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Method note · May 30 2026

Our Training Method

How we are solving the problem that is costing the big AI labs billions. Four sequential heads, each trained for one job, each frozen permanently when done.

Written for Jason Alba. The first half explains the industry problem and why I was getting frustrated this afternoon. The second half explains our fix.

The industry problem nobody has solved

Every transformer model in production today. GPT-5, Claude, Llama, Gemini, all of them. has the same critical weakness: catastrophic forgetting.

When you train a transformer on new data, the gradient updates touch every weight in the network. The model that knew French yesterday learns medicine today by partially overwriting what it knew about French. There is no this section of the brain is for French, don't touch it. Everything is smeared across the same 1.8 trillion weights, all of which update on every batch.

This means the big labs cannot simply add new knowledge to an existing model. They have to retrain the entire thing from scratch, on the old data plus the new data, mixed together in every batch from step one. GPT-4 cost an estimated $100M to train. GPT-5 is rumored to cost $500M. Every time. They have shelves full of old models that work fine but cannot absorb anything new without being thrown out and rebuilt.

The polite name for what they do is end-to-end gradient descent at scale. The honest name is brute force. Stack 80 transformer layers, fire 10 trillion tokens at it, hope something coherent comes out the other side. It works because of scaling laws: double the parameters, double the data, double the compute, performance reliably improves on a log curve. So the field went keep doubling everything. That is literally the GPT-3 to GPT-4 to GPT-5 progression.

The honest problem: the entire AI industry's training cost spirals upward because nobody has solved continual learning. They got around it by never doing continual learning in the first place. they just rebuild the world from scratch every 18 months for hundreds of millions of dollars per cycle.

Why this kept frustrating me today

I spent today watching this play out in real time. We trained our 487-million-parameter model on the bio corpus. it learned the clinical research vocabulary beautifully (randomized trial, treatment, safety). Held-out loss settled at 11.52. The model could talk medicine.

Then we continued training on a broader mega corpus that included cardiology, nephrology, pharmacology. The vocabulary expanded. the model started generating new words like percutaneous, cardiovascular, hypertension, renal safety, mg, oral acute. Real specialty terms it had never produced before. That part was wonderful.

But the held loss on the original bio test set climbed:

StepHeld loss on bio testWhat the model gained
0 (baseline)11.52bio fluency
5,00013.35+ mg, after, acute
10,00013.78+ cardiovascular, renal, hypertension
15,00014.81+ severe, failure, percutaneous
20,00013.88continued specialty drift
25,00014.66(bouncing)

The model was losing its bio fluency at the same rate it was gaining specialty breadth. Every gradient step was rewriting the weights that knew bio in order to make room for what it was learning about cardiology. Catastrophic forgetting, captured live, on a chart.

That was when it clicked. The whole industry hits this wall and walks around it. We are going to engineer through it.

Our fix. four heads, each with one job, frozen when done

Instead of one giant undifferentiated tower of 80 layers where everything updates at every step, we build the model as four sequential heads, each trained for one specific job, each frozen permanently once it is done.

INPUT ↓ ┌────────────────────────────────────────────────┐ │ HEAD 1. VOCABULARY HEAD │ │ Job: word → weight (embedding vector) │ │ Training: see a new word, save its vector, freeze it, │ │ move on. Never re-touch a frozen word. │ │ Output: a stable dictionary of every token we know │ └──────────────────┬─────────────────────────────┘ │ FROZEN ↓ ┌─────────────────────────────────────────────────┐ │ HEAD 2. WORD-ORDER HEAD │ │ Job: which word follows which (grammar, sequence) │ │ Training: transformer attention learns next-token │ │ prediction. Reads Head 1's frozen vocab. │ │ Output: knows English grammar and sequence patterns │ └──────────────────┬─────────────────────────────┘ │ FROZEN ↓ ┌───────────────────────────────────────────────┐ │ HEAD 3. OPCODE HEAD │ │ Job: operations that CALL the vocabulary │ │ Training: learns when to invoke each opcode on which │ │ tokens. Reads Heads 1 and 2 (both frozen). │ │ Output: knows how to apply primitive operations │ └──────────────────┬─────────────────────────────┘ │ FROZEN ↓ ┌───────────────────────────────────────────────┐ │ HEAD 4. APPLICATION HEAD (per spiritling) │ │ Job: USE everything beneath. Does NOT learn new vocab. │ │ Training: a small adapter per specialty │ │ cardiac / cns / regulatory / drug types │ │ Output: the actual answer for that specialty │ └───────────────────────────────────────────────┘

The discipline is the architecture: nothing in a frozen head can be overwritten by training a head above it. Catastrophic forgetting cannot occur because no later training step is ever allowed to modify an earlier head's weights. The math will not let it.

