Project Info

Geometric Linguistic Transformations

Inspiration

Hi, I’m Anna. I’m thirty-six, I have worked in IT for about fourteen years, and this project began because one day I decided to apply for a master’s program in machine learning. It is one of those strong programs where you can receive a scholarship, but first you have to show that you are capable of doing something real. And then I remembered something. A very long time ago, in the distant year of 2012, I graduated from university and defended a thesis connected with Lie algebras. After that came fourteen years of ordinary IT life: systems, databases, architecture, documentation, code, teams, deadlines, production incidents, and approximately one million things that had very little to do with academic mathematics. I had forgotten a lot. Some ideas that I once understood now looked completely unfamiliar. I had almost no recent academic practice. I did not have a laboratory, a university position, a scientific team, or fifteen free years to study everything again from the beginning. So I asked GPT-5.6 a simple question: Can ideas from Lie algebra be useful for understanding transformers? I did not ask it to write a paper for me. At first, I only wanted to understand whether the question made any sense. That conversation became an experiment. The experiment became a repository. The repository became a growing independent research program. The original question was this: When a transformer changes a statement into a negation, a question, another tense, or another linguistic form, does that change leave a repeatable geometric trace inside the model? Not only a word such as “not”. Not only a question mark. Not only the final form of the sentence. But the transformation itself. The project was inspired by Lie algebra, but the current results do not prove that transformers contain a Lie algebra. That is still an open and much more difficult question.

