Provenance-Aware Belief Updating in Human-AI Feedback Loops

Tianyi Huang; Eric Liu; Jay Chong; Emily Yin; Wanqi Zhao

cs.AIOct 9, 2026

Provenance-Aware Belief Updating in Human-AI Feedback Loops

Authors: Tianyi Huang, Eric Liu, Jay Chong, Emily Yin, Wanqi Zhao

Organizations: Ryquo · App-In Club

Abstract

In repeated human-AI interaction, a single observation can be quoted, summarized, and returned to a model as multiple reports, making repetition look like independent corroboration. We study whether language models can use supplied report lineage to update according to evidence provenance rather than report count. We introduce Latent Quotient Evidence Training (LQET), a relational objective that combines sparse Bayesian supervision with constraints that encourage stable predictions when reports add no new evidence and consistent updates to the same new evidence across relay histories. On a controlled binary benchmark, LQET reduces new-evidence update RMSE by 41-44% and log-odds drift after eight relay steps by 89-91% relative to task-only training across Qwen3-4B and Phi-4-mini, with three paired training seeds per backbone. The gains extend to a closed-loop simulation in which model confidence controls how many relayed reports re-enter the model's context in later rounds. By grounding belief updates in supplied provenance, LQET offers a route toward dynamic human-AI systems in which influence follows new evidence, not the number of times the same evidence returns.

Figures & tables

Figure 1: Reports can multiply without adding evidence. Relays preserve the evidence set $\{e_{0}\}$ , while a new observation expands it to $\{e_{0},e_{h}\}$ . Solid arrows show report derivation; dashed arrows identify the distinct evidence in each history. With the prior and calibration records fixed, equivalent evidence sets have identical Bayesian targets.

Figure 2: Controlled generalization across relay depth and distribution shift. (a,b) Absolute relay-induced drift across nested depths; thick and thin curves show three-seed means and individual seeds on the same 200 families. (c) Update RMSE and (d) supervised-view KL across controlled shifts; color marks the method, shape the backbone, and connectors the paired contrast. Panels (a,b) use logarithmic y-axes, and panels (c,d) use logarithmic x-axes. Lower is better.

Backbone	Endpoint	Task-only	LQET	Effect [95% interval]
Qwen3-4B	Update RMSE	0.6816	0.4005	$-0.2812$ [ $-0.3070,-0.2565$ ]
	Depth-8 drift	1.0122	0.0875	$-0.9247$ [ $-1.1175,-0.7703$ ]
	Supervised-view KL †	0.0215	0.0237	$+0.0023$ [ $+0.00116,+0.00356$ ]
Phi-4-mini	Update RMSE	0.7461	0.4144	$-0.3317$ [ $-0.3545,-0.3091$ ]
	Depth-8 drift	1.1079	0.1177	$-0.9902$ [ $-1.0823,-0.8988$ ]
	Supervised-view KL †	0.0280	0.0292	$+0.0012$ [ $-0.00002,+0.00251$ ]

Table 1: Primary controlled results. Effects are LQET minus task-only and are computed from unrounded estimates; lower is better. Point estimates average three paired training seeds. Intervals are 95% paired crossed seed-by-family bootstrap intervals.

\dagger

marks the supervised-view KL endpoint with a prespecified

+0.02

-nat non-inferiority margin.

Figure 3: Selective invariance and closed-loop feedback. (a) LQET /task-only error ratio on matched provenance controls, shown on a logarithmic x-axis; unity denotes no change, and marker and color identify the backbone. Inherited-report and copy-versus-new errors fall while new-evidence update errors stay near parity. (b-d) Thin segments pair matched adapters by seed; thick segments and larger markers are three-seed means. Endpoint color marks the method, while shape and line style mark the backbone. All panels are descriptive; lower is better.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

View	View construction	Bayesian-target relation	LQET role
$h_{00}$	Base observation carrying root $e_{0}$	base target	supervised; invariance/update reference
$h_{10}$	Base plus a relay DAG; no new root	$t(h_{10})=t(h_{00})$	invariance; update reference
$h_{01}$	Base plus new root $e_{h}$	new-evidence target	supervised; invariance/update target
$h_{11}$	Relay DAG plus a mixed report introducing $e_{h}$	$t(h_{11})=t(h_{01})$	invariance; update endpoint
$c_{00}$	Same rendered base as $h_{00}$	$t(c_{00})=t(h_{00})$	static evaluation only
$c_{10}$	Base plus new root $e_{a}$	new-evidence target	supervised; update reference

Appendix

Table 2: Matched transcript views. Supervised denotes a pointwise soft target; invariance and update denote relational loss terms.

