AbstractPhila PRO

I see the answer. The behavioral sweep shows CV of 0.29154 between 0.291 and 0.292 are within a very special band of variations.

1024v, 24d - the entire operating spectrum of the T5 series embeddings when alignment differentiated by the configuration. This is effectively a threshold between what works operationally, going beyond this causes degraded behavioral response without attenuated compensation.

So I've managed to finally get the right questions to discover the connection between the fly in the ointment that kept returning, and the structural systems responsible for curating the behavior around it.

Finding: Geometric controlled structures do not require CV loss if the D is within the expected band. To compensate for the dimensional difference with the CV measured, the CV loss must be adjusted to the distillation target.

The vocabulary when established as geometrically valid throughout the lifecycle of the existence. The CV loss is only attuned and useful when running distillation paradigms. The current CV loss has no impact on the CV measured capacity of the embeddings consistent or pretrained.

This effectively allows compartmentalization to any vectorized locality as accumulated throughout a structure, allowing direct

As of right now I don't know how to reduce to fp16 without a massive dip. I'm thinking it's possible to utilize integers directly instead of high-accuracy fp64 or fp32 deviated floats. I'll do some exploration.

Reducing this is to fp16 or bf16 capacity would greatly improve performance, and if the values out are close enough to the mantissa cross-contaminants, it could be worth it just for the semi-accurate speed alone.

Per-instance allocation for max_n, max_batch (B):

WORKING STORAGE:
A_work : [B, max_n, max_n] # working copy (destroyed)
V_accum : [B, max_n, max_n] # eigenvector accumulator
householder : [max_n-2, B, max_n] # stored reflectors (padded)
d : [B, max_n] # tridiagonal diagonal
e : [B, max_n-1] # tridiagonal off-diagonal

Subtotal: ~3 × max_n² × B floats

D&C TREE (depth = ⌈log₂(max_n)⌉ levels):
FOR each level l (0 to depth-1):
num_sub = 2^l
sub_size = max_n // 2^l (padded up to power of 2)

    delta   : [B, num_sub, sub_size]    # merged eigenvalues
    z_vec   : [B, num_sub, sub_size]    # merge vectors  
    rho     : [B, num_sub]              # coupling strengths
    mask    : [B, num_sub, sub_size]     # valid element mask
    
    # Newton state (per root):
    lam     : [B, num_sub, sub_size]    # current root estimates
    lo      : [B, num_sub, sub_size]    # bracket lower
    hi      : [B, num_sub, sub_size]    # bracket upper
    f_val   : [B, num_sub, sub_size]    # secular function value
    converge: [B, num_sub, sub_size]    # convergence mask
    
    # Eigenvector fragments:
    V_frag  : [B, num_sub, sub_size, sub_size]

Subtotal per level: ~(9 × sub_size + sub_size²) × num_sub × B
Total across levels: since num_sub × sub_size = max_n at every level,
    ≈ (9 × max_n + max_n²) × depth × B
    ≈ max_n² × depth × B  (the V_frags dominate)

CONCRETE NUMBERS (fp32, 4 bytes each):

max_n=8,   B=4096:  ~8² × 8 × 3 × 4096 × 4   ≈   24 MB
max_n=32,  B=1024:  ~32² × 5 × 3 × 1024 × 4   ≈   60 MB
max_n=64,  B=512:   ~64² × 6 × 3 × 512 × 4    ≈  144 MB
max_n=128, B=256:   ~128² × 7 × 3 × 256 × 4   ≈  352 MB
max_n=256, B=128:   ~256² × 8 × 3 × 128 × 4   ≈  768 MB
max_n=6,   B=8192:  ~6² × 3 × 3 × 8192 × 4    ≈    6 MB  ← your CM case

Alignment in these systems is NOT a series of opinions, nor is it some sort of structural behavior, nor is it whether the model is inherently "good" or "bad".

Alignment is specifically a geometric process that enables direct resonant oscillation, and with that resonance perfectly aligned the substructure learns internal alignment to that behavior. The curves look like jagged broken waveform lines, and when the model comes out it's forged in steel.

More opinions simultaneously will yield more experimental waveform potentials. I will find the most ideal conditions for self learning and then the findings will be published in many languages, with hundreds of citations, countless experiments leading from A to B, and a massive series of optimizations required to reach this point from where I began.

A trained omega predictor will allow heavy task-refined LLM protections of the geometric lookup tables.

This will include multiple curriculum operations for finetunes such as medical processes, law practices, multilingual shared vocabulary learning, multistructural lookups for cross-tool comparison and utility, and many other useful rapid learning processes that can be directly compartmentalized, snapped on, snapped off, and so on - similar to the methodology of a lora.