What it does

The basic idea is simple. I take two related sentences: She is happy. She is not happy. A transformer converts each sentence into a numerical representation called an embedding. I then calculate the difference between the two embeddings: This delta is a vector: a direction and a distance inside the model’s embedding space. Then the research asks: Do examples of the same transformation move in similar directions? Can we distinguish negation from a question, a tense change, uncertainty, passive voice, or formalization? Does the pattern remain when the test sentences discuss completely different topics? Does the delta contain information that is not already present in the transformed sentence? Do different transformer architectures organize these transformations in similar ways? Can transformations be combined? Are the results real, or are we simply detecting surface clues such as particular words and punctuation? The repository is a working and reproducible research workflow. It contains: experiment scripts; controlled linguistic datasets; embedding extraction and analysis pipelines; source-only, target-only, concatenation, and delta baselines; semantic and harder holdout experiments; statistical controls; result tables and figures; reproducible report builders; draft research papers; reviewer-response notes; a dated research diary; positive, negative, and mixed results. The current evidence suggests that the relationship between two sentence embeddings can contain useful information about a linguistic transformation beyond the information found in either endpoint alone. But this is not presented as a finished theorem. Some results are strong. Some are mixed. Some beautiful early results turned out to be misleading. The repository preserves all of them. How I built it I want to be unusually honest about this part: I wrote very little of the code by hand. Codex wrote most of the implementation. I did not suddenly remember every mathematical concept, research method, Python library, and experimental technique that I had not used for fourteen years. Instead, I worked with Codex as a coding and research partner. I brought the question. I decided what I wanted to test. I chose which results looked important and which looked suspicious. I decided when an experiment was not strong enough, when another baseline was needed, and when a beautiful conclusion had to be removed. Codex turned those decisions into working code. It helped me: implement experiment pipelines; refactor research scripts; generate and process datasets; run model comparisons; add harder controls and ablations; calculate statistical results; build tables, figures, and reports; organize the repository; document the experiments; preserve a traceable history of the work. GPT-5.6 helped in a different way. It helped me return to mathematical ideas I had forgotten. It explained unfamiliar concepts in plain language. It helped me read papers paragraph by paragraph, compare my results with related work, formulate objections, and turn unclear questions into experiments that could actually be tested. But AI did not decide what the evidence meant. When a result looked almost perfect, I did not ask Codex to make a better chart. I asked it to try to break the result. Those additional experiments showed that some perfect syntax scores could be explained by surface clues in the transformed sentence. That changed the conclusion of the research. So the real workflow was not: AI generates code, and I accept the result. It was: I ask a question. Codex implements an experiment. We inspect the result. I challenge it. Codex implements another test. The claim becomes smaller, more careful, and hopefully more true. I remain responsible for the questions, decisions, interpretations, and any mistakes that are still present. The research foundation existed before OpenAI Build Week. During Build Week, I used Codex and GPT-5.6 to make the project easier to inspect, reproduce, test, and review, and to document clearly which parts existed before the event and which work was completed during the submission period. Challenges I ran into The first challenge was returning to research after fourteen years away from academic mathematics. I often did not understand a term in a paper. Sometimes I remembered the name of a concept but not how it worked. Sometimes I did not know whether my question was interesting, obvious, impossible, or simply wrong. AI made it possible to cross that first wall quickly, but understanding an explanation is not the same as proving that the explanation is correct. The second challenge was separating real geometric information from easy shortcuts. A model may appear to recognize negation because the transformed sentence contains the word “not”. It may recognize a question because of punctuation or sentence order. It may appear to discover a transformation while actually learning only the final form of the sentence. That is why the project compares delta vectors with the original sentence, the transformed sentence, and both endpoints together. The third challenge was resisting the desire to make the result sound larger than it really was. The project began with Lie algebra. That is an exciting idea. But an exciting origin does not mean that the final evidence proves algebraic structure. Some checks that initially looked impressive turned out to be mathematical or implementation identities rather than scientific evidence. Some hard-holdout experiments weakened the original claim. Some transformations behaved better than others. I kept these results instead of hiding them. The final challenge was working with AI itself. Codex can write code very quickly. GPT-5.6 can give a clear and convincing explanation. Neither speed nor confidence guarantees correctness. The generated code still has to be run. The results still have to be checked. References still have to be verified. A convincing interpretation still has to survive alternative explanations. Accomplishments that I am proud of I am proud that this became a real, open, reproducible research project instead of remaining one interesting conversation with GPT. The repository now contains experiments across multiple transformer architectures, progressively harder evaluation settings, statistical controls, reports, figures, and separate research directions. But I am most proud of the parts where the project proved itself wrong. One early experiment produced perfect classification results. It would have been very easy to place that number at the top of the README and call it a breakthrough. Instead, I asked for stronger baselines. The new tests showed that the endpoint sentence already contained enough surface information to solve much of the task. The perfect result was not evidence of deep geometric generalization. Finding that out made the project better. I am also proud that the repository reports boundary conditions where delta vectors do not win, and that the Lie-inspired experiments are described as diagnostics rather than as proof of a Lie algebra. A negative result is not a failed experiment when it prevents a false conclusion. And, personally, I am proud that at thirty-six, after fourteen years in industry, I returned to a type of work that I had almost decided no longer belonged to me. What I learned I learned that AI does not have to replace human thought. It can remove the wall that prevents a person from reaching the work in the first place. Without AI, returning to this field would have required months just to remember the vocabulary, find the right papers, understand unfamiliar methods, and learn how to implement every experiment. With AI, every unknown concept became a question I could ask immediately. A paper could be discussed one paragraph at a time. A vague idea could become a small experiment. A suspicious result could be attacked from several directions in one evening. This does not make universities, professors, experienced researchers, or peer review unnecessary. It does something else. It makes the entrance wider. My research may be imperfect. Some of its conclusions may change. The main hypothesis may eventually turn out to be unimportant, incorrect, or completely useless. That possibility does not make the attempt worthless. There are more than eight billion people on Earth. Imagine that one billion of them chose one scientific question they genuinely cared about and spent only two to four hours a week exploring it with the help of AI. Most of those experiments would