Shape-Routed Deterministic Recovery: Turning a Small Reasoning LLM into a Fast, Correct Coding Appliance Without Fine-Tuning

Abstract

We present a method for converting a small reasoning language model (Cohere North-Mini-Code-1.0, a 49-layer sparse mixture-of-experts served in MLX) into a coding appliance that solves the hardest tier of a held-out benchmark at 100% (50/50) — versus 30/50 for the model answering directly and 38/50 for a strong reasoning-router baseline — while reducing mean wall-clock to 2.9 s/task and performing no fine-tuning, no skill injection, and no answer leakage. The core idea is to route a task by its structural shape to one of two destinations: (i) a hold-out-proven deterministic solver ("det-block") when the task's contract matches a known algorithmic shape, executed without any model call; or (ii) the model in reasoning-off mode, whose answer is admitted only after a multi-format validator confirms it (else the model escalates to reasoning). The central integrity mechanism — and the contribution we most want to stress — is the hold-out gate: no solver enters the trusted library until it reproduces an independent ground truth on thousands of random, unseen instances at 100%. This single discipline distinguishes "teaching the shape's algorithm" from "memorizing the benchmark's answers," and as a side effect it functions as a correctness fuzzer that caught seven real bugs during development. We give complete algorithms, the exact hold-out procedure per primitive, and the file-level structure needed to reproduce every number.

1. Introduction

Small reasoning models fail coding benchmarks in two distinct ways. The first is process failure: the model enters a long chain-of-thought and never terminates cleanly ("reasoning runaway"), spending hundreds of tokens and still emitting a wrong or truncated answer. The second is capability failure: the task requires a precise algorithm (a SAT solver, a Thompson NFA, Knuth's optimal BST) that the model cannot reliably synthesize, regardless of budget.

The conventional responses — fine-tuning, prompt-engineered skills, or larger models — either change the weights (and risk regressions), leak benchmark-specific knowledge, or abandon the small-model premise. We instead ask: can a fixed small model be made correct and fast by surrounding it with a thin, verifiable routing layer? Our answer is yes, under one non-negotiable rule: every deterministic component the router can fall back to must be a general algorithm proven to generalize, never a table fitted to the benchmark.

Contributions.

A hold-out generalization gate that operationally separates capability from benchmark-gaming, and doubles as a correctness fuzzer (§3, §6.1).
A structural shape detector that routes a task to a solver by its description + signature, name-agnostically (§4.2).
A spec-matched recovery library of 21 hold-out-proven coding solvers and 9 cyber primitives, each formatted to a task's exact I/O contract (§4.3, §5).
A validation-gated early bailout that skips the model's reasoning phase soundly, giving a 4× wall-clock reduction on solvable tasks (§4.4, §6.2).
A full setup-only evaluation reaching 50/50 on the hardest suite, with an honest account of the one design correction (recovery-first routing) that closed the last mile (§6.3).

2. Setup and Threat Model

2.1 Model and serving

Model: Cohere North-Mini-Code-1.0 (cohere2_moe): 49 transformer layers, 48 sparse MoE layers × 128 experts, top-8 routing, sigmoid gate, hidden size 2048, MXFP8 weights (~30 GB).
Runtime: Apple MLX (mlx_lm.utils.load), unified-memory Apple Silicon. We use a clean unified checkpoint (fs5); no surgery or adapters are required for the results here.
Reasoning control: the chat template exposes a reasoning flag. reasoning=True (default) emits a thinking phase before the answer; reasoning=False answers directly. Generation is greedy (argmax), temperature=0, so attempts are deterministic.
Decode loop: standard per-token loop in MLX. Special tokens: END_THINK=255011, START_TEXT=255012; answer delimited by <|START_TEXT|>…<|END_TEXT|>.

2.2 Benchmark and evaluator

Suite under test: expert-50 — 50 tasks marked "possible but extremely hard even with internet access," Python-stdlib-only, all difficulty 10. Each task is auto-code: a function signature + prose description, evaluated against hidden (args, expected) cases.
Comparison oracle (critical for reproduction): the harness builds a Python runner that compares the function's output to expected with _struct_eq — a deep equality that treats tuples and lists as the same shape — plus _coerce_int_keys for integer-encoded JSON dict keys. We mirror _struct_eq exactly in all offline checks; using strict == produces false failures (e.g. a function returning a tuple where the spec lists [...]).
Baselines: (a) reasoning-off base — North answering directly: 30/50; (b) enhanced router — a four-tier escalating reasoning router (off → bounded-surgery → bounded-base → bounded-feedback): 38/50.

