Judgment models answer semantic questions by scoring a finite set of candidate outcomes. Can reusable programs turn these local decisions into powerful multistep reasoning? We introduce \method, a framework that jointly constructs judgment schemas and composition programs for frozen judgment models. A generative teacher designs the procedure offline; the judgment model resolves local semantic questions online, and the saved program composes its decisions into an answer. We study three allocations of design effort between humans and the teacher, focusing on construction through a shared interface. We instantiate the framework with Kev. On three selected BIG-Bench Hard tasks, nine independently constructed programs solve all 450 executions of 150 development inputs. A separate deployment study freezes three programs after development-set reference-agreement refinement and evaluates them on 600 held-out questions. These programs achieve near-perfect 99.67% macro accuracy, versus 64.00% for direct Kev and 68.80% for final-answer-only Qwen3.5-4B. They attain comparable observed accuracy to Qwen's unrestricted response policy (99.07%) with an 8.43-fold online speedup: 0.255 versus 2.150 seconds per question. These results show how reusable programs can substantially expand the reasoning capability of a compact judgment model while keeping its parameters fixed.
Figures & tables
Figure 1: ABACUS composes local judgments into reusable multistep reasoning. (a) For each task, a teacher jointly designs judgment schemas and a composition program from a task description, four solved examples, and a shared interface. Admission selects a complete proposal. (b) A new navigation instance is decomposed into local action judgments; the saved program combines them with distances to update position and heading. The colored steps trace a return to the origin. The same schemas and update rules are reused for subsequent instances. Construction is offline. The judgment model is frozen throughout; this implementation uses Kev.
Design level
Human design
GLM design
Online inference
Human-designed workflow
Judgment questions, state, and update rules
None
Event and belief updates with local rereading and thresholds
Task-specific interface
Domain objects and judgment scopes
Semantic attributes, candidate labels, and scoring program
Candidate winning frequencies under factorized local judgments
Shared interface
Common constructors, tools, and admission checks
Unit selection, judgment schemas, and composition program
Local argmax followed by reusable program execution
Table 1: Three allocations of procedure design. Each level is evaluated on its corresponding task and cohort. The final column makes the online inference rule explicit.
Task
Semantic decisions supplied by Kev
Computation supplied by the program
Judgments
Web of lies
Truth or lie in each claim; affirmative or negative answer meaning
Propagate the current truth state and match the final query
8.0
Navigation
Forward, backward, lateral movement, or turn; answer meaning
Accumulate coordinates and heading; check return to the origin
8.8
Temporal sequences
Waking time, observed activity, closing time, or other statement
Compare candidate intervals with event and boundary constraints
9.9
Table 2: Interfaces generated by ABACUS. Representative task programs. All listed semantic judgments use local evidence. Counts are mean judgments per input on the task’s 50 development inputs.
Figure 2: ABACUS deployment on 600 held-out questions from three selected tasks. Programs are frozen after the deployment selection procedure. (a) Task accuracy for ABACUS, direct Kev, and Qwen4B final-only and free-response policies. (b) All seven Qwen policies and both Kev controls, with empirical envelopes computed in linear latency and displayed on a log axis. Task-conditioned mixtures use task identity to allocate answer policies; the task-independent envelope uses common mixture weights. All curves summarize the same five collection rounds. Qwen uses its non-thinking mode throughout; free response allows unrestricted explanation within the output capacity.
Task
Admitted
Correct
Seconds
Web of lies
3/3
150/150
0.245
Navigation
3/3
150/150
0.265
Temporal sequences
3/3
150/150
0.252
All tasks
9/9
450/450
0.254
Table 3: ABACUS joint construction. Three independently constructed programs per task, each evaluated on the same 50 development inputs. Accuracy is measured on this development cohort.
Policy
Accuracy (%)
Seconds
Kev direct
64.00
0.022
Kev teacher prompt
71.67
0.053
Qwen4B final only
68.80
0.108
Qwen4B brief 32
79.57
0.294
Qwen4B brief 64
88.70
0.436
ABACUS
99.67
0.255
Table 4: Held-out deployment performance. Macro averages over three tasks and five collection rounds. The appendix reports the complete seven-budget Qwen grid.
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Study
Program selection
Evaluation
Joint construction
Independent complete proposals; structural, sensitivity, and example checks; first passing proposal retained
Three independent constructions per task, three tasks, 50 development inputs per task: 450 executions of 150 distinct inputs
Held-out deployment
Joint proposals and admission followed by reference-agreement refinement on ten development inputs
Three frozen programs, 200 held-out inputs per task, five collection rounds: 3,000 ABACUS predictions
Task-specific construction
Teacher-generated attributes and scoring programs; first registered build
MuSR team allocation and murder mystery, 200 stories each
Manual workflow
Human-designed event and belief updates
208 questions in 52 object-placement stories
Appendix
Table 5: Program construction and evaluation cohorts. Each construction run generates an artifact; each measurement round evaluates a fixed artifact.
Setting
Value
Solved examples per task
4
Development inputs per task
50
Maximum complete proposals
4
Total teacher token budget
256,000
Sensitivity inputs / draws per input
20 / 64
Maximum constant-output fraction
0.5
Appendix
Table 6: Joint-construction and runtime settings.
Run
Task
Correct
Mean seconds
Teacher tokens
Proposals
1
Web of lies
50/50
0.195
36,817
1
1
Navigation
50/50
0.246
37,403
1
1
Temporal sequences
50/50
0.225
25,932
1
2
Web of lies
50/50
0.332
55,101
1
2
Navigation
50/50
0.257
31,197
1
2
Temporal sequences
50/50
0.270
27,865
1
Appendix
Table 7: Independent construction results. Each task–run row evaluates 50 development inputs. Teacher tokens include generation and local annotations.
