Plan Canvas: Fixed Reasoning Regions for Continuous Language Flows

Miaohe Niu; Pengxiang Li; Jingbo Zhu; Tong Xiao

cs.CLOct 5, 2026

Plan Canvas: Fixed Reasoning Regions for Continuous Language Flows

Authors: Miaohe Niu, Pengxiang Li, Jingbo Zhu, Tong Xiao

Organizations: School of Computer Science and Engineering, Northeastern University, China · Hong Kong Polytechnic University, China · NiuTrans Research, Shenyang, China

Abstract

Continuous language flows generate text by denoising all positions of a target canvas together. The natural way to add reasoning to such a model is to write a trace ahead of the answer, but the trace length changes from question to question. The answer start is therefore unknown during denoising, and the model has to decide the trace length, the place of every trace token, and the answer at the same time. We propose Plan Canvas to fix the boundary between the trace and the answer. A plan region of fixed capacity holds a compact trace, supervised padding fills its unused positions, and the answer starts at a fixed position. The fixed regions also allow separate denoising clocks for the plan and for the answer. With the trace text, backbone, and canvas length of the free-trace baseline held fixed, Plan Canvas improves accuracy on ProsQA and on Deep ProsQA, a graph benchmark with longer proofs. On Deep ProsQA, accuracy rises from 73.0% to 87.0%, the share of questions answered with a valid path rises from 30.8% to 59.1%, and the gain is largest on the longest proofs.

Figures & tables

Figure 1: Training and sampling use the same ELF backbone with fixed plan and answer regions. Each training example selects either flow matching with region corruption or token cross-entropy with separate decoder corruption. The branch probabilities are 0.8 for flow matching and 0.2 for token cross-entropy in the reported configuration. During sampling, the prompt stays fixed while region clocks control Euler updates of every target position. The model predicts clean states, which define velocity, and switches to token decoding once both regions reach time one.

	ProsQA		Deep ProsQA
Layout	Full canvas $S$	Readout $G$	Full canvas $S$	Readout $G$
Direct answer	720	16	784	16
Full trace	800	96	960	192
Free trace / answer then trace	752	48	848	80
Plan Canvas, either clock interface	752	48	848	80

Table 1: Sequence budgets in token positions, shared by training and evaluation within each target layout. Prompt caps are 704 positions for ProsQA and 768 positions for Deep ProsQA across all layouts. The readout window is computed from these fixed caps and never from a reference answer’s content or length.

	ProsQA			Deep ProsQA
Target layout	Accuracy	Valid path	Correct / invalid	Accuracy	Valid path	Correct / invalid
Direct answer	87.6	–	–	57.7	–	–
Full trace	91.0	79.8	12.2	73.5	58.5	20.3
Free trace	91.4	75.0	17.0	73.0	30.8	42.5
Answer then trace	88.2	79.4	8.8	80.2	38.5	41.7
Plan Canvas, single clock	96.8	90.6	6.2	82.1	55.0	27.1

Table 2: Answer accuracy and path checks on the test splits, in percent of all test questions. A valid path starts at a fact about the entity, follows directed edges of the question graph, and ends at the predicted concept. Correct / invalid counts correct answers with an invalid or missing path. Free trace, answer then trace, and both Plan Canvas variants share the trace text, canvas length, and readout window, and shaded rows use the fixed plan region.

Target	Emitted plan	Answer
Proof	fimpus, nulpus, molpus, slilpus, rupus, chepus	chepus
Free trace	fimpus nulpus molpus slilpus rupus scapus scapus broopus pripus	pripus
Single clock	fimpus nulpus molpus slilpus rupus chepus, then padding	chepus
Segment clocks	fimpus nulpus molpus slilpus rupus chepus, then padding	chepus

Table 3: Emitted plans for Deep ProsQA test question 450, which asks whether Eva is a chepus or a pripus among 40 stated facts and rules. The underlined pair repeats a concept and then makes a hop that is not an edge of the question graph.

Figure 2: Shape of the emitted paths on the Deep ProsQA test split, in percent of all test questions. Panel (a) counts paths that contain the same concept twice, grouped by shortest proof length. Panel (b) gives the distribution of the emitted path length minus the shortest proof length.

Figure 3: Deep ProsQA test accuracy under three changes. Panel (a) groups the test split by shortest proof length, with 111 or 112 questions per length. Panel (b) evaluates the same checkpoints with 32, 64, 96, and 128 synchronous Euler iterations, counting two guided backbone calls per iteration and one decoder call. Panel (c) trains the segment-clock canvas with different plan capacities, and the dashed line marks the free trace.