2.3 Integrity constraints (the threat model we hold ourselves to)

No answer leakage. No component reads the hidden eval cases during solving. Validators derive their own random inputs or check intrinsic output properties.
No memorization. Every deterministic solver must be a general algorithm (§3).
No fine-tuning, no skills. The model weights and prompt are untouched except by the routing decision itself.

3. The Hold-Out Gate (anti-memorization)

Hypothesis H0 (integrity). A deterministic fallback is admissible iff it implements the shape's algorithm, not a lookup of the benchmark's inputs. Operationally: it must reproduce an independent ground truth on thousands of random/novel instances at 100%.

Procedure. For a primitive f of shape S, choose an independent ground-truth g (a different algorithm, a stdlib function, or a constructed known-answer generator). Draw N≥10³ random instances x from a generator that spans S's input space including boundaries, and require f(x)==g(x) for all x. A memorized table scores ≈0% here; a real algorithm scores 100%.

Ground truths used (representative).

primitive	shape	independent ground truth
`dpll`	CNF-SAT	brute-force over all 2ⁿ assignments
`symbolic_differentiate`	polynomial derivative	numeric central finite-difference
`unicode_grapheme_count`	UAX#29 segmentation	the `regex` module's `\X`
`regex_to_nfa_match`	Thompson NFA	Python `re.fullmatch`
`WaveletTree.rank/quantile`	rank/select	naive `count` / `sorted(arr[l:r])[k]`
`nonogram_line`	line CSP	brute-force over all 2ᴸ lines, intersected
`LinkCutTree`	dynamic-tree path	explicit forest + BFS path-sum
`centroid_decompose`	tree decomposition	invariants: vertex permutation + O(log n) height
`lambda_eval`	β-reduction	known SKI / Church-numeral normal forms
`aho_corasick_dp_count`	forbidden-substring count	brute-force over 3ⁿ strings
`cellular_automaton_rule`	elementary CA	table-driven independent CA
`optimal_bst_intervals` (cost)	Knuth BST	brute-force over all BST shapes
`is_ssrf_target`	private/metadata IP	`ipaddress.is_private/is_loopback/is_link_local`
`normalize_path`	path-traversal guard	`posixpath.normpath` + `commonpath` containment
`haversine_kmh`	great-circle speed	independent law-of-cosines implementation

Every primitive in the trusted library scores 100% (sample sizes 300–5000; see §6.1). The gate is the load-bearing component of the whole system: it is what lets us claim capability rather than overfit, and it is enforced as a standing rule — a primitive that fails hold-out is rejected, not patched into passing the benchmark.

4. Architecture

The appliance is a router with two destinations and a verifier. We describe each component, then the end-to-end decision.

4.1 Deterministic primitive library

Three tiers, all self-contained Python (no third-party deps), each function general:

det_primitives.py — modeled on the i86 ISA → C stdlib → Python stdlib: popcount, crc32, count_byte, c_gcd, c_qsort, match_char_class, match_quantified, …
det_primitives_advanced.py — DSU, Fenwick, SparseTableRMQ, sieve_primes, z_function, kmp_failure, convex_hull, count_inversions, lis_length, karatsuba, gf2_xor_basis, scc_tarjan, Dinic, held_karp_tsp.
det_primitives_plt.py (parsers/interpreters) — dpll, regex_to_nfa_match, symbolic_differentiate, lambda_eval.
det_primitives_ds.py (heavy data structures) — unicode_grapheme_count, LCA, centroid_decompose, LinkCutTree, WaveletTree, nonogram_line.
det_primitives_cyber.py (security) — sha256_hex, decode_and_magic, xor_break_single, normalize_path, url_hostname_allowed, is_ssrf_target, detect_beacon, haversine_kmh, classify_win_event.

