LNSP vs LLM/GPT Scaling Comparison

LNSP vs LLM GPT Scaling Graph

11/30/25

Trent Carter and Chat GPT 5.1

Question: Can you think about how LNSP and more specifically LVMs would graph on this chart?

Short version: if that chart is “how good do you get as you burn more PF-days on a single monolithic LLM?”, then LNSP/LVM is more like “cheating” by splitting the job in two. On the original axes:

• X = total training compute

• Y = validation loss (lower is better)

• Color = parameter count

I’d expect _three_ different overlays for your world:

Teacher-inclusive curve (LLM + GTR-T5 + all CPESH generation)

LVM-only curve (just the tiny vector model training)

System-level effective curve (what a user experiences per unit compute once the teacher is amortized)

Let me walk through each.

⸻

1. What the original chart is really showing

That Sutskever slide is basically:

• For each model size N, train it longer (more tokens → more PF-days).

• Plot validation loss vs compute.

• You get “banana” curves: big vertical drop at first (under-trained), then they bend right and saturate (data-limited / parameter-limited).

• The dashed line is the compute-optimal frontier: best loss you can get for a given compute budget if you pick the right model size and training length.

So: “Throw more compute at the scaling law and the model just gets better at everything.”

⸻

2. How an LVM run maps onto those axes

For LNSP/LVM you’ve decomposed the problem:

Teacher phase (token world)

• Big LLMs + GTR-T5 produce CPESH / concept vectors.

• Massive one-time cost: tokenization, prompting, embedding → PF-days potentially in the same ballpark as a mid-sized LLM pretrain, if you did it at Internet scale.

Student phase (vector world – the LVM)

• Tiny AMN/GRU/Mamba nets learn on already-compressed 768-D concepts.

• Training looks like contrastive loss / triplet loss / margin loss plus your echo-loop constraints.

• Compute is _orders of magnitude_ lower than the teacher.

Inference phase

• Runtime work is: encode query (GTR-T5), LVM forward, FAISS lookup, vec2text.

• Very cheap per query compared to a full LLM forward.

So if you literally drop “LVM training” on that chart, you have to decide:

Does X (compute) include the teacher, or only the student?

⸻

3. Curve A – Teacher-inclusive LNSP

If you count _everything_ (CPESH extraction + GTR-T5 passes + LVM training):

• Your X-axis position shoots way to the right: the GTR-T5 + LLM interrogation is the dominant PF-cost.

• Your Y-axis loss (say, 1–R@5 or some retrieval loss) would likely be very low compared with a same-compute vanilla LLM, because:

• You’ve already baked in a ton of teacher knowledge.

• The LVM is specialized for “semantic GPS” + retrieval, not for “do everything text-to-text”.

Visually:

• The _teacher-inclusive_ curve probably hugs something close to the existing dashed frontier: you’re still limited by the fact that the “real work” is done in a big token model.

• With more compute, you’d primarily improve by:

• Using smarter/more diverse CPESH.

• Scaling the base teacher (better embeddings, better vec2text).

• Running more passes / augmentations.

So that curve is not magically off-frontier; it’s a different factorization of the same scaling story.

⸻

4. Curve B – LVM-only scaling (the interesting one)

Now ignore teacher cost and ask:

If I only plot _LVM training compute_ vs _LVM validation loss_ (e.g., negative MRR or echo-loop error), how does it look?

This is where you win.

Why the LVM curve is “left-shifted”

• Compute: your AMN/GRU/Mamba models are tiny (5–10MB today). A full epoch over, say, ~1M concepts is _cheap_ in PF-days terms.

• Loss: because the input space is already semantic (768-D GTR-T5, CPESH-curated), the function the LVM is approximating is _simpler_ than raw next-token prediction.

That means:

• For the same PF-days as a small-ish LLM run, your LVM might do multiple _full_ passes over the entire concept universe, with hard negatives, curriculum, etc.

• You’d sit far left on the X-axis but already quite low on Y.