Policy
Lies
Temporal
Navigation
Macro
Kev direct
59.50
69.50
63.00
64.00
Kev teacher prompt
56.50
94.00
64.50
71.67
Qwen4B final only
52.30
89.80
64.30
68.80
Qwen4B brief 16
64.30
89.60
74.60
76.17
Qwen4B brief 32
68.40
89.00
81.30
79.57
Qwen4B brief 64
85.00
92.90
88.20
88.70
Appendix
Table 8: Deployment study: complete held-out accuracy (percent). All three tasks and all budgets; five collection rounds. The macro column weights tasks equally.
Policy
Lies
Temporal
Navigation
Macro
Kev direct
0.018
0.029
0.018
0.022
Kev teacher prompt
0.048
0.061
0.050
0.053
Qwen4B final only
0.097
0.131
0.097
0.108
Qwen4B brief 16
0.215
0.275
0.182
0.224
Qwen4B brief 32
0.269
0.344
0.270
0.294
Qwen4B brief 64
0.383
0.476
0.449
0.436
Appendix
Table 9: Deployment study: complete held-out mean client latency (seconds per question). All three tasks and all budgets; five collection rounds. The macro column weights tasks equally.
Policy
Accuracy (%)
95% interval
Seconds [95% interval]
Token proxy
Kev direct
64.00
[60.33,67.83]
0.022 [0.022,0.022]
120.3
Kev teacher prompt
71.67
[68.33,74.83]
0.053 [0.053,0.053]
557.0
Qwen4B final only
68.80
[65.77,71.80]
0.108 [0.108,0.108]
693.0
Qwen4B brief 16
76.17
[73.47,78.80]
0.224 [0.219,0.234]
722.3
Qwen4B brief 32
79.57
[77.07,82.07]
0.294 [0.286,0.309]
738.8
Qwen4B brief 64
88.70
[86.70,90.77]
0.436 [0.415,0.463]
772.2
Appendix
Table 10: Deployment study: full macro results and paired bootstrap intervals. The token proxy is an accounting statistic, not measured FLOPs.
Task
Direct Kev
Program + Kev
Team allocation
130/200
187/200
Murder mystery
111/200
152/200
Manual object placement
100/208
162/208
Appendix
Table 11: Supporting narrative studies, each with its corresponding direct Kev control.
Task
Inputs
Direct Kev
Program policy
Web of lies
200
59.50
99.00
Navigation
200
63.00
100.00
Temporal sequences
200
69.50
100.00
Logical deduction
200
64.50
68.50
Causal judgment
135
54.81
54.81
Date understanding
200
77.50
77.50
Appendix
Table 12: Original six-task deployment scope. Accuracy (%) averages five collection rounds. Date understanding uses the declared direct-Kev fallback. These records provide the context for selecting the three tasks in the main study.
Decision needs vary with each application, language, and deployment environment. The Decision Model Factory turns those needs into specialized, sovereign models on demand. A brief recipe guides the training, calibration, verification, and evaluation of a selected backbone, delivering a deployable decision model under the operator's control. The same workflow creates a new specialist whenever the requirements change. Across Japanese decision tasks, compact deployment, and long-context passage ranking, five factory-built models improve upon their backbones; three surpass the strongest results in a fixed public Japanese benchmark comparison. A dedicated runner computes only permitted-answer probabilities and reuses shared context, more than doubling serving speed on matched multi-question workloads with essentially unchanged decision scores. Together, the factory and runner make fast, task-specific decision models practical to build and deploy whenever needed.
Decision models such as Jev score candidate answers or actions. A small decision head trained label-free can recover about 99% of a frozen language model's multiple-choice accuracy while using only two-thirds of its transformer layers. It learns the full model's answer probabilities with KL divergence, without correct-answer labels for training. One backbone pass reads the question and all options together; the head returns probabilities for every option. We call this model FunDM (Fun Decision Model). Using 24 of Qwen3-8B's 36 layers and skipping the LM head, its +1T variant reaches 75.0% mean accuracy over eight benchmarks, versus 75.7% for the full model. On MMLU-Pro, both heads achieve 1.56 to 1.57 times batched vLLM throughput with about one-third lower peak GPU allocator memory. Both heads score higher than released Contrastive Language Models (CLM), fine-tuned CLM, and CLM-shaped heads trained from scratch on the eight multiple-choice benchmarks and coding-agent selection. Separately trained agent heads learn judge probabilities without pass/fail labels and select passing runs for 74.4 to 74.6 of 100 held-out tasks on average, versus 74 for the full-model judge and 52.0 for a CLM-shaped action-trained head. Code is available at: https://github.com/Ujjawal-K-Panchal/FunDM
Typed decision models need an interface that can use additional reasoning while retaining candidate outputs. We train a shared candidate-answer reader on a frozen Qwen3.5-4B backbone to unify direct decisions with on-demand, interruptible reasoning. The reader returns distributions from empty and partial reasoning prefixes. A benefit gate starts reasoning, a natural-state trigger requests explicit reads, and an entropy rule accepts acquired answers and cancels generation. Measurements distinguish answer-query work, generated output, and pipeline time. Across 768 questions from ProofWriter, LogiQA 2.0, and ARC-Challenge, accuracy rises from 70.96% for direct reading to 84.38%. Relative to 512-token terminal reading, accuracy improves by 7.29 percentage points with 2.25% more mean output work. Relative to 1,024-token terminal reading, pipeline time falls by 46.30% with an accuracy difference of -1.17 points. Exact-prefix controls isolate the saving from interruption, while read-scheduling controls distinguish reduced observation work from shorter response time.
Bin Zheng, Zheng Chen
University of Electronic Science and Technology of China