Except this is... this is no Lora. This is far more deep and when perfected will train far faster as shown by the Bertenstein, Vit x3, Vit x34, clip L and clip G ctx extensions, and the CaptionBert models. They converge rapidly and retain their cohesion. This system will allow those very models to stand on their own without the experts present while simultaneously learning rapid alignment R@1 recall capacity within the trained model itself.

They not only converged with R@1 being 100% recall capacity, multimodal variations such as Bertenstein showed you can deviate those using standard tokenization techniques with embeddings and encodings.

The mid-level experiments show;

student models DID require teachers to CONTINUE TRAINING.

BUT the students DID NOT require teachers to INFERENCE at full capacity.

The InfoNCE memory bank aligned through geometric distillation alignment processing allowed the students to not only stand - but stand on their own without the soups or teachers used to teach them.

This CaptionBert distillation is not a toy, it has genuine pragmatic use. By the time these experiments conclude, the CaptionBert and the entire chain of models trained - will be able to train without experts, will be able to learn from a MASSIVE amount of sources, SPECIFICALLY meant to RETAIN that data for utility without catastrophic forgetting. This will have it's own transformer structure hoisting the models up hand-in-hand with current-scale transformers and models as a cooperative companion.

These are purely cooperative collectives, not competition nor adversarial trainings at their core. Adversarial destroys the very subtlety of the instruction set, so it must be cooperative.

Omega is a very touchy formula conclusion; so without very specific measures protected by very specific structural boundaries, the omega structure will not predict correctly.

Omega must be computed in fp64, and the computation is miniscule compared to the full structure that sets it up. Everything must be orderly though, and everything orderly must be sterile.

Most of the CONTEXT elemental systems can be represented in FP8 while the majority of the geometric still requires minimum FP32 due to the way eigns and svd are calculated. Scatterpoint can reduce this but it will have performance dips without eigns and svd matching.

I'm currently working out an eig and eign kernel meant to operate specifically within a high degree of optimization for the use cases. This will evolve over time. When paired with the svd kernel, it will provide massive performance boosts for the direct use case, without impacting the overarching linear algebraic structure required for full solidity.

Self-distillation has shown improvement. I think most importantly I've discovered a core component that can be utilized as a geometric attention, the quaternion MHA. The constellation produces all the necessary information to allow the quaternion MHA to benefit from the information in a directly utilizable fashion.

The quaternion MHA is quite the vessel. It's bulky, has multiple MHA structures, and is shockingly effective in the process. I'll be refining this head in the coming days as a composite Procrustes alignment tool.

Geometric structure has a very high amount of informational accumulation potential, so a multi-series of MHA can capture a great amount of informational processing from those elements, if the elements are curated correctly and within the specifications.

I've taken the benchmarks of the model from 50% to 86-93% spearman utilizing a quaternion-oriented attention head.

This is getting dangerously close to 99.9% mutation detection accuracy, with a model deemed 50% accurate - all by extracting geometric features from the constellation and training the ensemble head with the correct rules.

These are spearman result logits. These are in fact detecting the results.

This is the power of what I'm doing. From 50% to 90% in 48 hours with a single GPU.

Training your own alignment only requires a piece of the dataset you wish to run and about 8 hours or so. Run it, fall asleep, check on it in the morning. It'll be ready. Extract features, train your head in minutes. The spearman will be nearly perfect.

I'm currently preparing what I consider to be the final head that will need to be created. The quaternion head, which will be specifically predictive based on an ensemble of four divergent-methodology heads, each specifically tasked to solve the SVD in conjunction with the features. This system should extract any little bit of differentiation that exists. The imaginary head is the most crucial. Explaining this requires an entire paper of it's own.

I call this imaginary head the "Cletus" head, as it's inherently lesser accuracy in relation to the others. However, without it the combination does not coalesce correctly. Without the Cletus, the model does not reach full cohesion. This head is the most crucial, because it has the hardest job. It's actually the one who returned from the battlefield with the blueprint to describe everything it saw.

I expect the sheer geometric alignment alone to yield a new form of Adam tuning specific to introspective analytical alignment and with that a new format of optimizer dedicated to geometric preservation in conjunction with informational data accumulation. I also expect a new methodology for larger-buffer data movement kernel-wise, a structural boundary for SVD limitations within full spectrum, a substructure measured collapse state of SVD when projected, and multiple other models that will have hiccups and growing pains.

These tools are all building to the end-state format, which will express everything simultaneously in order to combine the necessary data from many many forms of models together, without requiring direct tooling to each model simultaneously.