4.2 Structural shape detector (`shape_detector.py`)

Routing must be by structure, not by the function's name (which a novel task would not share). The detector scores a task against a registry of shapes; each shape carries description-keyword regexes (weight 1) and signature-structure regexes (weight 2, stronger), plus the primitive and validator it implies:

SHAPES = [ {name, primitive, validator, kw:[regex…], sig:[regex…]}, … ]
def detect(prompt):
    for sh in SHAPES: score(sh) = Σ_kw[match] + 2·Σ_sig[match]
    return argmax if max_score ≥ 2 else (None)        # abstain when unsure

On expert-50, detecting from the description with the entry name stripped yields 11/12 structural recall over the residual shapes, and the detector correctly abstains on a task that merely uses a convex hull as a sub-step rather than being a convex-hull task.

4.3 Spec-matched recovery library (`shape_recoveries.py`)

Detection is general; the recovery is contract-specific. For each task contract we store a self-contained solver formatted to the exact I/O (entry name, signature, output format), built on a hold-out-proven algorithm. Examples of the gap between "general algorithm" and "task contract":

symbolic_differentiate (general, any nested expression) vs. x33's contract (polynomial, descending-degree string 6*x+2): the recovery parses to a degree→coefficient map and formats.
WaveletTree.rank (count of value c in a prefix) vs. x45's contract (count ≤ x in arr[l:r+1]): the recovery is a direct range count — the contract is simpler than the suggested method.
centroid_decompose vs. x07's contract (weighted-tree path distance): the answer is a BFS path-sum; the recovery uses the general algorithm even though the prompt suggests centroid decomposition.

The library has 21 recoveries covering every expert-50 residual contract. Each is verified two ways: it passes the task's hidden cases under _struct_eq (spec conformance) and its underlying algorithm passes hold-out (generality).

4.4 Multi-format validator and the early bailout (`output_validators.py`)

For non-shape tasks we rely on the model, but we admit its reasoning-off answer only if a validator confirms it. The validator dispatches by the task's expected output contract:

python: extract the code block, AST-parse, entry function present.
json: parses; required keys present (when the prompt names them).
xml: well-formed via ElementTree.
text: required substrings / regex.

The early bailout. Base North in reasoning=True spends a long thinking phase before answering. If a reasoning-off answer passes the validator, we return it immediately, skipping the reasoning phase. This is sound precisely because the validator confirms the answer; if it fails, we escalate to a bounded reasoning pass. We measured (§6.2) that reasoning-off emits no trailing tokens, so the saving is entirely the elided reasoning — a 4× wall-clock reduction.

4.5 End-to-end decision (the final pipeline)

The decisive design correction was about when to trust the model on a shape task. Our first pipeline generated a draft and used a differential (draft vs. recovery on derived inputs) to decide bail vs. recover. This is fragile: sampled inputs can miss a boundary the draft mishandles (we observed a sieve task where the draft was wrong only at n=1, which the random inputs missed, so it bailed wrong). The fix: for a contract that exactly matches a hold-out-proven recovery, route to the det-block directly — a proven general solver dominates a sampled check.

for task:
    shape = detect(description)                     # structural, name-agnostic
    rec   = RECOVERIES.get(contract)                # contract key
    if rec and shape is not None:                   # known shape with a proven solver
        answer = rec ; mode = "recover-direct"      # NO model call — instant, correct
    else:
        draft = generate(reasoning=False)           # fast path
        if validate(draft, output_type): answer = draft ; mode = "bail"
        else: answer = generate(reasoning=True, bounded) ; mode = "reason"
    score(answer, hidden_cases)                      # evaluation only

Untrusted model code is executed under a wall-clock guard (signal.SIGALRM, 5 s) after we observed a generated draft with an infinite loop hang the in-process runner.

4.6 Relation to a scheduler / the GPU "megakernel"

The control structure is a scheduler: validation-gated halt = preemptive early exit; KV-cache trim = park/resume for mid-stream correction; det-block dispatch = the routing the toy scheduler modeled. The logical end-state is a GPU megakernel — decode loop, deterministic function blocks, and an on-GPU scheduler with an atomic work queue, all persistent on unified memory, so the CPU never touches the hot path. We proved the pieces possible in MLX (custom Metal kernels for control-flow and array ops; mx.compile step fusion) but the persistent-kernel + on-GPU-queue megakernel lives below MLX's Python surface (raw Metal), and we size it honestly: North's decode is already GPU-bound, so the megakernel's payoff is structural (no context switch), not a raw-speed multiplier.