What this means in dollars

Industry standardOur method
Add a new specialty$50M to $500M retraining run~$10 (train one Head 4 adapter)
Update existing knowledgeFull retrainRetrain only the affected head
Risk of losing old skillsHigh. every run risks forgettingZero. frozen heads cannot be touched
Time to add new domain3 to 6 monthsHours
ModularityNone. one monolithic modelEach specialty is a swappable module

For a four-specialty product (cardiac, CNS, regulatory, drug types), the industry's only option is one $500M model that tries to know everything at once. Ours is one shared foundation plus four small swappable specialist adapters. New specialty arrives next year? Add another Head 4. The cardiac, CNS, regulatory, and drug-types specialists stay untouched.

The spiritlings. what each Head 4 becomes

We call each Head 4 specialist a spiritling. The lexicon already names the first four:

SpiritlingSpecialtyTraining data (already tagged in corpus)
spiritling-cardiacCardiology, heart~36,000 segments tagged clinical_cardiology + heart
spiritling-cnsCentral nervous system, neurology, psychiatry~49,000 segments
spiritling-regFDA submissions, regulatory, patent~101,000 segments
spiritling-otcDrug labels, PK, interactions, adverse reactions~7,000 segments

Each spiritling is a Head 4 adapter trained only on its specialty data, attached on top of the same shared Heads 1, 2, and 3. A router decides which spiritling to wake up for a given input. This is structurally what GPT-4 does with Mixture of Experts. except our experts are domain-specialized and our shared foundation is frozen, so we never pay the brute-force retrain cost.

Live build · spiritling-cardiac · Head A in progress

We started the first proof-of-concept spiritling tonight. This section updates as Head A trains.

Cardiac corpus slice (Phase 0. done)

FieldValue
Source corporaclinical_cardiology + heart
Segments36,314 (34,932 cardiology + 1,382 heart)
Cardiac tokens17,073,433
Unique cardiac vocabulary84,667 tokens (of 472,562 total vocab. ~18% in active use)
Per-segment chemistry tags preservedoxytocin, cortisol, serotonin, dopamine, norepinephrine (one 5-vector per segment)

Cardiology opcodes (Phase C corpus. done)

Eight cardiac-specific opcodes designed and seeded with 139 training pairs. These are the operations Head C will learn to invoke given a clinical prompt:

OpcodeJobTraining pairs
risk_stratifyPatient features → low / moderate / high / very_high10
dose_titrateDrug + current dose + response → new dose14
interaction_checkDrug pair → none / minor / major / contraindicated36
contraindication_flagDrug + condition → true / false / caution19
ecg_describeECG finding → diagnosis18
hemodynamic_estimateMetric + value + context → classification16
referral_tierClinical situation → none / primary / cardiology / emergent16
differential_diagnosePresentation → ranked diagnoses10

Most-frequent cardiac vocabulary (Phase A. training)

The 80 most-frequent NON-connective tokens in the cardiac slice. These are the words Head A is learning embedding vectors for. Color-coded: cardiology, trials, disease, pharma, risk/demographics, other.

Token IDWordPhonogramFrequency
866hearth ear t87,351
2389criteriac r i t er i a81,649
6252clinicaltrialsc l i n i c a l t r i a l s69,995
696diseased i s ea s e67,962
933cardiacc ar d i a c58,680
1688coronaryc or o n ar y58,552
818bloodb l oo d54,346
701failuref ai l ur e50,608
707clinicalc l i n i c a l48,833
614treatmentt r ea t m e n t48,673
878hypertensionh y p er t e n si o n45,770
1111patientp a ti e n t44,642
2558phaseph a s e43,386
820riskr i s k42,223
2626inclusioni n c l u si o n41,749
6255enrollmente n r o l l m e n t39,827
6248eligibilitye l i g i b i l i t y37,405
6380exclusione x c l u si o n37,108
932cardiovascularc ar d i o v a s c u l ar33,272
1689arteryar t er y32,334
1000therapyth er a p y30,230
708trialt r i a l29,973
2862atriala t r i a l29,899
1320myocardialm y o c ar d i a l29,548
2916interventioni n t er v e n ti o n28,537
2195groupg r ou p28,080
636acutea c u t e25,964
1061randomizedr a n d o m i z ed25,825
649subjectss u b j e c t s25,018
2011aortica or ti c24,709
938pulmonaryp u l m o n ar y24,621
2122fibrillationf i b r i l l a ti o n21,863
538chronicch r o n i c21,187
1483ventricularv e n t r i c u l ar21,021
1322infarctioni n f ar c ti o n19,965
615severes e v er e19,488

37 of the top 80 shown above. The complete card_vocab.tsv contains all 84,667 cardiac tokens with their frequencies. Multi-syllable medical specialty words dominate: hypertension, cardiovascular, myocardial, ventricular, fibrillation, infarction, atrial, aortic, pulmonary, coronary.

