Cognitively Decoupled Meta-Induction for Out-of-Distribution Generalization

Yuqian Wang; Yuanzheng Wang; Chaojun Xiao; Ke Xu; Bingxiang He; Jinghan Tan; Zijun Chen; Lu Chen

cs.LGOct 19, 2026

Cognitively Decoupled Meta-Induction for Out-of-Distribution Generalization

Authors: Yuqian Wang, Yuanzheng Wang, Chaojun Xiao, Ke Xu, Bingxiang He, Jinghan Tan, Zijun Chen, Lu Chen,

Organizations: Beijing Institute of Technology · University of Chinese Academy of Sciences · Department of Computer Science and Technology, Tsinghua University · Peking University ·

Abstract

In-context learning (ICL) tackles downstream tasks conditioned on demonstrations. This paradigm relies heavily on neighbor-based matching between queries and demonstrations, limiting out-of-distribution (OOD) performance. For better generalization, rule-based inductive reasoning derives task-level regularities, which we term task-level inductive representations (TIR), before directly answering. However, existing methods lack generalizable inductive ability across diverse tasks. Inspired by meta-learning, we propose Cognitive-Decoupling meta-Induction (CoDI) for TIR-based inductive reasoning on general tasks. CoDI comprises a Cognitive-Decoupling Framework for query-blind TIR induction, and a Dual-Loop Meta-Inductive Learning method for cross-task inducer optimization. Empirically, CoDI achieves substantial performance gains on five ID and OOD benchmarks, and preserves OOD gains without explicit induction at inference. Code is available at https://github.com/Yuqian-Wang2277/codi-meta-induction.

Figures & tables

Figure 1: ICL (left) surface-matches and fails OOD. TIR-based reasoning (right) induces a task-level rule that generalizes to both ID and OOD.

Figure 2: Overview of CoDI. The Cognitive-Decoupling Framework induces query-blind TIR with SG and executes each query with AS . Dual-Loop Meta-Inductive Learning applies candidate TIRs in the inner loop and optimizes SG across tasks in the outer loop via GRPO with EIR and ICR.

				BIG-Bench
Type	Model	Method	BBH ( $\Delta$ %)	ID ( $\Delta$ %)	OOD ( $\Delta$ %)	MATH-500 ( $\Delta$ %)	StratQA ( $\Delta$ %)	ReClor ( $\Delta$ %)	Avg.
w/o Training	Gemma-3-4B	FS	$37.41$	$26.00$	45.00	54.00	58.95	48.00	44.89
		S-FS	25.00 $-33$ %	18.33 $-30$ %	28.00 $-38$ %	60.00 $+11.1$ %	59.97 $+1.7$ %	46.40 $-3.3$ %	39.62
	Qwen3-4B	FS	$35.56$	$29.33$	53.33	63.13	69.97	83.60	55.82
		S-FS	27.78 $-22$ %	30.00 $+2$ %	38.33 $-28$ %	65.20 $+3.3$ %	64.19 $-8.3$ %	81.20 $-2.9$ %	51.12
		GEPA §	79.59	61.65	56.88	61.20	71.32	79.80	68.41

Table 1: Exact-match accuracy comparing CoDI with FS, S-FS, GEPA, MetaICL, and closed-source APIs on BBH, BIG-Bench ID/OOD, MATH-500, StrategyQA, and ReClor (w/o and w/ training).

\Delta

=(\text{score}-\text{FS})/\text{FS}\times 100

; red / blue = gain/loss. † Unfine-tuned; Gemini-3-flash = gemini-3-flash-preview . § GEPA: gemini-3-flash-preview optimizer, Qwen3-4B executor, four reflective iterations.

