Method
How we study learning
Dynamical Synthesis is our proposed framework for learning through interaction. Controlled experiments help us test what contributes to a change in performance.
System boundary and state
Dynamical Synthesis describes system activity as a combination of internal processing and external input. An implementation must define its boundary, the information in its state and the rules that govern its actions and learning.
I = W(I) + you
I represents system activity, W its internal processing and you external input. This is shorthand; it does not specify a learning algorithm or prove that a system is stable.
A more explicit formulation writes the next state as s[t+1] = F(s[t], u[t]; θ[t]) and the action as a[t] = π(s[t], u[t]; θ[t]). Here u is incoming information, θ the learned parameters, F the state update and π the action rule.
Feedback and authority
An external message may repeat the system’s own answer without adding evidence. Proposed tests would trace the source of feedback and ask whether new observations or verified calculations help correct an error.
Information also does not grant permission. The system must separately specify who may change a task or operating limit. Testing these controls through successive updates remains a research goal.
Prediction and memory
Fish represents text as numerical vectors, called embeddings, to retrieve stored experience. Before each memory search, it combines the incoming message with a weighted representation of its actual previous reply, then normalises the result.
The predictor records an expected next message before the real message arrives. Prediction scores compare their embeddings and, when available, the probability assigned to the observed tokens. The score version is recorded with each result; answer correctness is checked separately.
Maintaining stored experience
Source and review rules determine which exchanges can enter active memory or training. Maintenance reduces memory weights and removes records below a configured threshold from retrieval, while preserving the original exchanges in the archive.
Reference settings include a previous-reply weight of 0.70 and a request for six memories. Individual studies may use different settings or disable retrieval altogether.
Training and update checks
Prediction and response generation use separate low-rank adapters while the base model stays fixed. Prediction training targets the next incoming message; response training uses reviewed answers or worked solutions.
Test examples are kept out of training. Reusing earlier training examples, known as replay, is a separate intervention whose contribution must be measured. A candidate update is checked for improvements and losses before it can be adopted.
Keeping an accepted reference
Experimental copies keep a previous configuration available for recovery. The continuation study permitted activation only on the isolated copy, and its reported updates were not adopted.
The planned curriculum study will test retention after a process restart with retrieval disabled. Its runner, checkpoint restoration and fresh optimizer state still require explicit verification before the main experiment.
How answers are checked
The main mathematics studies combined answer-structure checks, exact calculation and a separate review of the complete answer. A correct number alone was not enough if the response solved the wrong problem.
The model returned a structured graph of operations. A compiler translated valid graphs into Wolfram expressions, and a local Wolfram kernel evaluated them against reference answers. A separate AI reviewer could then reject incorrect or irrelevant reasoning, with model identities hidden.
The base model and an adapter trained on questions paired with other questions’ answers served as controls. Later plain-text studies used their own scoring procedures; the place-value follow-up used exact calculation without the extra AI review.
Interpreting the comparisons
Paired gains and losses were analysed with an exact McNemar test and a conservative confidence bound. Additional study criteria covered earlier-task losses and invalid outputs, so a score increase could still fail the protocol.
Plans were recorded locally rather than publicly preregistered. Shared task templates limit the independence of answer pairs, and AI review can make errors. Independent replication remains necessary.
Loopseed
A research programme at Dilate Technologies.
© 2026 Dilate Technologies