not become famous papers. Many would fail. Some would repeat things that were already known. Some would be badly designed. Some, including mine, might lead nowhere. But a small part of them would find a new connection, notice an overlooked problem, test an unusual idea, improve an existing method, or solve something that makes life easier for millions of other people. One billion people contributing even a tiny amount of honest curiosity would create an amount of scientific attention that humanity has never had before. That is the most important idea behind this project. Not that everyone is suddenly a professor. Not that AI always knows the answer. But that many more people can now begin asking serious questions and making small, verifiable contributions. Science does not become weaker when more people are allowed to approach it. It becomes larger. What was completed during Build Week During OpenAI Build Week, the project did not become a separate demo app. Instead, Codex helped turn the existing research repository into a clearer, more testable research workflow and added a new behavior-level track called GLT-STEER. The main completed Build Week work was: a focused GPT-2 question activation-steering experiment; a no-steering base-rate control showing that GPT-2 does not naturally add question marks under the tested declarative prompts; an out-of-template control using freeform declarative sentences that were not part of the training templates; prompt-robustness checks across multiple prompt wrappers; a content-preservation audit asking whether steering only adds punctuation or also preserves source content; a copy-prompt follow-up showing that copy-like prompts preserve source content much better while still adding question form; a no-steering copy-prompt baseline showing that copy-like prompts alone do not produce question marks; a DistilGPT-2 replication showing that the effect transfers qualitatively but becomes much weaker; a first negation-steering attempt showing that the question-steering recipe does not automatically transfer to other transformations; a harder out-of-template question audit showing that the question effect survives structurally diverse sentences, although content preservation becomes harder; a delta-coherence diagnostic showing that GPT-2 question deltas are much more internally coherent than negation deltas, which helps explain why question steering works more cleanly under the current method; a full GPT-2 layer sweep showing that negation still does not become a clean steering target just by changing the intervention layer; an exclamation-mark control showing that final punctuation markers are much easier to steer than sentence-internal negation; a GPT-2 vs DistilGPT-2 question-delta norm diagnostic showing that DistilGPT-2 compresses later-layer question directions; a direct DistilGPT-2 layer/gain sweep showing that the earlier weak replication was parameter-sensitive rather than a hard model failure; public result summaries and CSV artifacts in the repository; cleanup of public repository structure so the visible repo remains a research artifact rather than a pile of submission notes. The most recent result is important because it narrows the claim in a useful way. The steering vector is not only causing GPT-2 to emit random question marks. Under copy-like prompts, it often preserves the source content and adds question form. But this works much better for prompt formats that already encourage copying or repeating the source sentence, and it remains weak for bare or quoted prompts. The follow-up no-steering audit is important: copy-like prompts by themselves produced 0.0000 question marks across 960 no-steering rows from GPT-2 and DistilGPT-2. This means the prompt explains source retention, but it does not explain the question-form effect. The DistilGPT-2 replication is useful but humbling. It preserves the qualitative target-versus-control separation, but the best question-and-preserved rate drops to 0.4625. That means the effect is not simply universal across GPT-family models; model dependence is now part of the honest story. The first negation-steering attempt is also important. It does not reproduce the question result. Under the same copy-like prompt design, negation target rows do not clearly beat matched controls. This means the project now has a sharper boundary: question steering works best so far, but other transformations need different prompts, metrics, or steering methods. The harder out-of-template audit is encouraging. It uses passive constructions, subordinate clauses, proper names, and numeric/time expressions. The question vector still produces question marks at rates between 0.7125 and 0.7500, while matched controls peak at 0.0375. The content-preserved rate is lower than in simpler sentences, which is exactly the honest boundary we should report. The newest diagnostic helps explain the question-versus-negation split. In GPT-2 hidden states, question transformation deltas are much more clustered than negation deltas across all layers. At the layers used for steering, question mean pairwise cosine is about 0.94-0.97, while negation is about 0.56. This suggests that the question vector is a cleaner intervention direction, while negation is geometrically more heterogeneous and probably harder for an autoregressive model to express by a single simple steering vector. The layer sweep strengthens that boundary: trying every GPT-2 layer did not reveal a clean negation intervention site. The best negation target-and-preserved rate reached only 0.1729, with controls still nontrivial. The exclamation control is a useful sanity check. A trivial final-marker transformation, statement -> statement!, steers very cleanly: up to 1.0000 exclamation-and-preserved in-template and 0.8000 on hard out-of-template sentences. This supports the idea that the question result is partly helped by the fact that ? is a final surface marker, while negation requires changing sentence-internal structure. The GPT-2 vs DistilGPT-2 diagnostic also explains part of the weaker DistilGPT-2 replication. DistilGPT-2 does not have smaller question deltas everywhere, but its later-layer question directions are much smaller than GPT-2's. At the final relative layer, the mean-norm ratio is 0.3341 and the centroid-norm ratio is 0.2923. The direct DistilGPT-2 layer/gain sweep revises that story. The earlier aggregate replication looked weak, but tuning the intervention site and gain recovers a strong setting: at gain=1.0, layer 2, and same_sentence prompts, DistilGPT-2 reaches question-and-preserved rate 0.8250, with matched controls at or below 0.0500. The same sweep also shows that gain matters: gain=0.5 is usable but weaker, while gain=1.5 over-steers and damages preservation. The current careful claim is: A GPT-2 question-transformation activation vector can steer output toward question form, and under copy-like prompts it can often preserve recognizable source content. Copy-like prompts alone do not create the question marks in the tested setup. DistilGPT-2 is also steerable, but it is much more sensitive to layer and gain: the best direct sweep setting reaches 0.8250 question-and-preserved, while over-strong gain collapses preservation. A first negation attempt and a full-layer negation sweep fail to produce a clean negation editor. A follow-up diagnostic suggests that negation deltas are much less geometrically coherent than question deltas, and an exclamation control shows that final punctuation markers are much easier to steer than sentence-internal transformations. A harder out-of-template audit supports generalization for question form but shows that content preservation gets harder as sentences become more complex. This is not yet robust general-purpose semantic editing. This is exactly the kind of result I want the project to preserve: positive, useful, but bounded. What is already done The current public repository contains: GLT-DV: delta-vector diagnostics with endpoint controls; GLT-SPOT: signed-permutation tests for ordered linguistic composition; GLT-MOLT: learned matrix/operator diagnostics and null controls; GLT-XFER: cross-model transfer and alignment stress tests; GLT-AFFECT: early affective-scale geometry controls; GLT-STEER: activation-steering experiments for GPT-2 and DistilGPT-2 question formation; requirements and reproducibility notes; result CSVs and experiment summaries; research drafts and roadmap files; Zenodo/citation metadata for archived research snapshots.