Configuration	ID	BBH	OOD
CoDI (EIR+ICR, full)	64.67	82.22	63.00
Reward component ablation
w/o ICR ( $\beta{=}0$ , EIR only)	$62.67$	$69.81$	$53.67$
w/o EIR (ICR only)	$49.00$	$69.07$	$53.67$
w/ raw Acc reward	$31.67$	$48.15$	$56.67$
w/ LLM Judge reward	$49.00$	$69.44$	$57.33$

Table 2: Qwen3-4B component ablations.

Strategy Format	ID	BBH	OOD	ICR
CoDI (semi-structured)	64.67	82.22	63.00	84.73
Free-form (no schema)	$46.00$	$53.52$	$40.00$	$75.59$
CoT-style (implicit structure)	$59.56$	$72.84$	$49.33$	$75.57$
Semi-structured section ablation
w/o [INDUCTIVE_RULE]	$42.33$	$49.44$	$39.67$	$74.27$
w/o [TASK_PROCEDURE]	$1.33$	$1.48$	$2.67$	$71.67$

Table 3: Qwen3-4B ablation comparing alternative TIR formats and individual schema sections.

Panel of Figure 3 — Figure 3: Trained CoDI-4B exceeds untuned 32B SG on BIG-Bench OOD with $8\times$ fewer parameters.

Panel of Figure 4 — Figure 4: Mean LOO rule sensitivity drops 73.4% after training, supporting cross-example abstraction.

Panel of Figure 5 — Figure 5: Post-CoDI raises OOD accuracy while shortening traces and example recitation, refuting a length-driven account and supporting rule-directed reasoning.

Panel of Figure 6 — Figure 6: BIG-Bench OOD accuracy (%) vs. shot count $K$ on Qwen3-4B (CoDI vs. few-shot ICL). The shrinking CoDI lead with more shots indicates parametric induction gains rather than richer context.

Panel of Figure 7 — Figure 7: Radar chart of Pre- and Post-CoDI strategy scores on six induction modes (Gemini-3-flash).

Few-shot ( $K{=}3$ ). BIG-Bench Navigate; decide return to origin. Ex1 N2,S2 $\to$ Yes; Ex2 E3,W3 $\to$ Yes; Ex3 N1,S1,E2,W2 $\to$ Yes (4 moves, returns). Test query. N4,S2,E3,W1 . Move combination unseen in supports; return to start? Gold No (final $(2,2)\neq(0,0)$ ).
Method	Solving process	Pred.	Behavior
FS	Compare query with all supports in context. Select Ex3 as the nearest match (four moves). Reuse the Yes label from Ex3 without coordinate tracking. Apply an action-count shortcut rather than origin logic, never checking whether the final position returns to $(0,0)$ .	Yes ✗	surface matching
S-FS	Induce a strategy from supports only without seeing the query. Rule text states track N/S/E/W and test the origin. At solve time, pattern-matches the test query to Ex3 and copies that move sequence instead of applying the rule. Output Yes without independent coordinate calculation or endpoint verification.	Yes ✗	example recitation
CoDI	SG induces a coordinate rule verified on Ex1–Ex3. AS initializes $(0,0)$ and parses four instructions. Updates coordinates to $(0,4)$ , $(0,2)$ , $(3,2)$ , and $(2,2)$ . Tests $(2,2)\neq(0,0)$ and outputs No.	No ✓	task-level regularity

Table 4: Navigate case study on a matched BIG-Bench Navigate episode (

K{=}3

; untrained FS/S-FS, trained CoDI, Qwen3-4B). Rows compare solver processes on the same episode. ✗/✓mark incorrect and correct predictions.

Panel of Figure 8 — Figure 8: Pairwise GPT-5 judgments favor CoDI on Correctness and Transferability but not on Executability or Conciseness, defining the polish-oriented boundary of RL-optimized TIR.