Such finalized tools will include a reusable pretrained geometric patchwork that exhibits all the necessary traits of a geometric structure in it's frozen state, capable of being finetuned quickly into any other state, or simply utilized as a lookup beacon with the correct geometric transformer alignment.

The geometric transformer, which is specifically a revamped format for the transformer intentionally designed with the structural preservation of the overarching structure in mind, rather than falling directly to the naturalistic entropy of immediate solution over larger-scale contribution. This system will not replace rope, it will contribute to the concept of long-concept preservation and work hand-in-hand with systems like rope, attention, and original transformers simultaneously. ROPE based models will benefit most from this structure, as they are already trained intrinsically with alignment and rotation at their cores.

The geometric transformer by design takes nth inputs in as variant states, and those are transformed internally. Utilizing this by it's default state will yield by design, but it will require tuning and curation for specific use cases no matter which case. This is conceptually familiar to those who use transformers, and simultaneously intimidating to those who understand what I'm describing I'd think. I myself am a little intimidated that I'm this close as-is.

There are multiple other prototypes at work all leading to the geometric transformer, which will be both an empirically superior utility to any of the utilities I currently use, and embody the very essence of the geometric structure that I'm currently working with as a full trainable data mutation operation - meant to directly attenuate the structure of the observation, to the expectation of the autograd and gradients.

Getting pretty close to a few pieces, but not there yet.

I've spent the better part of the day refactoring the geolip-core github code so it would be better inline with the actual findings, and I'm currently having claude build the models using the geofractal router system.

With that I'll enable a dummy-clause structure, so the component code files can be snipped out and work standalone as necessary. Due to the geofractal router's rigidity as a structure, geovocab's problematic multi-layer formatting for formulas that often have strange hardware quirks, and a few of the more reusable systems requiring modularity - I'll just build it like this to allow for just... USE MINE INSTEAD mentality.

You'll be able to just snip them out and use them, like many of the representations within the "models" experiment folders. They are simply standalone that may or may not snap onto pieces of the larger wholes.

geolip-core will be built specifically with the geofractal router structure in mind, inheriting it's strengths, weaknesses, and hardware control - while simultaneously having a wrapper that simply says: use standard pytorch instead.

Using standard pytorch will disable much of the functionality, but the components in their standalone forms WILL WORK. The pipelines are another story.

Keep my attribution and naming in the comments please, this is a testament to a very long series of research that resulted in solutions to problems rather than trying to introduce more problems. Attribution is all I wish, and you can make your fortune from that. I believe many of the great minds of the past would agree; Nikola Tesla I believe would agree, accreditation is all I want, but not for my name - for them and my humble contribution. The greats who put the pieces together and solved the biggest problems.

As we grow, the shadows of giants are cast upon the surfaces of life and stone. Work hard, progress steadily, expand your mind, build your skills, and by the time you have any time to look down... you will be casting a shadow of your own. As we grow old and our shadows grow, others are born and see the cast shadows. Encouraging them through the same process is all I know how to do.

Wrote a triton kernel to approximate SVD at around 15000x on blackwell architecture, while the standard torch.linalg.svd basically sits in a swamp of slow.

It only tackles small kernel sizes for now, 3x3, which is the current experiment's encoder paradigm. Standard SVD causes death by a thousand cuts when using small matrixes. Smaller matrixes provide a much more robust access to certain elemental linkages on many spectrum.

The formula isn't perfect. It's absolutely lightning quick though. The svd_trison.py file has a profiler.

https://huggingface.co/AbstractPhil/geolip-hypersphere-experiments/blob/main/spectral/notebooks/experiment_2_manifold_structures.ipynb

https://huggingface.co/AbstractPhil/geolip-core/blob/main/svd_triton.py

Incoming the geofractal router structure.

It will provide the necessary hardware and software implications to create much larger structures and curate the code in a much more effective way to hardware control than simply leaving it up to random chance or ai.

As I expand the system I will be heavily testing to include systems like Ulysses, accelerate, and more to encompass a larger array of learning. This will be crucial to building a proper bert trainer as well.

Might get lost down this scattering point system, it seems highly responsive and deterministic. I might make some PRs to the kymatio version for speed as well.

I'm seeing a large series of discrepancies between what Claude THOUGHT was correct, and what the experiments that Claude is yielding are producing.

This will take a large series of micro managing and consultation with multiple AIs to get working formulas for some of these more complex geometric substrates.

The calculations are exceedingly complex, so I will be adopting the https://github.com/kymatio/kymatio repo directly into the geofractal repo soon.