Wirkung
die Wirkung, German noun — effect. What a cause leaves behind once it has acted.
Wirkung Inc. is a research company. We find the exact structure inside expensive computation — in AI inference and in mathematics — and build systems that never compute the same thing twice.
Latest Kolibri-1, the full 78B mixture of experts, at one million tokens in a constant 0.21 GB per requestThe thesis
Knowledge is compute. A result found once can replace the search that produced it. Scarcity as method.
An exact formula, a proven rank bound, the route a model took through its own layers: each of them can stand in for the work that found it. Most of today's AI spend is the same work being done again on fresh hardware.
Everything we build applies one rule from a different side: discover the exact form, certify it, keep it, and let the next run start from there. The hardware next to the result gets cheaper every time. That is how a model written for a datacenter GPU ends up running on a 16 GB desktop, and then on a server with no GPU at all.
X = Xknown (rail · proof · rule) + R (actually computed) — we push R toward zero.
Flagship release · October 2026
Aleph Alpha's Kolibri-1 — the full 78B mixture of experts, all 384 routed experts, 3.46B active — with an attention state that no longer grows with the context. Same weights. No retraining. Every answer checked against the text.
| native Kolibri-1 | this release | |
|---|---|---|
| Requests on two H100 at 1M tokens | 5 | 30060× |
| Decode at 262k tokens, one RTX PRO 6000 | 209 tok/s | 957 tok/s4.6× |
| RULER at 1M tokens, 13-task mean | 68.6 single pass | 93.9M-Rail |
| The same 131k context asked again | 20.0 s | 0.11 sfrom the map |
| A new question to a 1M-token document read once | 160 s | 6.6–11.6 s |
Two layers on top of the unchanged weights: a constant attention state — an exact band of the last 1,024 tokens plus a fixed store of far tokens, one exact softmax — and M-Rail, which learns readable rules from Kolibri's own practice runs, gates every answer against the text and keeps each run as a 143-byte track.
Open models
Every model ships with its paper, its evaluation scripts and the numbers on its card. Published under the Hugging Face organization tfwnotops.
The full mixture of experts at a million tokens in 0.21 GB per request. RULER 93.9 at 1M; 300 concurrent requests on two H100.
0.208 GB
attention state per request, at every length huggingface.co/tfwnotops ↗1.18 GiB
attention state at every context length40 of 40 pass keys at +0.0084 nat per token. The whole model at 32k tokens on a 16 GB Mac mini M4, 157 ms per token. Answers seen before return from the map in 0.05 ms.
Model card ↗ 27B ternary · crystallized attention5 decays
per head, found by the engine, not designedThe first constant-state model of the line: full-attention heads replaced by a crystallized carrier — a key bias times five exponential decays with a rank-8 term — plus exact index correction.
Model card ↗ 1.5B · Apple Neural Engine470 tok/s
on the Neural Engine of a Mac miniA whole transformer compiled into a causal graph with a 14.4 MiB state and no KV cache. Answers are stored as reusable .mrail tracks.
What we build
the exact discovery engine
It searches for closed forms and constructions, certifies each candidate exactly, installs proven results into its own search, and learns as much from failed attempts as from successes. Four instructions learned from its own exact solutions raised the solved part of an untouched test set from 19 to 36 of 179 at 3.6× the search work — deeper brute search reached 26 for 7.7×.
It proposed a replacement for softmax attention in about a minute, found the carrier forms inside our models, and produced every tensor result on this page. Wirkung runs on CPUs and scales out across cheap instances, one engine learning from the others.
A persistent, lossless record of what a model has already computed, shared across instances and devices. Repeated work is read from the rail instead of recomputed; every run makes the next one faster. A million-token run is kept as a 143-byte track. A company's rail is its own property. Open format: mrail on PyPI.
GPU workloads on machines that have no GPU. sGPU presents a GPU to the program and serves the computation from the rail and from exact CPU block algorithms derived by the engine. A 27B open model currently runs natively this way on a GPU-less server. Next on the roadmap: graphics APIs. The project lives at sgpu.de (coming soon).
A model format in which the network lives on disk as a graph and streams through the accelerator as needed, so it no longer has to fit in memory. A full model has run through the Apple Neural Engine on a desktop this way.
Attention heads replaced by recurrence and a fixed exact store, with a state that does not grow with the context. Inference cost stays flat as the conversation gets longer — from a 1.5B on the Neural Engine to a 78B mixture of experts at a million tokens.
Mathematics
Pratt's balanced tripartition tensor Pn links Strassen's asymptotic rank conjecture to the Set Cover Conjecture. In October 2026 Wirkung moved the bound for P₃ — an 84 × 84 × 84 tensor — four times.
The 212 identity is verified on all 24,010 coefficients in rational arithmetic by two independent checkers and by an exact evaluation of the torus limit.
Papers
Every certified success and every failure of the engine's search episodes — near-misses, abstentions and preference pairs included — with exact certificates. CC BY 4.0.
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