Shape-wise:

• You’ll still get bananas: under-trained regime → loss drops vertically as you add epochs; then saturation as you fully fit the CPESH manifold.

• But the frontier for a given parameter count is better because:

• The effective intrinsic dimension of the task is much lower (compressed semantics).

• Inputs are de-noised (Wikipedia-backwards weirdness is partially fixed during CPESH extraction).

• The model is specialized: it doesn’t need to model syntax, morphology, style.

If we over-simplify:

• For “equivalent” capacities, an LVM curve might sit below a vanilla LLM curve in the retrieval / QA subspace, and you get there with 10–100× less incremental compute.

So on the chart, I’d draw:

• A family of LVM_small, LVM_med, LVM_large curves:

• All starting at WAY less compute.

• All bending into a “frontier” that is steeper in the low-compute regime (big early gains per PF-day) and then flattens once you’ve squeezed everything from the teacher embeddings.

⸻

5. Curve C – System-level effective scaling

From a _user_ or _Verdict_ perspective, what matters is:

For a fixed _ongoing_ compute budget (per day, per month), how good is the system?

Here the teacher cost is a fixed capital expense:

• You pay once to build the concept bank.

• After that, 99% of the marginal compute is:

• LVM continual learning (nightly updates).

• GTR-T5 encodes for fresh content.

• FAISS maintenance.

So if you re-draw the x-axis as “ongoing PF-days per month” rather than “one time training run”, your LNSP/LVM system looks like this:

• The initial point has a huge invisible fixed offset (teacher precomputation), but you don’t feel that every month.

• The ongoing curve is almost flat in compute but still improving because:

• You’re in continual-learning mode (new domains, RL from Verdict runs, active learning from lane overrides).

• Each PF-day buys you updates across the entire knowledge base.

In Sutskever-diagram terms, that’s like plotting a model that slides down and right over time without you paying frontier-scale PF-days each time. It doesn’t violate scaling laws, but it changes the economics:

• Frontier LLM: every big version is a fresh rightward jump on the chart.

• LVM system: one big jump for the teacher + lots of small left-region improvements from the vector student.

⸻

6. Where the LVM curves will break the analogy

A couple of honest caveats:

Loss is different.

• The original y-axis is cross-entropy on next-token prediction.

• For you it’s something like retrieval error, echo-loop cosine deficit, or downstream task loss (5CAT).

• The exponents in the power law will _not_ match; I’d expect something closer to “data-limited” behavior because CPESH is finite and clean.

Capacity ceilings move.

• Your effective ceiling is set by GTR-T5 + vec2text, not just LVM params.

• Past a certain LVM size, scaling it further does nothing unless you upgrade the teacher or increase CPESH richness.

Multi-tower compute.

• A true scaling law for LNSP needs three compute axes:

• Teacher PF-days (token world).

• Embedding PF-days (GTR-T5 over corpus).

• LVM PF-days (vector world).

• You’re compressing that into one axis, so any simple overlay will hide important structure.

⸻

7. The useful takeaway for you

If you actually plotted this for your experiments (and you should):

• Define a single scalar “validation loss” for LVM (e.g., -\log(MRR) or 1–R@5, plus maybe an echo penalty).

• Track total LVM training FLOPs per run (ignore teacher for this view).

• Plot several architectures/sizes.

My prediction:

• You’ll see very clean power-law-ish slices even at your tiny scales, because everything is so controlled (same GTR-T5, same CPESH manifold).

• The frontier you get for LVM-only compute will look _absurdly good_ compared to a same-compute mini-LLM that tries to do full text-to-text.

Which is exactly the argument you want:

“Given a fixed ongoing compute budget, a vector-native LVM that stands on a frozen teacher gives you more reliable, interpretable QA per PF-day than training yet another small LLM from scratch.”

If you want, next step I can help you specify exact metrics and logging hooks so you can start drawing your own version of that Sutskever scaling plot for LVM experiments.