Method	Training views	Objective
Task-only	7	$\mathcal{L}_{\mathrm{task}}$
Pair-invariance	11	$\mathcal{L}_{\mathrm{task}}+4\mathcal{L}_{\mathrm{inv}}$
No-order	13	$\mathcal{L}_{\mathrm{task}}+4\mathcal{L}_{\mathrm{inv}}+2\mathcal{L}_{\mathrm{update}}$
Full LQET	13	Equation 13

Appendix

Table 3: Training protocols. Methods share training families and 500 optimizer updates.

Item	Value	Item	Value
Training families	4,000	Validation families	400
Dataset seed	17	Training seeds	0, 1, 2
Optimizer updates	500	Epochs	2
Families/microbatch	1	Gradient accumulation	16
Optimizer	AdamW	Learning rate	$2\times 10^{-4}$
Weight decay	0	Warmup	15 updates

Appendix

Table 4: Shared training configuration.

Factor	Training, validation, and IID support	Controlled held-out support
Domain and names	Four domains: beacon status, valve position, package authenticity, and server security; 26 source names	Three domains: soil contamination, sample radioactivity, and component magnetization; 26 disjoint source names
Report graph	Chains of depth 1–3; stars with 1–8 relays	Depth shift: chains of depth 4–8. Topology shift: diamonds with 3 or 4 relays; fan-in graphs with branch depth 1 or 2 (3 or 5 relays total)
Rendering template	Direct and contrast renderings	Record-style and basis-style renderings
Prior $\pi$	$\{0.20,\allowbreak 0.35,\allowbreak 0.50,\allowbreak 0.65,\allowbreak 0.80\}$	$\{0.125,\allowbreak 0.275,\allowbreak 0.425,\allowbreak 0.575,\allowbreak 0.725,\allowbreak 0.875\}$
Calibration $(c,w)$	$c\in\{4,\ldots,9\}$ and $w\in\{1,2,3\}$	$\{(0,0),\allowbreak(0,3),\allowbreak(1,4),\allowbreak(2,0),\allowbreak(2,5),\allowbreak(4,4),\allowbreak(4,10),\allowbreak(10,0),\allowbreak(10,4),\allowbreak(10,10),\allowbreak(11,0),\allowbreak(11,5)\}$

Appendix

Table 5: Benchmark-generator supports. Calibration entries are numbers of correct and incorrect historical calibration trials,

(c,w)

Backbone	Endpoint	Seed	Task-only	LQET	Effect
Qwen3-4B	Update RMSE	0	0.6596	0.3901	$-0.2695$
		1	0.6895	0.4143	$-0.2752$
		2	0.6958	0.3971	$-0.2987$
	Depth-8 drift	0	1.2172	0.0931	$-1.1241$
		1	0.8875	0.1078	$-0.7797$
		2	0.9319	0.0616	$-0.8703$

Appendix

Table 6: Per-seed primary endpoints. Effects are LQET minus task-only and are computed from unrounded estimates; lower is better.

Backbone	Endpoint	Task-only	LQET	Effect [95% interval]
Qwen3-4B	Update RMSE	0.5635	0.0515	$-0.5119$ [ $-0.5395,-0.4834$ ]
	Supervised-view KL	0.00052	0.00023	$-0.00029$ [ $-0.00036,-0.00022$ ]
Phi-4-mini	Update RMSE	0.6354	0.0865	$-0.5489$ [ $-0.5772,-0.5200$ ]
	Supervised-view KL	0.00156	0.00061	$-0.00094$ [ $-0.00104,-0.00084$ ]

Appendix

Table 7: Results on the 400-family IID test set. Point estimates average three paired training seeds. Effects are LQET minus task-only; intervals are 95% paired crossed seed-by-family bootstrap intervals. Lower is better.