Task Type	Gem.-Flash FS / S-FS	GPT-5 FS / S-FS	Qw3-4B (CoDI)
Ctx.Param.Conf.	75.00 / 65.00	70.00 / 65.00	90.00
VitaminC	85.00 / 80.00	65.00 / 40.00	78.33
Elem.Math	99.00 / 89.00	95.00 / 75.00	97.67
Track.Shuf.	100.00 / 91.67	85.00 / 90.00	99.44
Bool.Expr.	90.00 / 95.00	100.00 / 85.00	98.33

Table 5: CoDI-induced strategies yield the largest OOD gains on rule-transfer-critical types under a fixed Qwen3-4B AS .

Appendix figures & tables14 assets

Supplementary material from the paper’s appendix.

Appendix

Hyperparameter	Value
Model configuration
Strategy Generator ( SG )	Qwen3-4B (trainable)
Answer Solver ( AS )	Qwen3-4B (frozen, non-thinking mode)
SFT demonstrations	Gemini-3-flash proposals, execution-filtered
Task filtering / splits	Qwen3-32B scoring + author spot-checks
Hardware	8 $\times$ A800 (80 GB)

Appendix

Table 6: Hyperparameters for CoDI training.

Tag	Name	Ind.?	Description
E	Example-recitation	No	The unit recalls, quotes, or closely paraphrases a specific support example without abstracting beyond it.
D	Direct-application	No	The unit applies facts or procedures to the current instance without first stating a cross-example pattern.
P	Pattern-abstraction	Yes	The unit states a general rule or invariant intended to hold across instances (inductive content).
R	Rule-application	Yes	The unit applies a rule or pattern that was already stated earlier in the trace.

Appendix

Table 7: Cognitive tags for sentence-level units inside <think> . “Ind.?” indicates inductive (rule-level) content; descriptions define the annotation target.

Metric	Pre	Post	$\Delta$	$p$
$L_{\mathrm{think}}$	5276	4171	$-1105$	$<10^{-3}$
$q_{E/R}$	1.079	0.674	$-0.405$	$3.0{\times}10^{-4}$
$r_{D\to P}$ (%)	4.36	6.21	$+1.85$	$4.0{\times}10^{-5}$
$\bar{\ell}_{P}$	89.4	108.6	$+19.2$	$8{\times}10^{-6}$
Acc OOD (matched, %)	45.2	92.4	$+47.2$	$<10^{-3}$
$n_{E}^{(\mathrm{ph1})}$	18.54	9.06	$-9.48$	$2.1{\times}10^{-4}$

Appendix

Table 8: Pre/Post-CoDI trace metrics on Qwen3-4B matched OOD tasks with valid thinking traces (

K{=}3

; subset of Table 1 OOD). Acc.: McNemar;

n_{E}^{(\mathrm{ph1})}

\rho_{E}

: paired

t

; remaining metrics: paired trajectory tests.

Mode	Gem. Pre	Gem. Post	G5 Pre	G5 Post
Compositional	1.23	1.51	1.18	1.46
Procedural	1.86	2.93	1.81	2.86
Constraint	1.96	3.46	1.88	3.38
Schema	2.47	3.19	2.41	3.12
Analogical	1.22	0.59	1.15	0.54
Pattern	1.09	0.47	1.14	0.53

Appendix

Table 9: Pre-/Post-CoDI six-mode scores (Gem.: full cohort, Fig. 7 ; G5:

n{=}40

). All six Post

-

Pre

\Delta

share the same sign across annotators.

Metric	Gem. $\Delta$	G5 $\Delta$	Sign
$L_{\mathrm{think}}$	$-1105$	$-968$	✓
$q_{E/R}$	$-0.405$	$-0.382$	✓
$r_{D\to P}$	$+1.85$	$+1.72$	✓
$\bar{\ell}_{P}$	$+19.2$	$+18.6$	✓
$n_{E}^{(\mathrm{ph1})}$ / $\rho_{E}$	$-9.48$ / $-4.36$	$-9.12$ / $-4.08$	✓
Six-mode signs	6/6	6/6	✓

Appendix

Table 10: Post

-

Pre trace deltas: Gem. (full cohort) vs. G5 (

n{=}40

). Sign agreement only (Appendix D.2 ).

