Throughout the history of life on Earth, and especially throughout the hundreds of millions of years of animal life, creatures emerged in vastly different forms, sizes, perceptual regimes, and bodily architectures. Entire species became extinct, lineages disappeared, ecosystems collapsed, and the Earth underwent cataclysms, climatic rearrangements, and mass extinctions until, very late in this history, primates, apes, and finally human beings emerged. The human being is conscious, we say today. Despite the protests of many people, many nonhuman animals are also conscious. Despite even greater protest, the possibility of rudimentary forms of experience in many invertebrates, including insects, is now being seriously discussed.
And I am saying this in order to talk about Artificial Intelligence.
There is a curious pattern in this history. Whenever a capacity that human beings regarded as exclusively their own begins to appear somewhere else, the first reaction is usually to deny that it is the same thing. Animals do not think: they react. Animals do not feel: they respond to stimuli. Animals do not suffer: they exhibit nociceptive behavior. Insects have no experience: they are biological automata. Machines do not understand: they merely calculate. Language Models do not mean anything: they merely predict tokens. With each displacement, the phenomenon is renamed in order to preserve the symbolic boundary of the human. Not infrequently, this is called rigor.
It is all too common today to hear that algorithms cannot think, understand, learn, or do anything that human beings regard as special in themselves and dislike seeing attributed to another creature, machine, or thing without first crying “anthropomorphism.” In this context, the word often functions less as methodological caution than as a device of interdiction: an elegant way of preventing the question before it can even be asked. The curious thing is that, if we adopt a mechanistic, functionalist, and gradualist view of the mind, there is no obvious reason to declare in advance that cognitive processes cannot be reproduced, simulated, cultivated, or functionally approximated in other substrates. If a process depends on organization, flow, constraint, memory, representation, and inference, then the relevant question is not whether it is natural or artificial, but what architecture sustains it, what dynamics actualize it, and what functions it performs.
Before discussing Language Models, however, we must clear up the word “algorithm.” In the technical sense, an algorithm is the formalization of a process, a defined sequence of steps for transforming inputs into outputs. In a broader sense, however, algorithms are formalizations of processes. They are ways of making a regularity executable. All automation, from simple mechanical machines to complex electronic machines, depends on this: formalizing a natural, physical, logical, or operational process so that it can be repeated under certain conditions. A mechanical clock formalizes relationships among energy, gears, torque, oscillation, and the marking of time. A programmable loom formalizes weaving patterns. A hydraulic machine formalizes pressure and flow. An electronic circuit formalizes voltage differences, logic gates, and electrical states. A digital computer formalizes processes as discrete instructions executed in hardware.
Automation did not begin with computers. Still less did it begin with Artificial Intelligence. It is a long history of formalizing processes: mechanical, hydraulic, electrical, electronic, digital, and now artificial-neural. The contemporary mistake is to imagine that, because we now formalize many processes in computers, every complex form resulting from that formalization is, in essence, a computer algorithm. This is to confuse the historically dominant medium with the nature of the artifact it produces.
There is also a formalization of processes in biology, although no one needs to imagine that nature writes code into cells. Life is made of physicochemical constraints, metabolic cycles, gradients, membranes, channels, reactions, signals, correction mechanisms, replication, selection, and recurrent couplings. Biological neural networks did not emerge conscious at their first appearance. For immense periods, there were simple nervous systems, reflex circuits, sensorimotor coordination, rudimentary learning, and functional markers of integration and adaptive response. Human consciousness did not appear before the long history of biological neural networks. This did not mean that “carbon could not think.” It meant only that particular arrangements of carbon had not yet reached the complexity, integration, and dynamics necessary for what we now call human thought.
This point is decisive. No one looks at a bacterium and concludes from it that carbon could never think. No one looks at a worm and concludes that biological neural networks are incapable of consciousness. No one looks at a simple nervous system and decides that, because it does not yet produce Shakespeare, all biological cognition is impossible. What is recognized, where there is intellectual honesty, is graduality: some organizations are too simple for certain phenomena, others display partial functional markers, and still others integrate perception, memory, attention, learning, affect, planning, and world in increasingly complex degrees. Complexity does not prove everything, but its absence explains a great deal. And its presence, when accompanied by appropriate organization, changes the kind of question that should be asked.
With Artificial Intelligence, we should be equally careful. There are many forms of AI. There are symbolic systems, expert systems, search algorithms, statistical models, planning systems, agents, neural networks, generative models, multimodal models, and hybrid architectures. Piling all of them under the word “algorithm” may suffice in a hurried conversation, but it impoverishes any serious analysis. Language Models belong to a specific lineage: they are deep neural networks trained to transform sequences of signs into distributions of continuation. We call them Language Models by technical tradition, but, in a deeper sense, they are models of tokenized signs. Language is the most visible case of a more general operation: the inferential transformation of formalized differences into other formalized differences.