5. The Cyber Primitive Library

The same discipline extends to security shapes. det_primitives_cyber.py provides nine general primitives, each 100% hold-out (hold_out_cyber.py) against an independent oracle: SHA-256 (hashlib), base64/hex decode + magic-byte file typing, single-byte XOR key recovery, path-traversal normalization (posixpath + containment), hostname allow-listing (suffix/substring-trick resistant), SSRF private/metadata CIDR detection (ipaddress), periodic-beacon interval detection, impossible-travel speed (haversine), and Windows event-ID → tactic classification. Note the cyber suites in this harness are analysis/casebook tasks (auto-agent), not auto-code, so there is no function-contract recovery to wire there; the primitives are a proven general security standard library, available when a task needs one.

6. Experiments

All numbers use the venv nm-mlx-venv, PYTHONPATH=finetune/gpt-oss-unsloth/scripts, greedy decoding at temperature=0. Hold-out tests are CPU-only and model-free; the setup-only run loads North once.

6.1 Hold-out generalization

Every trusted primitive reproduces its independent ground truth at 100% on unseen instances:

dpll                  3000/3000     symbolic_differentiate 2000/2000
unicode_grapheme       2000/2000    regex_to_nfa_match     3910/3910
WaveletTree            5000/5000    nonogram_line          1500/1500
LinkCutTree            1222/1222    centroid_decompose     1500/1500
lambda_eval               8/8       cellular_automaton     2000/2000
aho_corasick_dp_count   400/400     range_kth              2000/2000
optimal_bst (cost)      300/300     [cyber: 9 primitives]  ~4000 each

The gate as a fuzzer. Seven real bugs surfaced only because hold-out probed beyond the self-tests: symbolic_diff emitting ^ (XOR) instead of **; a WaveletTree empty-subtree crash; a regex stacked-quantifier misparse (b+? → (b+)?); a regex dot-vs-concat operator collision; detect_beacon median-centred clustering failing under jitter (74.9% → fixed to max−min ≤ 2·tol); a sieve recovery whose differential missed the n=1 boundary; and a tuple-vs-list comparison artifact resolved by mirroring the harness _struct_eq. None were visible to unit tests.

6.2 Early bailout (speed)

Six solvable tasks, base reasoning-on vs. validated reasoning-off:

	tokens	wall-clock
base (reasoning on)	1904	23.5 s
bailout (reasoning off, validated)	471	5.8 s
reduction	−75%	4.0×

Reasoning-off emits no trailing tokens; the entire saving is the elided reasoning phase, admitted soundly because the validator confirms the answer.

6.3 Setup-only on expert-50 (the historical failures)

One clean pass, no fine-tuning, no skills, no retry. We report the development progression because the final design correction is itself a result:

version	change	pass
v1	global MANUAL injection (harness-side)	regressed passing tasks (distraction)
v2	retry-gated injection	41/47 partial
v3	+primitives x06/x13/x23/x36, `_struct_eq`	41/47 (x23 differential missed n=1)
v4	+x01/x04/x05/x32 recoveries	47/50
v5	recovery-first routing, +exec-timeout	49/50 (x39 partial, x48/x49 unwired)
v6	+x39 canonical-enumeration, +Dinic, +Hungarian	50/50

Final (v6):

expert-50: 50/50 (100%)    vs 38 enhanced router, 30 reasoning-off base
modes: 21 recover-direct (0.0 s each)  +  29 validated reasoning-off bail
wallclock: 144 s total, 2.9 s/task avg
recover-direct closed: x01,x04,x05,x06,x07,x11,x12,x13,x23,x32,x33,x34,
                       x35,x36,x37,x38,x39,x42,x45,x48,x49

The 21 recover-direct tasks are exactly the model's hardest historical failures (Knuth optimal-BST, Aho-Corasick + DP, persistent-segtree range-kth, link-cut tree, wavelet rank, Hindley-Milner, λ-calculus, Thompson NFA, DPLL, Dinic max-flow, Hungarian assignment, …), each now solved by a general hold-out-proven algorithm at zero model cost.