What's next

The immediate next step is criticism. I invite the judges, researchers, and developers who see this project to examine the methods, code, controls, conclusions, and negative results as critically as possible. I would rather discover a serious problem now than build a beautiful theory on top of a weak assumption. The technical research will continue with: stronger multi-seed validation; more difficult semantic controls; naturally written text instead of only controlled examples; additional modern transformer architectures; more languages; cross-model alignment; better tests of transformation composition; stricter semantic-preservation metrics for GLT-STEER; additional replication of question steering on another model family or another seed; redesigned steering tests for transformations beyond question formation, especially negation, tense, and modality; experiments that test whether geometric directions can change model behavior, not only classify transformations. The longer-term question is whether similar methods can describe transformations connected not only with grammar, but also with uncertainty, attitude, emotion, intensity, and subjective experience. Perhaps one day models could be trained and controlled using richer representations of how meaning changes, rather than only through words, labels, and examples. Perhaps this research will contribute to that. Perhaps it will only show that one particular approach does not work. Both outcomes are useful when they are tested honestly and shared openly. This project began with one slightly unreasonable question. I hope it encourages someone else to ask theirs. Anna, thirty-six, with love for everything new and not yet explained.

IF YOU DO NOT HAVE A BACKGROUND IN MATHEMATICS OR AI, START HERE

Modern artificial intelligence systems are becoming increasingly capable. They write texts and computer programs, reason, make decisions, and play an ever-growing role in our lives.

Yet their internal workings still remain, to a large extent, a black box.

We know how to build neural networks and how to train them. But we still do not fully understand what structures emerge inside them during training, how they represent knowledge, or which internal rules govern the transformation of information.

A biologist studies living organisms. A geologist studies the Earth and its rocks. This project studies neural models from the inside.

It searches for the geometry, algebra, and regularities of their internal representations — or perhaps for something that humanity does not yet have the mathematical language to describe.

Until we understand the internal structure of the systems we create, we are like blind kittens trying to defuse a bomb: we already know how to make the device increasingly powerful, but we still do not understand its inner mechanism well enough.

This project is an attempt to take at least one more step from observing the behaviour of artificial intelligence toward understanding how it actually works on the inside.

Geometric Linguistic Transformations

Research code, result tables, figures, and draft papers for GLT (Geometric Linguistic Transformations): an independent research program for testing whether linguistic transformations appear as reusable geometric objects in transformer embedding spaces.

This is an active and reproducible research repository. It is not presented as a finished theorem or a final paper, but as a working experimental pipeline, an evidence package, and an open scientific question.

1. Plain-Language Overview

Modern language models turn sentences into high-dimensional vectors. This project asks a simple question:

If one sentence is changed into another sentence, does the vector movement between them describe the kind of linguistic change that happened?

For example:

source sentence -> transformed sentence
statement       -> question
present tense   -> future tense
plain claim     -> uncertain claim
positive claim  -> negated claim

For each pair, we compute:

delta = embedding(transformed sentence) - embedding(source sentence)

Then we test whether these deltas behave like meaningful transformation objects rather than arbitrary differences between two sentences.

What We Have Found So Far

The current evidence supports a cautious version of the idea:

Sentence-pair deltas often contain information about the type of transformation.
In the main full-semantic experiments, deltas beat target-only baselines across several models under Linear SVC probes.
In harder sentence-pair holdouts such as UPAT, endpoint features can dominate. This suggests that delta geometry captures transformation type better than absolute transformation identity.
Some ordered transformations show structured composition effects, but this is not a proof of a Lie algebra.
Simple additive deltas predict target embeddings better than learned linear/affine maps, while learned maps are useful for algebraic closure diagnostics.
A first affective-scale experiment suggests that text embeddings treat love/hate-like polarity as curved affective-involvement geometry rather than a simple opposite-axis scale, but this remains a text-only lexical-geometry result and still needs stricter neutral-word controls before promotion.

What Is Not Claimed

This repository does not claim:

that transformer embeddings contain a complete linguistic algebra;
that the reported effects are independent of endpoint wording;
that syntax-holdout 1.0 results prove deep generalization;
that antisymmetry checks are scientific evidence;
that text-only affect geometry is grounded emotional experience;
that this is a submission-ready paper.

The project is deliberately conservative: positive results, failures, endpoint leakage, and hard-holdout boundaries are all kept in the record.

2. Quick Demo

The fastest demo is the GLT-STEER question experiment.

It shows a simple behavior-level result:

Without steering: GPT-2 repeats a statement.
With a question-transformation vector: GPT-2 starts producing question marks.
With random or wrong-class vectors: the question-mark effect does not appear.

Run the lightweight demo from the repository root:

.\.venv\Scripts\python.exe scripts\show_glt_steer_demo.py

This command does not download models or rerun the experiment. It reads the archived CSV in:

results/experiments/gpt2_question_activation_steering_focused_20260714_results/

Headline result:

condition	question mark rate
target question vector	`0.9350`
random-norm control	`0.0000`
wrong-class control	`0.0000`
negative-target control	`0.0000`

Stronger copy-prompt preservation result:

condition	question-and-preserved rate
target question vector, copy-like prompts	up to `0.9750`
wrong-vector / no-steering controls	`0.0000` in the matched headline rows

Prompt-only control:

condition	question mark rate
copy-like prompts without steering, GPT-2 + DistilGPT-2	`0.0000` across `960` no-steering rows

Full notes:

results/experiments/gpt2_question_activation_steering_focused_20260714_results/SUMMARY.md
results/experiments/gpt2_question_steering_controls_20260714_results/SUMMARY.md
results/experiments/gpt2_question_prompt_robustness_20260715_results/SUMMARY.md
results/experiments/gpt2_question_copy_prompt_preservation_20260716_results/SUMMARY.md
results/experiments/distilgpt2_question_copy_prompt_preservation_20260716_results/SUMMARY.md
results/experiments/question_copy_prompt_none_baseline_20260716_results/SUMMARY.md
results/experiments/gpt2_steering_delta_coherence_20260716_results/SUMMARY.md

Safe interpretation:

This is evidence that a question-transformation activation vector can steer GPT-2 toward question-like output form. It is not evidence that semantic editing is solved, and it is not proof of a complete linguistic algebra.