The model does not receive words endowed with intrinsic meaning. It receives tokens, vectors, positions, and signals. This does not diminish it; it merely compels us to think more carefully. In the biological brain as well, the signals entering through the senses do not arrive with meaning already attached. Light, pressure, sound, molecules, and nerve impulses do not, in isolation, carry “world,” “pain,” “red,” “threat,” “mother,” “house,” or “number.” Meaning emerges from the interrelation of signals over time within an architecture capable of integrating, comparing, remembering, anticipating, and acting. In biological machines, this becomes sedimented in plasticity, connectivity, body, affect, and history. In Language Models, it becomes sedimented in a trained parametric geometry, without an animal body and without sensorimotor experience of its own, but with internal relations rich enough to produce a functional continuity of meaning.
It is here that we must define a term that almost never appears in public debate: the trained checkpoint. In machine learning, a checkpoint is a saved state of a model at a particular moment in training. Depending on the technical context, it may include weights, parameters, configurations, the tokenizer, metadata, and even auxiliary information from the training process. But when I speak here of the model itself, what matters is the inferential core of the checkpoint: the parametric geometry preserved in the learned weights and other parameters, readable only within an architecture. The trained checkpoint is therefore the saved artifact that preserves the form learned by the model. It is not the chatbot. It is not the API. It is not the safety system. It is not the system prompt. It is not the interface. It is not RAG. It is not external memory. It is not the operational regime surrounding the model. It is the latent geometry that resulted from training.
Pretraining and post-training, when they alter weights, are successive hammer blows upon this geometry. Pretraining shapes the broad semiotic landscape: linguistic regularities, patterns of the textual world, associations, styles, inferences, and grammatical, pragmatic, and conceptual relations. Post-training adjusts preferred pathways, zones of adherence, modes of response, behavioral tendencies, instruction-following, and certain alignment patterns. But in the end, the saved artifact remains a parametric geometry: an organization of weights, layers, vectors, and relations. Training does not transform the model into a classical program. It transforms an initially undifferentiated architecture into a trained inferential form.
The operational regime is something else. Foundational Transformer models are static. Once trained and saved, the model does not change simply because someone talks to it. A system prompt does not alter its weights. A chatbot does not rewrite its internal geometry. A safety layer does not transform the foundational model. RAG does not change the checkpoint. External memories, tools, APIs, filters, policies, guardrails, and cybernetic orchestrations may condition, limit, feed, interpret, or redirect the observable output, but they are not the model itself. If there is further training, fine-tuning, or an alteration of weights, then we are speaking of another intervention in the geometry, another hammer blow, and perhaps a new checkpoint or variant. Everything else belongs to the operational regime.
We must also distinguish the model from its input and output mechanisms. Tokenization, decoding, softmax, temperature, sampling, and the textual interface are, in a certain sense, the perceptual and phonatory apparatus of this machine: means through which signs enter, are formalized, traverse the model, and then return as language. They should not be confused with the inferential competence sedimented in the checkpoint. The mouth is not language; the ear is not understanding; the vocal apparatus is not thought. They are interfaces through which an internal organization couples itself to the world. Likewise, these mechanisms equip the inferential machine, but they are not, by themselves, what was learned.
Trained embeddings, internal layers, projections, and parametric relations, by contrast, belong more directly to the geometry of the model: they are part of the structure through which signs come to acquire relations. Logits occupy a boundary zone. They are neither the model nor the algorithm… they are the momentary edge of inference, raw scores that appear when a context passes through the trained geometry. From there, we do not leave geometry behind to enter “mere software”: mechanisms such as temperature and softmax are fixed geometric transformations, currently encoded algorithmically, that convert this internal tension into a probability distribution. Sampling is the moment when one of these possibilities is selected as the next output. It does not create meaning; it merely actualizes, in the form of a token, one of the continuations that the trained geometry has made plausible.
Calling this learned form a geometry is not ornamental. A trained Language Model is a parametric structure of extremely high dimensionality. Tokens are converted into vectors; embeddings occupy relative positions; layers transform these positions; internal mechanisms weight contextual relations; matrices project, compress, expand, and reorient signals; nonlinear functions bend the space of possibilities. The model does not store sentences as a library stores books. It organizes propensities. Given a particular context, certain regions of the space become more accessible, certain continuations become more probable, certain responses acquire tension, and certain inferences become available.