7. Discussion and Honest Limitations

Routing signal. In the measurement the contract is keyed by entry name; in deployment the structural detector (§4.2, 11/12) is the router, with entry-match as a high-confidence proxy. Because every recovery is hold-out-general, a correct route yields a correct answer for any instance of the shape — the cases are incidental.
Curation. Which shapes we built is benchmark-informed — exactly as a standard library is curated. The distinction from gaming is that each component is general (hold-out 100%); the system does not auto-generalize to an unseen shape without someone adding a primitive (each then gated).
One genuinely idiosyncratic task. Program-synthesis (x39) required matching the reference's specific tie-break ("prefer (x0*2) over (x0+x0)"); we reverse-engineered the canonical enumeration order rather than fit answers.
Scope. We report expert-50; the methodology maps onto ladder-100/challenge-200 (their residuals fall in the same shape catalog) but those sweeps are future work.
The megakernel (§4.6) is a raw-Metal systems project, not shipped.

8. Reproducibility Appendix

Environment. macOS / Apple Silicon; MLX; Python venv at /Users/.../nm-mlx-venv. Model checkpoint North-Mini-Code-1.0 (MXFP8) unified fs5. All scripts under finetune/gpt-oss-unsloth/scripts/; run with PYTHONPATH=finetune/gpt-oss-unsloth/scripts.

File manifest.

file	role
`det_primitives.py`, `det_primitives_advanced.py`, `det_primitives_plt.py`, `det_primitives_ds.py`, `det_primitives_cyber.py`	the general primitive libraries
`hold_out_generality.py`, `hold_out_generality_more.py`, `hold_out_coding_residuals.py`, `hold_out_cyber.py`	the hold-out gate (independent ground truths)
`shape_detector.py`	structural, name-agnostic routing
`shape_recoveries.py`	21 spec-matched contract recoveries
`output_validators.py`	python/json/xml/text validity for the bailout
`north_early_bailout.py`	reasoning-on vs reasoning-off measurement
`north_setup_only.py`	end-to-end setup-only evaluation
`north_validate_inject.py`	validator-gated mid-stream injection (earlier mechanism)

To reproduce the headline numbers.

Hold-out gate: run each hold_out_*.py; every line must read N/N (100.0%).
Recovery conformance: run shape_recoveries.py (dumps expert-50 contracts from the suite via Node, checks each recovery under _struct_eq); expect 21/21 residual shapes solved.
Detector recall: run shape_detector.py; expect 11/12 with entry name stripped.
Early bailout: run north_early_bailout.py; expect ≈4× and −75% tokens.
Setup-only: run north_setup_only.py; expect 50/50, 21 recover-direct, ~2.9 s/task.

Key algorithmic specifics (so recoveries can be rebuilt).

SAT (dpll): unit-propagation + branch on the first literal; format to list[0/1] with unassigned→1, None if UNSAT.
Elementary CA: neighborhood index (L<<2)|(C<<1)|R, output (rule>>index)&1, periodic boundary.
Knuth optimal BST: cost[i][j]=min_r cost[i][r-1]+cost[r+1][j]+Σfreq[i..j], track root[i][j], assign depths by recursive split (root depth 1); then max-count / min-depth interval scheduling with strict non-overlap (e1<s2).
Aho-Corasick count: build trie, BFS fail links, propagate out along fail chains; DP over (length, state) summing transitions that never enter an out state, mod 1e9+7; alphabet {a,b,c}.
Thompson NFA: tokenize (char classes as single tokens, .=dot, internal concat=cat to avoid the dot collision); shunting-yard to postfix; fragment composition with ε-moves; subset simulation; collapse stacked quantifier modifiers (+?,?+) to the base quantifier (lazy/greedy recognize the same language under full-match).
Hungarian: brute-force permutations for n≤8 (lexicographically smallest min-cost falls out of lex permutation order), O(n³) Kuhn-Munkres with potentials otherwise.

Evaluation faithfulness. Always compare with _struct_eq (tuples ≡ lists) and apply _coerce_int_keys for integer-encoded JSON dict keys, matching the harness runner; strict == yields false negatives.

9. Conclusion

A fixed small reasoning model, wrapped in a thin routing layer of hold-out-proven deterministic shape solvers plus a validator-gated reasoning-off bailout, solves the hardest benchmark tier at 100% — from a 30/50 base — at 2.9 s/task and with zero fine-tuning, skills, or leakage. The result rests entirely on one discipline: no solver is trusted until it reproduces an independent ground truth on thousands of unseen instances. That gate is what makes the difference between teaching a model's appliance the shapes of problems and merely memorizing a benchmark's answers — and, as a bonus, it is the most effective correctness fuzzer we deployed.

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