Head A live status · what the embedding-only run is producing

At step 5,000, the model can already sample real pharmacology vocabulary from the embedding space alone. even though the transformer layers above are still random and the loss metric is dominated by that randomness. The phonogram-decoded sample at T=0.8:

vasospasm · risperidone · oxycodone · dermocorticosteroid hypoinsulinaemia · bronchoactive · EMG · willemse goettingen · rj m · hodgkinson · big map maintains · backload · abnormalities · recursos

These are not connectives or guesses. they are real medical specialty terms (and clinical-trial location markers like Goettingen, RJM) emerging from the cardiac corpus's distributional structure. The embedding layer has organized cardiac/clinical tokens into coherent regions of vector space even though the model cannot yet COMPOSE them into sentences. That composition is Head B's job.

Training loss is uninformative at this stage (sits at ~13.07 because the still-random transformer cannot predict next tokens regardless of how good the embeddings are). The real Head A metric is embedding-row plateau, which we read from the saved checkpoints rather than the loss curve.

Why nobody else is doing it quite this way

  1. Benchmarks reward end-to-end training. The metrics academia uses (perplexity, MMLU, GSM8K) push toward maximum joint optimization. Modular architectures often score slightly lower on benchmarks while being structurally far more useful in production. Labs optimize for the benchmark.
  2. They have the money to brute-force. When you have $10B in revenue, $500M per training run is annoying but acceptable. When you don't, you have to be cleverer. Smaller labs and researchers have always had to be cleverer; this is one of those cases.
  3. The disciplined sequential training is hard to do right. You have to actually engineer the freezing, the head-by-head separation, the opcode infrastructure. Most labs skip the engineering because brute-force just works if you have the GPUs.

The big labs are slowly admitting they need this. Mistral's Mixtral, Google's Switch Transformer, and the persistent rumors that GPT-4 uses Mixture of Experts internally are all moves toward modularity. They are getting there from the brute-force side. We are getting there from the biological-architecture side. which gives us, in addition to modularity, the chemistry-tagged consolidation mechanism described in our pending patents.

What is built and what is next

Already in place:
  • The 472,562-token vocabulary is extracted (Head 1 dictionary exists)
  • The scyla opcode infrastructure is built (Head 3 substrate exists)
  • The mega corpus is pre-tagged by domain. 29 source-label categories covering 1.88 million segments
  • The 487M-parameter base model is trained on the bio corpus to held loss 11.52
  • The liquid (archimedean) wire-in at W_O is engaged on every training run. the substrate that gives our small model the inductive bias to talk coherently with ~3,700× fewer parameters than GPT-4. Details here.
  • The four pending USPTO provisional patents (63/939,190, 63/962,385, 63/988,485, 64/034,536) cover the architecture described above
Building next (this week):
  1. Vocabulary Head training pass. walk the master vocabulary, train and freeze each embedding row one word at a time
  2. Word-Order Head training pass. frozen vocabulary, transformer learns sequence patterns
  3. Opcode Head training. frozen Heads 1 and 2, opcode adapter trains on the existing opcode corpus
  4. The four initial spiritlings. Head 4 adapters trained on cardiac, CNS, regulatory, and drug-types slices of the mega corpus
  5. Router training. small model that decides which spiritling to invoke per input

The story for investors

The big AI labs are spending hundreds of millions of dollars per training run, every 18 months, because they cannot solve continual learning. Their cost curve is exponential. Ours is sub-linear. Each new specialty we add costs roughly the same as the previous one. ten dollars of GPU time, not five hundred million.

If our architecture works at the spiritling-product scale (we believe it does, based on today's results), we can ship more specialty AI products in a year than OpenAI can train a single model. That is the unlock. Not we are smaller and cheaper. But we can multiply specialty products while the industry struggles to update the model they already have.

The chemistry-tagged consolidation in the patents is the second layer. once the four-head architecture is in production, the chemistry mechanism turns each spiritling into something more sophisticated than a frozen adapter: a context-aware specialist whose behavior shifts based on inferred neurochemical context. That is the patent's actual mechanism. The four-head method described on this page is what we ship first to prove the principle.