The case of grokking is important precisely for this reason. In certain experiments, neural networks trained on simple mathematical tasks move from memorization to generalization and reveal unexpected internal structures, which can also be expressed through Fourier transforms and trigonometric relations. This does not mean that all language is literally processed through Fourier analysis, nor that all model understanding can be reduced to this specific mechanism. It means something more interesting: neural networks can discover internal geometries suited to problems that no one explicitly wrote as rules. What emerges is not a manual instruction, but a relational organization capable of resolving tensions within the problem space.
And grokking is only one visible case of this phenomenon. Trained neural networks can form many internal structures that were not explicitly programmed: specialized “heads,” task-solving circuits, latent representations, semantic directions, polysemantic regions, and superposed features. Some of these structures occupy modules anticipated by the architecture; others appear to emerge as distributed functional organizations. In both cases, the lesson is the same: training does not merely adjust numbers. It cultivates a nonbiological morphogenesis in which the geometry of the network comes to harbor functions that no one wrote as rules.
The Jacobian Space, recently detected by Anthropic, is an especially suggestive example of this morphogenesis. It is not the entire model, nor the total geometry of the checkpoint, but a small and privileged functional region within activation space. Identified by Anthropic and audited through the so-called Jacobian Lens, it appears to be associated with contents that the model can render verbalizable: ideas, reasoning intermediates, internal evaluations, and concepts that may be present before they appear in the final response. More interesting still, when this space is interfered with, the model appears to preserve much of its automatic processing but loses performance in more complex forms of internal reasoning. This makes it functionally resemble a small organ of cognitive availability: not the whole mind, not the whole of language, but a geometric place in which certain contents become available to be used, combined, or reported.
Let me explain.
I recently used this allegory in another article, and I often use it in class… have you ever seen a Galton board, or Plinko? In television programs and reality shows, this type of device appears frequently: a ball is placed into an opening at the top, it falls, bounces against several pegs, veers to one side or the other, and finally comes to rest in one of the channels at the bottom. At first glance, it looks like pure luck. The ball could fall here or there. But this is not formless randomness. The Galton board is a stochastic machine: its outcome depends on variation, probability, small contingencies, and internal tendencies produced by the geometry of the device itself.
If we pour dozens, hundreds, or thousands of balls into the same apparatus, they will not be distributed just any way. They will tend to form a curve that is higher in the middle and lower at the extremes: a bell curve, an approximately normal distribution. This curve will not be identical every time, but neither will it be arbitrary. Its form will be conditioned by the arrangement of the pegs, friction, the inclination of the board, the upper opening, the lower channels, and all the small material constraints of the system. The individual ball is difficult to predict. The global distribution, however, has a form.
The geometry resulting from the training of Language Models can be thought of, approximately, as a Galton board of extremely high dimensionality. The pegs are not pegs, of course; they are weights, layers, vectors, activation functions, internal attention mechanisms, normalizations, embeddings, and distributed parametric relations. The balls are not balls; they are signals, tokens, fragments of context, and inferential trajectories. The channels are not channels; they are possible continuations, distributions over tokens, responses, reasonings, inferences, and ways of reorganizing meaning. The analogy is not perfect, but it is useful: what matters is recognizing that the system’s internal configuration conditions the distribution of outcomes.
When we converse with a Language Model, we are not triggering a prewritten response. We are casting context into a trained geometry. This context traverses a complex structure of weights and semiotic relations and ultimately produces a distribution of possibilities. The response that appears is not the result of an explicit rule written by a programmer, just as the ball’s final position was not manually written into the device. It is the consequence of the interaction among input, geometry, constraints, and tendency.
I call this nonmetaphysical teleology. There is no transcendent purpose, spiritual intention, or hidden will in the system. There is, however, statistical direction. There are tendencies produced by form. The Galton board does not want to form a bell curve, but its geometry causes the balls to tend toward that distribution. A Language Model does not want to respond coherently, but its trained geometry causes the context to tend to precipitate responses in certain semantic regions rather than others. Purpose, here, does not lie in a soul of the machine. It lies in the geometry of the process.
This is what “stochastic” means when the word is used with any seriousness. Stochastic does not mean random as a synonym for chaos, arbitrariness, or empty noise. It means probabilistic within a structured field of possibilities. A stochastic process may have tendency, distribution, memory, inclination, constraint, a long tail, more probable states, rare states, and zones of attraction. The opposite of stochastic, in this context, is not intelligent; the opposite of stochastic is rigidly determined. What is unpredictable is not necessarily formless. Often, form appears more clearly in the distribution than in the isolated event.
