emergent tasks, and network interpretability findings in LLMs. The benefit of this perspective is that it emphasizes qualitative understanding: we see LLM development not just as engineering trial-and-error, but as navigating the phase space of a complex system. Concepts like “critical thresholds” or “collective modes” give us intuitive handles for why making a model bigger might suddenly let it do logic puzzles, or why two very different architectures might end up with similar capabilities if they tap into the same order parameters of language.
For interdisciplinary scientists, drawing this connection demystifies some of the hype around LLMs: these models follow the same deep principles of self-organization that many natural systems do. For machine learning researchers, the synergetic view could inspire new metrics (e.g. identifying order parameter-like variables in networks), new training regimes (perhaps keeping the system near criticality to enhance emergent features), or simply a better mental model for anticipating how adding data or parameters could transform model behavior.
In Hermann Haken’s legacy, synergetics was about finding unity in diversity – explaining very different phenomena with a common set of principles. It is fitting, then, that we apply it here to reconcile the behavior of artificial neural networks with patterns we know from nature. An LLM, after all, is a composition of many simple units yielding something much greater than the sum of its parts. Like a flock of birds wheeling in unison or neurons synchronizing in the brain, the parts of an LLM cooperate to produce coherent language – an emergent order arising spontaneously from chaos. Synergetics gives us a language to celebrate and scrutinize this order: the order parameters (key features) emerge and enslave the rest, bifurcations mark the coming of new abilities, and through self-organization, complexity births intelligence.
In closing, by developing this connection between Haken’s synergetics and modern LLMs, we hope to foster a deeper understanding that transcends disciplinary boundaries. The next time an LLM surprises us with an ability that seemingly came from “nowhere” at scale, we might smile and recall that in complex systems, more is indeed different – and that an orchestra was quietly tuning up beneath the noise, waiting for its cue to play.