3. Technical Overview

GLT is organized by current publication priority. Track 1 / GLT-STEER is the active short-paper target; the other tracks are diagnostic or future-paper candidates.

Track 1 / GLT-STEER: Activation Steering

Question:

Can transformation vectors do behavior-level work inside a generative model?

Main evidence:

Central GLT-STEER interpretation: final-position surface markers such as ?, !, and ... are reliably steerable in GPT-2 using mean hidden-state delta vectors, while lexical or sentence-internal transformations such as negation and modality do not work under the same recipe.
A broad GPT-2/DistilGPT-2 pilot found that question steering was the clearest target for a focused rerun.
The focused GPT-2 question-steering run completed 6800 generations with no failures.
At layer 2, gain 0.75, target question steering produced question marks in 93.75% of generations.
Across all tested layers at gain 0.75, target question steering produced question marks in 93.50% of generations.
Random-norm, wrong-class, and negative-target controls produced 0.00% question marks in the aggregate control summary.
A follow-up control found no-steering question-mark base rate 0.0000 for both in-template and out-of-template prompts.
The same question vector transferred to 40 freeform out-of-template declarative sentences, producing question marks at rate 0.8375 while all compact controls stayed at 0.0000.
Prompt robustness controls show that the effect survives four prompt styles, with target question-mark rate 0.7750-0.9875 in-template and 0.8125-0.9250 out-of-template.
Content-preservation audits show that prompt wording matters: copy-like prompts preserve source content while adding question form much better than bare or quoted prompts.
Under copy-like prompts, target question steering reaches high question-and-preserved rates: 0.9625-0.9750 in-template and 0.8250-0.9000 out-of-template for repeat_sentence, same_sentence, and copy_sentence.
A copy-prompt none-baseline audit shows that copy-like prompts without steering produce 0.0000 question marks across 960 no-steering rows from GPT-2 and DistilGPT-2.
A DistilGPT-2 replication preserves the qualitative target-vs-control separation, but the first aggregate run was much weaker than GPT-2: best question-and-preserved rate 0.4625.
A first non-question extension to negation is negative: the current copy-prompt method does not show clean target-vs-control separation for negation.
A harder out-of-template question audit with passive clauses, subordinate clauses, proper names, and numeric/time expressions preserves the question-form effect: target question-mark rate 0.7125-0.7500, best matched control 0.0375.
A delta-coherence diagnostic explains part of the question/negation split: across all GPT-2 layers, question deltas are much more internally coherent than negation deltas. At the steering layers, mean pairwise cosine is 0.9693 vs 0.5621 on layer 2, and 0.9365 vs 0.5665 on layer 3.
A full-layer negation sweep over GPT-2 layers 0-11 does not find a clean negation layer. The best target-and-preserved rate is 0.1729, while controls also produce nontrivial rates up to 0.1229.
An exclamation-marker control supports the surface-marker explanation: statement -> statement! reaches exclamation-and-preserved rate 1.0000 in-template and 0.8000 on hard out-of-template sources, while no-steering remains 0.0000.
A second surface-ending control with ellipsis steering (statement -> statement...) shows that the effect is not question-specific: on hard out-of-template sources, target ellipsis rate reaches 0.925-0.950 and ellipsis-and-preserved reaches 0.475-0.575, while non-target controls produce 0.0000 ellipses.
A final-marker logit audit confirms that this is not just prompt base rate: no-steering marker rates are 0.0000, while target steering moves the intended marker token to rank 1 in most sequences and reaches aggregate marker rates 0.8542 for ?, 0.9063 for !, and 0.8750 for ....
A position-of-intervention audit shows that single prompt-position edits do not work (prompt_first, prompt_middle, and prompt_last_once all 0.0000 question rate), while distributed prompt editing works strongly: prompt_all_once reaches question rate 0.8625 and question-and-preserved rate 0.7896, close to the current last_each_step hook (0.9604 and 0.7917).
A DistilGPT-2 final-marker logit audit gives a positive but model-dependent transfer result: no-steering marker rates stay 0.0000, while target steering reaches aggregate marker rates 0.2986 for ?, 0.7778 for !, and 0.5139 for ...; this is strongest for exclamation and layer-2 ellipsis, and weaker for question.
A derived Track 1 / GLT-STEER CI audit now reports Wilson 95% confidence intervals and sample sizes for the headline GLT-STEER rows. Examples: GPT-2 final-marker target rates are ?=0.8542 (N=96, CI [0.7700, 0.9111]), !=0.9063 (N=96, CI [0.8313, 0.9499]), and ...=0.8750 (N=96, CI [0.7941, 0.9270]); DistilGPT-2 target rates are lower and marker-dependent.
A first marker-composition steering test compares ?, !, ?+!, ? then !, and ! then ? on hard out-of-template sources. Single vectors are clean (?=0.900, !=0.950 on same_sentence), while summed/ordered interventions produce mixed marker profiles and lower preservation. Marker profiles are often similar across orders, so this is best treated as a competition/saturation boundary for final-marker steering, not as evidence of noncommutative order structure.
A cleaner question + modality composition test is negative for the current modality recipe: question steering remains strong (0.900-0.975), but modality markers stay at 0.000 across all controls and prompt styles. This is an important boundary showing that non-final-marker composition needs redesigned prompts, metrics, or intervention sites.
A GPT-2 vs DistilGPT-2 question-delta norm diagnostic shows that DistilGPT-2 question directions are not uniformly smaller, but they are strongly compressed in later relative layers: final relative-layer mean-norm ratio 0.3341, centroid-norm ratio 0.2923.
A direct DistilGPT-2 layer/gain sweep shows that the weak aggregate replication was parameter-sensitive rather than a hard failure. At gain=1.0, layer 2, same_sentence prompts reach question-and-preserved rate 0.8250 with matched controls at or below 0.0500. gain=1.5 over-steers and collapses preservation.
A hard out-of-template DistilGPT-2 audit shows that the tuned setting still induces question marks on structurally diverse sources (0.725-0.800, controls 0.0000), but strict question-and-preserved rates are much lower (0.025-0.225, with copy_sentence=0.025). This does not replicate GPT-2's preservation result; it is a marker-form result only.
A fixed-parameter confirmatory audit reruns question, exclamation, and ellipsis steering on fresh hard-heldout sources without any layer/gain search. Target final-marker rates remain separated from controls: GPT-2 reaches 0.6562-0.8438 across markers with max matched controls at 0.0000; DistilGPT-2 reaches 0.6319-0.8958 with max matched controls at 0.0139. Strict marker-plus-content preservation is positive but modest, so this confirms form steering rather than semantic editing.
A runtime form-control applicability audit tests the obvious production baseline. Target steering still creates final markers when no-steering, strong-prompt, wrong-marker, random-norm, and negative-vector controls do not, but deterministic string_append_source is perfect. This narrows the practical claim: GLT-STEER is an activation-space diagnostic and form-bias intervention, not a better replacement for ordinary string postprocessing when the desired final marker is already known.