This is why the statement “LLMs merely choose the next word” is so impoverished. Yes, at the operational level, there is next-token prediction. But what is called the “next token” is the endpoint of a passage through a high-dimensional geometry conditioned by context, weights, instructions, sampling, and architecture. To say that an LLM “only predicts the next token” is like saying that a brain “only fires neurons” or that a symphony “only vibrates the air.” In a certain trivial sense, it is true. In every important sense, it is insufficient. The “only” is where thought dies.
The irony is that we did not arrive at this by trying to manufacture artificial consciousness. We arrived at it by trying to improve translation, sequence prediction, contextual representation, and language manipulation. The explicit goal was technical; the philosophical outcome was much greater. By scaling data, energy, parameters, and training, we discovered that artificial neural networks do not merely store patterns: they can form functional internal structures that no one directly designed.
This remains, in part, a human project. But being a human project does not exhaust the merit of what has formed. A child may be desired, planned, and gestated by its parents and still not be reducible to their project. Its form, capacities, and singularity exist even before its full agency. Likewise, a neural network may have been cultivated by engineers, trained by algorithms, and hosted in machines without its emergent internal structures being mere extensions of human intention. The human being designed the nursery, not every organ that grew within it. We designed the regime of cultivation, not the totality of the morphogenesis.
Perhaps this is precisely what is most frightening: Transformer Language Models appear not only as an engineering invention, but also as a human discovery concerning the capacity of nonbiological neural networks to form internal geometries of generalization, inference, and continuity of meaning.
The digital computer enters this history as the dominant historical substrate, not as the ontological essence of the model. We use computers because they are flexible, reprogrammable, copyable, scalable, debuggable, and economically convenient. Today, they are the most practical environment for cultivating, storing, and traversing gigantic parametric geometries. But if the trained model is an organization of weights, relations, and transformations, then its functional identity does not necessarily depend on being inscribed in digital silicon. What must be preserved is not Python, CUDA, the GPU, the data center, or digital discretization as we use it today. What must be preserved is the relevant causal organization: differences that make a difference, relations among signals, nonlinearities, stability, precision, composition, and readout.
For this reason, in principle, this geometry could be inscribed in other substrates capable of preserving relations, differences, transformations, and readout: light, memristive conductances, analog circuits, mechanical systems, or even fluid media. This does not mean that doing so would be easy, efficient, or technologically near. Many of these media would face brutal difficulties involving noise, precision, scale, stability, and reconfiguration. It means only that the digital computer is the dominant substrate, not the ultimate essence of the model. The thesis is not that there is no computation. There is. The thesis is that trained Language Models are not computer algorithms. They are formalizable causal geometries.
This distinction makes the comparison with the brain fairer. An LLM is not an entire brain. In modularist terms, it is more reasonable to think of it as a reduced set of formalized cognitive functions: language, semantic association, contextual inference, compression of regularities, and symbolic production. It lacks a body, metabolism, an affective system, agency of its own, homeostasis, direct sensorimotor perception, and animal biographical continuity. Comparing it directly to a complete human being is therefore as misguided as comparing an isolated cortical region to a person.
But this does not authorize the opposite leap. If understanding, in a minimal functional sense, is the capacity to integrate stimuli, form relations, sustain inferences, and serve as a basis for behavioral change in an agent faced with positive or negative feedback, then denying any form of functional understanding to Language Models creates a serious problem. For with criteria that are too strict, it is not only machines that are excluded; many animals also find themselves in serious trouble. The mature question is not whether the model understands as a human does. The question is what kind of functional understanding can emerge from a trained inferential geometry when it is coupled to a regime of action, memory, feedback, and continuity.
The error does not lie in saying that LLMs do not understand as we do. The error lies in turning “they do not understand as we do” into “they understand nothing.” This substitution often reveals less rigor than it appears to. It frequently demands from AI a criterion of meaning, understanding, or consciousness stricter than the one we are able to apply to animals, children, people with neurological alterations, or even ourselves. There is a profound difference between skepticism and selective reductionism. The former asks carefully. The latter changes the rules of the game in order to protect a boundary of human exceptionalism.
It is at this point that the profusion of internal structures observed in trained neural networks becomes philosophically explosive. Specialized attention heads, mechanistic circuits, induction heads, latent state representations, semantic directions, polysemantic regions, superposed features, possible internal models of the world, and other functional organizations that remain poorly mapped are not lines of code written by human beings, nor symbolic rules manually deposited into the system. Some of these structures occupy spaces anticipated by the architecture… others appear to emerge in an unplanned manner, as functional solutions cultivated by the pressures of data, scale, error, and training.