Parameter	Value	ID	BBH	OOD
$K$ (shots)	1	48.89	44.20	34.71
	2	55.67	68.52	48.00
	$3^{\star}$	64.67	82.22	63.00
	5	63.67	78.52	57.67
$\beta$ (ICR weight)	0.3	50.00	44.20	44.67
	$0.5^{\star}$	64.67	82.22	63.00

Appendix

Table 11: Hyperparameter sensitivity on Qwen3-4B for

K

\beta

\alpha

, and

k

( ⋆ : default; exact-match accuracy, %).

SG	AS	OOD $\uparrow$	$\bm{\Delta}$ vs. CoDI-4B AS
CoDI-4B	4B	61.93	$-1.07$
	8B	62.89	$-0.11$
	14B	51.14	$-11.86$
	32B	61.30	$-1.70$

Appendix

Table 12: Solver transfer with a fixed CoDI-4B SG . Deltas are absolute OOD points relative to the main-table CoDI-4B AS score of 63.00. The 4B row is a re-run under the swap protocol and need not equal 63.00.

Row	Task type	Split
T01	Movie recommendation	ID
T02	Dyck languages	OOD-subtask
T03	Penguins in a table	ID
T04	Geometric shapes	ID
T05	Formal fallacies	ID
T06	Temporal sequences	ID

Appendix

Table 13: Task index for the rows in Fig. 4 . Split labels follow Appendix J ; T10 is a BBH diagnostic.

Split	Hold-out	Rule	$R^{2}$	Jacc.	MAE
		ovlp.			(pp)
ID (ref.)	same subtasks	100%	0.91	–	3.1
OOD-subtask	28 subtasks	0%	0.68	0.74	6.2
OOD-task	19 tasks	0%	0.38	0.51	9.4
OOD-category	7 categories	0%	0.15	0.29	12.8

Appendix

Table 14: OOD shift on StrategyBench split levels (Qwen3-4B FS baseline). Rule overlap is template overlap with ID training. Jaccard is ability-profile similarity, not rule overlap. ID keeps the same subtasks with disjoint instances; MAE is mean absolute error in percentage points.

ID subtasks (training + eval)

Navigate, Word Sorting, Tracking Shuffled Objects, Boolean Expressions, Contextual Parametric Conflicts, Elementary Math, Formal Fallacies, Geometric Shapes, Hyperbaton, Implicatures, Logical Deduction, Movie Recommendation, Penguins in a Table, Reasoning about Colored Objects, Salient Translation Error Detection, Snarks, Sports Understanding, Temporal Sequences, Tracking Shuffled Objects (three objects), Web of Lies, Winowhy, and related BIG-Bench subtasks

OOD-subtask (held out, 28 subtasks)

Dyck Languages, Causal Judgment, Disambiguation QA, Epistemic Reasoning, Intent Recognition, Linguistic mappings, Nonsense-word grammar, Play Dialog Same or Different, Ruin Names, Strange Stories, Symbol Interpretation, Unit Conversion, and 16 additional held-out subtasks (full list in repository)

Appendix

Table 15: Representative ID and OOD-subtask inventories for main-text BIG-Bench evaluation; remaining names in the 28-subtask hold-out are in the public release. Date understanding (Fig. 4 , T10) is a BBH diagnostic and is not listed in either inventory.

Panel of Figure 9 — Figure 9: Prompt used for six-mode induction scoring. Each strategy receives an independent 0–5 score per mode; the composite is the mean over applicable modes (N/A modes excluded from averaging).

Panel of Figure 10 — Figure 10: Prompt for Gemini-3-flash sentence-level tagging of <think> units.

Panel of Figure 11 — Figure 11: Prompt used for strategy quality analysis.

Panel of Figure 12 — Figure 12: GPT-5 prompt for scoring each [INDUCTIVE_RULE] on abstraction, coverage, copying (reverse-scored), and transferability.

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