Natural Language Edge Labelling: Decoupling Intent from Execution in Structured LM Reasoning

Controllers for structured LM reasoning (e.g., Chain-of-Thought, self-consistency, and Tree-of-Thoughts) often entangle what to try next with how to execute it, exposing only coarse global knobs and yielding brittle, compute-inefficient, and hard-to-audit behavior. We introduce Natural Language Edge Labelling (NLEL), a labeller-tuner overlay that attaches a free-form natural-language directive to each search edge and translates it into a schema-bounded control vector for decoding, search (branch quotas, exploration $\beta$), generation bundle size, retrieval mixtures, and verification passes. A labeller $\Lambda$ emits labels from the parent state and a compact context; a tuner $\Psi$ maps $(P, L, C)\to \Pi$, with strict schema validation and trust-region projection around safe defaults. Downstream selection remains ToT-style with score $S=\mu+\beta\sigma$ and depth-annealed $\beta$. We show NLEL strictly generalizes CoT/ToT, prove an anytime-monotonicity property for top-$k$ selection under label-conditioned bundles, and bound selector shortfall by control-vector distortion, providing decision-relevant justification for guards like trust regions and verification passes. We instantiate $\Psi$ as a prompt-only JSON Parameter Emitter and preregister an evaluation on GSM8K, MATH (subset), StrategyQA, and ARC-Challenge with compute-aware reporting (success@compute, tokens-per-success) and ablations over $\Lambda$, $\Psi$, trust-region radius, and control quantization; preregistered forecasts anticipate accuracy gains at comparable token budgets and improved success@compute under constraints. NLEL offers an interpretable, model-agnostic interface that separates intent from execution for controllable, auditable LM inference.

Lateral Tree-of-Thoughts Surpasses ToT by Incorporating Logically-Consistent, Low-Utility Candidates

Modern deployments increasingly allocate large test-time compute (thousands of tokens or many node expansions) to boost reliability. Under such budgets, standard Tree-of-Thoughts-style search exhibits two pathologies: breadth saturation (additional samples mostly produce near-duplicates, so width stops growing) and depth myopia (noisy short-horizon utilities prune branches whose payoff appears after a few more steps). We propose Lateral Tree-of-Thoughts (LToT), a drop-in controller that separates utility from logical consistency and treats low-utility but consistent candidates as assets rather than waste. The frontier is split into mainlines (high-utility candidates used for exploitation) and laterals (consistent, initially low-utility candidates that receive short, cheap probes before judgment). LToT explores laterals via Lateral Racing with Short-Circuit (LR--SC): a capped successive-halving race that spreads tiny probes across a very wide lateral set, uses width-aware thresholds with repeat-to-confirm, and immediately promotes a branch once its envelope clears the mainline bar; mainlines are kept intentionally narrow so surplus compute is invested where width is cheap. We prove a pseudolinear lateral cost $\Theta(N_0 \log_{\eta} N_0)$ with logarithmically many rungs (initial lateral width $N_0$; culling factor $\eta>1$), in contrast to the exponential growth of uncapped mainlines. Empirical evaluations on benchmark tasks are in preparation and will be added in a future revision. In short, LToT turns large test-time budgets into principled diversity while preserving promotion discipline, mitigating saturation and myopia without inflating compute.

Application of a Shallow Neural Network to Short-Term Stock Trading

Machine learning is increasingly prevalent in stock market trading. Though neural networks have seen success in computer vision and natural language processing, they have not been as useful in stock market trading. To demonstrate the applicability of a neural network in stock trading, we made a single-layer neural network that recommends buying or selling shares of a stock by comparing the highest high of 10 consecutive days with that of the next 10 days, a process repeated for the stock's year-long historical data. A chi-squared analysis found that the neural network can accurately and appropriately decide whether to buy or sell shares for a given stock, showing that a neural network can make simple decisions about the stock market.