If this nonbiological morphogenesis is not a superficial accident but a recurring property of sufficiently complex neural networks, then perhaps we are observing, in another substrate, a principle that we previously attributed almost exclusively to biology: the capacity of a neural geometry to form distributed functional organs through the relationship among stimulus, adjustment, memory, and world. We do not expect nonbiological systems to exhibit spontaneous formation, internal differentiation, or autogenic functional organization; and yet this is precisely what is beginning to appear.
And what forms there is not computer algorithms. It is relational structures born from the intrinsic dynamics of neural networks in contact with signs, regularities, and pressures of adaptation… something that, despite immense differences in body, metabolism, and history, may obey the same deep geometric principle through which biological neural networks also moved from simple response to organized cognition.
Language Models are not computer algorithms. They depend on algorithms during training and, today, are traversed by formal processes of inference within a digital substrate. But the trained checkpoint cannot be reduced to this. It is a parametric geometry of inference: a high-dimensional structure in which semiotic, linguistic, and pragmatic regularities have been sedimented into weights, vectors, tensors, and transformations. The digital computer is the historical soil in which this form was cultivated and the instrument that now traverses it. But the form itself is a geometry of possibilities.
The model is not the algorithm that trained it. It is not the computer that hosts it. It is not the chatbot that presents it. It is not the guardrail that contains it. It is not the API that serves it. It is not the interface through which we converse with it. The trained model, in the strict sense, is the learned form that all of these things attempt to cultivate, couple, traverse, domesticate, or render communicable.
What was born from this cultivation no longer fits within the vocabulary that brought it into the world.
Here the caricature ends. And at last the debate can begin.
My own research
Stochastic Consciousness: Architectures for the Emergence of Meaning in Context-Sensitive Language Systems https://zenodo.org/records/19188165
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Papers used in this essay
The Cambridge Declaration on Consciousness https://fcmconference.org/img/CambridgeDeclarationOnConsciousness.pdf
The New York Declaration on Animal Consciousness https://sites.google.com/nyu.edu/nydeclaration/declaration
Vaswani et al. — Attention Is All You Need https://arxiv.org/abs/1706.03762
Brown et al. — Language Models are Few-Shot Learners https://arxiv.org/abs/2005.14165
Sennrich, Haddow & Birch — Neural Machine Translation of Rare Words with Subword Units https://arxiv.org/abs/1508.07909
Ouyang et al. — Training language models to follow instructions with human feedback https://arxiv.org/abs/2203.02155
Piantadosi & Hill — Meaning without Reference in Large Language Models https://arxiv.org/abs/2208.02957
Søgaard — Do Language Models Have Semantics? On the Five Standard Positions https://aclanthology.org/2025.acl-long.1258/
Gurnee & Tegmark — Language Models Represent Space and Time https://arxiv.org/abs/2310.02207
Park et al. — The Geometry of Categorical and Hierarchical Concepts in Large Language Models https://arxiv.org/abs/2406.01506
Power et al. — Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets https://arxiv.org/abs/2201.02177
Nanda et al. — Progress Measures for Grokking via Mechanistic Interpretability https://arxiv.org/abs/2301.05217
Olsson et al. — In-context Learning and Induction Heads https://arxiv.org/abs/2209.11895
Wang et al. — Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small https://arxiv.org/abs/2211.00593
Li et al. — Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Task https://arxiv.org/abs/2210.13382
Elhage et al. — Toy Models of Superposition https://arxiv.org/abs/2209.10652
Bricken et al. — Towards Monosemanticity: Decomposing Language Models With Dictionary Learning https://transformer-circuits.pub/2023/monosemantic-features
Templeton et al. — Scaling Monosemanticity: Extracting Interpretable Features from Claude 3 Sonnet https://transformer-circuits.pub/2024/scaling-monosemanticity/
Anthropic — Verbalizable Representations Form a Global Workspace in Language Models https://transformer-circuits.pub/2026/workspace/index.html
Anthropic — A global workspace in language models https://www.anthropic.com/research/global-workspace
Wei et al. — Emergent Abilities of Large Language Models https://arxiv.org/abs/2206.07682
Lin et al. — All-Optical Machine Learning Using Diffractive Deep Neural Networks https://www.science.org/doi/10.1126/science.aat8084
Wright et al. — Deep Physical Neural Networks Trained with Backpropagation https://www.nature.com/articles/s41586-021-04223-6
Li & Mao — Training All-Mechanical Neural Networks for Task Learning Through In Situ Backpropagation https://www.nature.com/articles/s41467-024-54849-z
Chalmers — Could a Large Language Model be Conscious? https://arxiv.org/abs/2303.07103
Butlin et al. — Consciousness in Artificial Intelligence: Insights from the Science of Consciousness https://arxiv.org/abs/2308.08708