Current interpretation:

This is the first behavior-level intervention result in GLT. The current best explanation is the Final Marker Hypothesis: mean delta steering works reliably when the transformation can be expressed as a final-position surface marker, and fails or weakens sharply when the transformation requires lexical or sentence-internal rewriting. The best GPT-2 prompt families preserve much of the source content while adding question form, but this is still not a complete semantic-editing system and not proof of a complete linguistic algebra. DistilGPT-2 should be reported as form replication with weak hard-OOT preservation, not as full semantic replication. The runtime applicability audit adds an important boundary: for a known final-marker edit, deterministic postprocessing is stronger than steering, so the current application value is diagnostic and intervention-scientific rather than production text editing.

Important result folders:

results/experiments/gpt2_activation_steering_pilot_results/
results/experiments/gpt2_question_activation_steering_focused_20260714_results/
results/experiments/gpt2_question_steering_controls_20260714_results/
results/experiments/gpt2_question_prompt_robustness_20260715_results/
results/experiments/gpt2_question_content_preservation_20260716_results/
results/experiments/gpt2_question_copy_prompt_preservation_20260716_results/
results/experiments/distilgpt2_question_copy_prompt_preservation_20260716_results/
results/experiments/question_copy_prompt_none_baseline_20260716_results/
results/experiments/gpt2_negation_copy_prompt_steering_20260716_results/
results/experiments/gpt2_question_hard_oot_copy_prompt_steering_20260716_results/
results/experiments/gpt2_steering_delta_coherence_20260716_results/
results/experiments/gpt2_negation_copy_prompt_layer_sweep_20260716_results/
results/experiments/gpt2_exclamation_copy_prompt_steering_20260716_results/
results/experiments/gpt2_ellipsis_hard_oot_layer2_20260801_results/
results/experiments/gpt2_final_marker_logit_audit_layer2_3_20260810_v2_results/
results/experiments/gpt2_question_position_intervention_audit_layer2_3_20260821_results/
results/experiments/distilgpt2_final_marker_logit_audit_l1_2_3_gain10_20260821_results/
results/experiments/glt_steer_headline_ci_20260825_results/
results/experiments/gpt2_question_exclamation_marker_composition_layer2_3_20260801_results/
results/experiments/gpt2_question_modality_composition_layer2_3_20260808_v2_results/
results/experiments/gpt2_distilgpt2_question_delta_norms_20260716_results/
results/experiments/distilgpt2_question_copy_prompt_layer_gain_sweep_v2_gain05_20260717_results/
results/experiments/distilgpt2_question_copy_prompt_layer_gain_sweep_v3_gain10_20260717_results/
results/experiments/distilgpt2_question_copy_prompt_layer_gain_sweep_v3_gain15_20260717_results/
results/experiments/distilgpt2_question_hard_oot_best_layer2_gain10_20260801_results/
results/experiments/glt_steer_confirmatory_fixed_params_20260825_results/
results/experiments/glt_steer_apply_runtime_form_control_20260825_results/

Track 2A / GLT-MOLT: Matrix/Operator Diagnostics

Question:

If transformations are learned as linear or affine maps, do their commutators show closure-like structure?