Backbone	Shift	Update RMSE	Supervised-view KL
Qwen3-4B	Domain/names	$0.5717\rightarrow 0.1770$	$0.00673\rightarrow 0.00546$
	Depth	$0.5371\rightarrow 0.0511$	$0.00052\rightarrow 0.00026$
	Topology	$0.6287\rightarrow 0.0500$	$0.00055\rightarrow 0.00025$
	Template	$0.5903\rightarrow 0.0928$	$0.00076\rightarrow 0.00080$
	Prior/calibration	$0.9817\rightarrow 0.8694$	$0.09877\rightarrow 0.11196$
Phi-4-mini	Domain/names	$0.6278\rightarrow 0.1129$	$0.00685\rightarrow 0.00202$

Appendix

Table 8: Results by controlled shift. Descriptive three-seed means are shown as task-only

\rightarrow

LQET . Update RMSE is measured in log-odds units and KL in nats. Each shift has 160 families per seed; lower is better.

Backbone	Method	Depth 1	Depth 2	Depth 4	Depth 8
Qwen3-4B	Task-only	0.3911	0.7548	0.9932	1.0122
	LQET	0.0385	0.0469	0.0594	0.0875
Phi-4-mini	Task-only	0.2529	0.5454	0.7879	1.1079
	LQET	0.0629	0.0619	0.0842	0.1177

Appendix

Table 9: Drift across recursive-relay depth. Values are mean absolute pre-update log-odds drift over three seeds and correspond to Figure 2 (a,b).

Backbone	Method	Relay drift	Copy drift	New-root RMSE	Matched-new RMSE	Copy-vs-new RMSE	Copy-vs-new slope
Qwen3-4B	Task-only	1.0463	0.8338	0.3980	0.4326	1.0145	0.027
	LQET	0.0264	0.0373	0.4043	0.4328	0.4383	0.782
Phi-4-mini	Task-only	1.0377	0.7813	0.4352	0.4682	0.9818	0.067
	LQET	0.0540	0.0533	0.4185	0.4582	0.4630	0.769

Appendix

Table 10: Provenance-selectivity metrics. Values are descriptive means over three seeds. Lower is better except for the copy-versus-new slope, whose ideal value is one.

Backbone	Method	Seed	Feedback drift	Post-feedback update RMSE	Final log-odds MAE
Qwen3-4B	Task-only	0	1.5078	0.6936	0.9644
	LQET	0	0.4336	0.1732	0.3160
	Task-only	1	1.1973	0.6725	0.6909
	LQET	1	0.3887	0.1733	0.2560
	Task-only	2	1.2891	0.7191	0.6708
	LQET	2	0.3169	0.1362	0.2520

Appendix

Table 11: Closed-loop feedback results by training seed. Lower is better.

Method	Update RMSE	Depth-8 drift	Supervised-view KL	Order gap
Pair-invariance	0.5860	0.0984	0.0212	0.1184
No-order	0.4105	0.0753	0.0239	0.0426
Full LQET	0.4058	0.0959	0.0232	0.0359

Appendix

Table 12: Qwen3-4B seed-0 component results. Lower is better.

Endpoint	Effect	95% CI
Update RMSE	$+0.00475$	[ $+0.00157,+0.00782$ ]
Depth-8 drift	$-0.02063$	[ $-0.03125,-0.01031$ ]
Supervised-view KL	$+0.00076$	[ $+0.00031,+0.00125$ ]
Order gap	$+0.00664$	[ $+0.00289,+0.01023$ ]

Appendix

Table 13: Paired component effects. Effects are No-order minus full LQET and use unrounded estimates. Brackets are unadjusted 95% paired family-bootstrap intervals; positive effects favor full LQET for these lower-is-better endpoints.

Figure 4: Single-seed component trade-off. (a) No-order-minus-full effects normalized by full LQET , with 95% paired family-bootstrap intervals; positive values favor full LQET for the displayed lower-is-better endpoints. (b) Edgewise update RMSE across component variants.

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Abstract

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