Configuration	Fixed	Marker	Prefix	Time	Deep ProsQA
Free trace	–	–	–	–	73.0
Fixed plan region	$\checkmark$	–	–	–	82.1
+ segment markers	$\checkmark$	$\checkmark$	–	–	84.0
+ time-prefix groups	$\checkmark$	$\checkmark$	$\checkmark$	–	85.9
+ position time	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$	87.0

Table 4: Deep ProsQA accuracy in percent as the parts of the segment-clock interface are added under tied training times. Fixed denotes the plan region, and Marker, Prefix, and Time denote segment markers, time-prefix groups, and the position-dependent time term.

Train times	Schedule	$(o_{p},o_{a})$	Joint	Calls	ProsQA	Deep
Tied	Synchronous	$(0,0)$	64	129	95.2	87.0
Tied	Plan-first	$(0,64)$	128	257	96.0	87.6
Tied	Answer-first	$(64,0)$	128	257	94.6	85.4
Mixed	Synchronous	$(0,0)$	64	129	95.2	87.9
Mixed	Plan-lead	$(0,32)$	96	193	95.4	89.0
Mixed	Plan-first	$(0,64)$	128	257	95.4	88.7

Table 5: Accuracy in percent under different offsets with the same weights and 64 active steps per region. Joint counts Euler iterations, Calls counts backbone evaluations including the decoder, and mixed training shares region times for half the examples.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

Layout	P valid	P test [95% CI]	D valid	D test [95% CI]
Direct answer	88.0	87.6 [84.4, 90.2]	58.2	57.7 [54.6, 60.7]
Full trace	90.3	91.0 [88.2, 93.2]	78.6	73.5 [70.7, 76.1]
Free trace	89.3	91.4 [88.6, 93.5]	71.0	73.0 [70.2, 75.7]
Answer then trace	90.3	88.2 [85.1, 90.7]	78.2	80.2 [77.6, 82.5]
Plan Canvas (single clock)	94.0	96.8 [94.9, 98.0]	82.0	82.1 [79.6, 84.4]
Plan Canvas (segment clocks)	94.3	95.2 [93.0, 96.8]	86.8	87.0 [84.8, 88.9]

Appendix

Table 6: Validation and test answer accuracy in percent, with P denoting ProsQA and D denoting Deep ProsQA. Bracketed values give marginal 95% Wilson intervals for the complete test splits under each fixed checkpoint.

Set	First / second	$\Delta$ (pp)	Paired 95% CI	W/L	$p$
P	Canvas single / Free trace	+5.4	[+3.0, +8.0]	34/7	$2.53\times 10^{-5}$
P	Canvas single / Full trace	+5.8	[+3.2, +8.4]	37/8	$1.54\times 10^{-5}$
P	Canvas single / Answer then trace	+8.6	[+5.6, +11.6]	52/9	$1.80\times 10^{-8}$
P	Segment tied, sync / Canvas single	-1.6	[-3.0, -0.2]	3/11	0.057
P	Segment mixed, sync / Segment tied, sync	+0.0	[-1.4, +1.4]	7/7	1.000
P	Tied, Plan-first / Segment tied, sync	+0.8	[+0.0, +1.8]	5/1	0.219

Appendix

Table 7: Paired test contrasts with first minus second accuracy differences, with P denoting ProsQA and D denoting Deep ProsQA. Differences and interval endpoints use percentage points, while W/L counts discordant questions won or lost by the first model. Canvas single denotes the single-clock canvas, segment variants specify tied or mixed training, and sync denotes synchronous generation. The percentile bootstrap interval and exact discrete test need not cross their respective thresholds at the same contrast. The last three rows are the component steps of Table 4 , whose bootstrap uses 10,000 replicates with seed 0.

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Oct 7, 2026, cs.LGJ/K move · Enter open · S save

Unrolled Flow Models for Reasoning

Faissal Izermine, Hanru Bai, Oscar Davis, T. Konstantin Rusch

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Open paper AskPDF arXiv

Flow matching enables language generation in few steps, but whether additional integration steps improve reasoning remains unclear. We prove that a flow parameterized by a two-layer Transformer can solve graph reachability, with the required number of integration steps increasing with the target's distance from the root. Yet, standard flow language models can fail to benefit from additional steps on reasoning tasks. We attribute this limitation to objectives that supervise each time point independently, without explicitly training successive steps to build on one another. To address this, we instead train through the model's own latent rollout over a randomly sampled subinterval of [0, 1], decoding only at the endpoint. On ProsQA, this raises accuracy to 97% and enables performance to improve with additional integration steps. For the longer rollouts required by reasoning tasks such as Sudoku and Maze, retracting the latent state onto a sphere stabilizes the dynamics and yields substantial gains over baselines with more than three times as many parameters. Sampling multiple rollouts further improves performance when paired with a parameter-free selection score, although reliable selection remains challenging for longer answers. Together, these results establish a theoretical basis for reasoning with flows and show how rollout training, stable latent dynamics, and rollout selection help realize this capacity in practice.

Abstract

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