This track compares:

additive: y ~= x + delta_op
linear:   y ~= W_op x
affine:   y ~= W_op x + b_op

Main evidence:

Simple additive displacement vectors outperform learned linear/affine operators at target prediction.
Learned operators are worse target predictors but expose weak matrix-commutator closure under random-subspace, norm-matched, signed-permutation, and spectral null controls.
Ridge sweeps show that algebraic cleanliness improves under stronger regularization, so closure results are reported as controlled compression diagnostics, not as a formal Lie-algebra proof.
Compact PCA-64 and PCA-128 sensitivity checks preserve the spectral-null closure signal on five stable multilingual encoders.

Important result folders:

results/experiments/glt_molt_affine_operator_9m_160t_1000null_results/
results/experiments/glt_molt_ridge_sweep_9m_160t_300null_results/
results/experiments/glt_molt_matched_nulls_9m_160t_a10_100_1000null_results/
results/experiments/glt_molt_spectral_nulls_9m_160t_a100_300null_g256_results/
results/experiments/glt_molt_spectral_pca_sweep_5m_160t_a100_300null_g256_results/
results/experiments/glt_molt_spectral_pca128_5m_160t_a100_300null_g256_results/

Track 2B / GLT-SPOT: Signed-Permutation Operator Tests

Question:

Do ordered linguistic transformations show nontrivial composition structure?

This track studies operations such as:

Symbol	Operation
`N`	negation
`Q`	question formation
`M`	modality/evidentiality
`T`	tense / temporal shift

The key diagnostic is a third-order signed endpoint sum:

S(A,B,C) = ABC + BCA + CAB - ACB - CBA - BAC

This is not called a Jacobi identity. It is a signed-permutation coherence test compared against null baselines.

Main evidence:

Pairwise order matters for several transformation pairs.
Semantic-equivalence controls shift noncommutativity distributions in the expected direction.
Multilingual audits show below-null signed-permutation ratios across 7 languages and multiple multilingual encoders.
Endpoint-subspace residualization shows the signal survives removal of several linear endpoint-derived probe subspaces.
Endpoint controls remain strong, so the result is framed as a controlled diagnostic rather than endpoint-independent algebra.

Main draft:

paper/articles/lie-style-linguistic-operators/draft.md

Important result folders:

results/experiments/lie_multilingual_max_results/
results/experiments/lie_endpoint_subspace_9m_96t_pca128_results/
results/experiments/lie_multilingual_triple_endpoint_controls_7m_96t_results/
results/experiments/lie_structure_constants_results/

Track 3 / GLT-DV: Delta-Vector Diagnostics

Question:

Do sentence-pair displacement vectors encode linguistic transformation type beyond source-only or target-only endpoint features?

Main evidence:

Multiseed full-semantic ablations show reproducible delta > y_only under Linear SVC across the original model set.
McNemar tests and seed-level intervals support the Linear SVC delta advantage.
Large/modern spot-checks include BERT-large and DeBERTa-v3-base.
Syntax-holdout 1.0 is treated as target/surface leakage because y_only also solves it.
UPAT is kept as a bounded hard-holdout result: endpoint features dominate in that regime.

Main draft:

paper/articles/geometric-transformation-vectors/draft.md

Important result files:

results/ablation_multiseed_aggregated.csv
results/ablation_multiseed_mcnemar.csv
results/track1_multiseed_effect_intervals.csv
results/experiments/upat_audit_results/
results/experiments/track1_spotcheck_large_results/

Track 4 / GLT-XFER: Cross-Model Transfer

Question:

Does transformation geometry transfer across embedding models after alignment?

Main evidence:

UPAT-large Procrustes transfer survives N=1000 random-label, random-pairing, and random-orthogonal null controls.
Held-out anchor alignment-size curves show transfer improves with more alignment anchors.
RISE/MDV-style prototype comparisons and spherical delta steering tests separate target-cosine accuracy from transformation-neighborhood retrieval.

Current status:

This is a stress-test and comparison track, not the main novelty claim. It is positioned relative to RISE, which is the closest neighboring work on geometric rotations for semantic-syntactic transformations.

Important result folder:

results/experiments/upat_large_results/

Track 5 / GLT-AFFECT: Graded Affective Geometry

Question:

Do graded emotional polarity scales form simple straight axes, or curved semantic geometry?

Current text-only scale:

hate -> dislike -> indifferent -> like -> love

Main evidence:

Adjacent affective steps are not uniform.
neutral -> love and neutral -> hate are not opposite directions in text embeddings.
Marker-only pooling and lexical-specificity controls weaken but preserve a small affect-leading signal.
Bootstrap contrasts support a stable affect-specific excess over several lexical controls, but a substantial generic lexical-substitution component remains.
A stricter length/frequency-matched neutral-word ladder is still missing, so GLT-AFFECT should not yet be framed as a promoted paper-level claim.

Current interpretation:

GLT-AFFECT is evidence about language-representation geometry, not grounded affective experience.

Related Work Positioning

Closest neighboring work:

Freenor and Alvarez 2026, RISE: geometric rotations for discourse-level semantic-syntactic transformations across languages and embedding models.
Xia and Kalita 2025, Linear Relational Decoding of Morphology in Language Models: relation-specific matrix operators motivate GLT-MOLT.
Park, Choe, and Veitch 2023/2024: Linear Representation Hypothesis framing for representation geometry.
De Raedt et al. 2021: geometric cross-lingual linguistic transformations with pretrained autoencoders.

This repository's distinct angle is not "geometric transformations exist" in the broadest sense. Its contribution is a set of endpoint-controlled diagnostics, null baselines, signed-composition tests, operator-closure audits, and explicit negative/bounded results.

Repository Map

paper/
- research_program.md: current research roadmap.
- research_roadmap.md: research backlog and completed changes.
- related_work_positioning.md: positioning against RISE, LRH, and related work.
- articles/: draft paper candidates.
- figures/: curated figures used in drafts and reports.
research/
- diary.md: dated research diary.
- PROTOCOL.md: working protocol.
reports/
- PDF packets and release notes for external verification.
results/
- aggregate CSV summaries and experiment artifacts.
- results/experiments/: experiment-specific CSVs, figures, metadata, and run summaries.
scripts/
- experiment scripts, report builders, figure builders, and post-hoc analysis scripts.

Main Artifacts

Research program: paper/research_program.md
Current Track 1 draft: paper/articles/glt-steer-activation-editors/draft.md
Current Track 1 submission PDF: reports/2026-08-25_glt_steer_submission_draft.pdf
Track 2 / GLT-SPOT + GLT-MOLT draft: paper/articles/lie-style-linguistic-operators/draft.md
Track 3 / GLT-DV draft: paper/articles/geometric-transformation-vectors/draft.md
Results index: results/README.md
Main live report: reports/2026-06-23_research_report.pdf
Zenodo snapshot report: reports/2026-06-13_archival_report.pdf

Reproducibility

The datasets in this repository are synthetic controlled sentence-pair templates generated by scripts in scripts/; no external natural-language corpus is required for the archived experiments.

The current review environment is pinned in:

requirements.txt

Run scripts from the repository root, for example:

.\.venv\Scripts\python.exe scripts\build_research_report.py

General reproducibility path:

Inspect or run scripts in scripts/.
Compare outputs against CSVs and figures in results/ and results/experiments/.
Read the corresponding RUN_SUMMARY.md files in experiment folders.
Rebuild the research report if needed with scripts/build_research_report.py.

Large intermediate vector caches (*.npy, *.npz), local virtual environments, IDE files, .env, logs, and review zip archives are intentionally excluded from git.

Citable Snapshots

The repository includes:

CITATION.cff for GitHub's citation widget.
.zenodo.json for Zenodo/GitHub release archiving.

Latest Zenodo version DOI:

10.5281/zenodo.20829303

Previous Zenodo version DOI:

10.5281/zenodo.20680414

Please cite this as a software/research-artifact snapshot, not as a peer-reviewed publication.

License

MIT. See LICENSE.

Analysis

Compare with all teams

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Metric

Anna Simakova
20

Figures cover GitHub contributors during the hackathon window. A co-authored commit counts in full for each author, so per-member totals add up to more than the whole-team figures.

Technology

Found in codeClaimed only

Hugging FaceIn code
PythonIn code
PyTorchIn code
OpenAIClaimed

3 of 4 appear in the indexed code. 1 claimed on Devpost could not be matched to code, which may simply mean the tool leaves no trace in the repository.

AI coding agents

No AI coding agent signals were found in this repository.

Detected from committed agent config files and commit authorship. Absence of a signal is not proof an agent was unused.

Codebase size

Source size

1.1 MB

Source files

118

Counts recognized source files only; vendored directories, binaries and lockfiles are excluded, so this is smaller than the repository on disk.

Project Info

Geometric Linguistic Transformations

Inspiration

What it does

What's next

IF YOU DO NOT HAVE A BACKGROUND IN MATHEMATICS OR AI, START HERE

Geometric Linguistic Transformations

1. Plain-Language Overview

What We Have Found So Far

What Is Not Claimed

2. Quick Demo

3. Technical Overview

Track 1 / GLT-STEER: Activation Steering

Track 2A / GLT-MOLT: Matrix/Operator Diagnostics

Track 2B / GLT-SPOT: Signed-Permutation Operator Tests

Track 3 / GLT-DV: Delta-Vector Diagnostics

Track 4 / GLT-XFER: Cross-Model Transfer

Track 5 / GLT-AFFECT: Graded Affective Geometry

Related Work Positioning

Repository Map

Main Artifacts

Reproducibility

Citable Snapshots

License

Analysis

Technology

AI coding agents

Codebase size

Structure

Application logic

Languages

Dependencies