FairFRESH: A Neuro-Symbolic Framework for Fair and Explainable Household Food Recommendation

Kodur Sai Vinay Sathvik; Kakoli Bora; Tejaswini R. M

cs.AIOct 22, 2026

FairFRESH: A Neuro-Symbolic Framework for Fair and Explainable Household Food Recommendation

Authors: Kodur Sai Vinay Sathvik, Kakoli Bora, Tejaswini R. M

Organizations: Department of Artificial Intelligence and Machine Learning, BNM Institute of Technology

Abstract

Recommender systems typically serve one user at a time. However, in households, members share a finite pantry and follow different dietary rules, making independent recommendations prone to resource conflicts and dietary violations. We formulate household food recommendation as constrained fair division and present FairFRESH, a neuro-symbolic framework that learns per-member utilities, allocates foods under explicit welfare objectives, enforces dietary rules through a deterministic filter, and explains recommendations using Shapley and Banzhaf attributions. Theoretically, we show that no finite penalty guarantees compliance near a dietary-rule threshold, establish approximation guarantees for greedy allocation under utilitarian and smoothed Nash objectives in the stock-free model before filtering, and characterize the scale invariance of Nash welfare. We also use the minimax theorem to analyze rotating shared meals. On NHANES-derived data, the learned utility model achieves Recall@20 of 0.293, outperforming five learned recommenders (at most 0.244) but not a previous-day repetition heuristic (0.321). On held-out four-person households, Nash allocation reduces Gini disparity by 42% relative to conflict resolution while improving Recall@20 from 0.180 to 0.197. It comes within 2% of an upper bound on the smoothed Nash optimum, and rescaling one member's utilities changes at most 1.5% of assignments. All recommendations satisfy the encoded dietary rules, while attribution scores correlate with utility loss upon component removal (r = 0.76). In simulation, shared meals reduce pantry use by about one-third, and weekly rotation increases the worst-off member's utility by 38% over the best fixed meal.

Figures & tables

Figure 1: Motivation. One shared pantry yields different safe recommendations for members with different dietary rules, so household recommendation is an allocation problem rather than a ranking repeated for each member.

Figure 2: FairFRESH. Taste, retrieval-augmented dietary, and pantry encoders, fused by multi-head attention, produce a utility for every member–food pair. An allocation rule (utilitarian, max-min, or Nash) assigns foods from the utility matrix, a symbolic filter removes unsafe foods, and a post-hoc module turns Shapley and Banzhaf attributions into natural-language explanations without affecting any decision.

Method	Recall@20	NDCG@20
Popularity	0.235 [0.221, 0.248]	0.253 [0.241, 0.265]
Repeat-D1	0.321 [0.304, 0.339]	0.376 [0.358, 0.393]
BPRMF	0.220 [0.206, 0.234]	0.234 [0.220, 0.249]
NeuMF	0.111 [0.105, 0.117]	0.141 [0.133, 0.149]
LightGCN	0.244 [0.231, 0.258]	0.262 [0.250, 0.274]
GRU4Rec	0.207 [0.195, 0.220]	0.234 [0.220, 0.247]

Table 1: Individual-level accuracy on 400 test users (mean over five seeds for trained baselines; 95% user-bootstrap confidence intervals in brackets).

Strategy	Recall@20	Min Util.	Gini	NSW
A) Independent	0.266 [0.250, 0.282]	9.79 [9.36, 10.21]	0.109 [0.100, 0.118]	12.76 [12.42, 13.09]
B) Conflict resolution	0.180 [0.165, 0.194]	5.35 [5.00, 5.70]	0.192 [0.180, 0.205]	8.54 [8.25, 8.81]
C) Utilitarian	0.194 [0.180, 0.209]	7.64 [7.31, 7.96]	0.146 [0.136, 0.155]	10.72 [10.45, 10.99]
D) Max-Min	0.188 [0.173, 0.202]	8.75 [8.41, 9.08]	0.088 [0.079, 0.096]	10.56 [10.27, 10.87]
E) Nash	0.197 [0.182, 0.211]	8.56 [8.23, 8.89]	0.112 [0.103, 0.121]	10.98 [10.70, 11.27]

Table 2: Household allocation on 100 held-out four-person households, with 95% household-bootstrap confidence intervals. Higher is better except for Gini. Bold marks the best coordinated strategy (B–E) in each column; A is an uncoordinated reference that may give the same food to several members.

Figure 3: Scaling with household size, plotted from Table 6 . (a) Gini of per-member utility (lower is more equal). (b) Minimum member utility (higher is better). Percentages mark the changes from

n=2

n=6

discussed in the text. Independent recommendation (dashed) is an uncoordinated reference (Section 5.3 ).

Model	Recall@20	CSR	Gini	NSW
Full FairFRESH	0.197	1.000	0.112	10.98
w/o Pantry (availability) Encoder	0.064	1.000	0.160	5.58
w/o Medical Constraint	0.194	0.856	0.124	9.23
w/o Fairness Optimizer (utilitarian)	0.194	1.000	0.146	10.72
w/o RAG Constraint Encoder	0.200	1.000	0.087	10.06

Table 3: Component ablation on the held-out four-person households of Table 2 , under Nash allocation unless stated. The full model’s Recall@20 (0.197) lies below its individual-level value in Table 1 (0.293) because each food goes to one member. CSR is measured against the full rule set.

Figure 4: Game-theoretic explainability on 500 held-out households of two to six members. (a) Attribution faithfulness: correlation

r

between each component’s attribution and the utility drop observed when that component is removed. (b) Mean Shapley and Banzhaf attribution per component, sorted by Shapley value. Safety is not a player, since the filter is a hard constraint rather than a source of utility (Section 3.5 ).

Indian recipes, simulated utilities
Strategy	Mean Util.	Min Util.	Gini	Full Meal	Pantry Used
Unstructured	5.34	4.92	0.029	28.6%	4.59%
Structured individual	5.26	4.86	0.030	100%	5.12%
Structured shared	5.06	4.74	0.024	100%	3.47%
NHANES foods, learned utilities
Unstructured	5.58	5.10	0.029	0.6%	10.74%

Table 4: Shared versus individual meals on four-person households (

K=6

; 100 households under each of five seeds). Values are means over seeds; standard deviations across seeds are at most 0.05 for utilities, 0.003 for Gini, 2.3 points for full meal, and 0.12 points for pantry used. Per-item utilities are min-max normalized. Higher is better except for Gini and pantry used. Bold marks the best value in each column within a setting.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

$n$	Utilitarian: greedy/opt.	Max-min: greedy/opt.	Nash: $\Phi_{\epsilon}$ /upper bound
2	0.986 [0.982, 0.990]	0.978 [0.973, 0.983]	0.996 [0.995, 0.997]
3	0.975 [0.971, 0.980]	0.957 [0.950, 0.964]	0.990 [0.988, 0.992]
4	0.976 [0.972, 0.980]	0.946 [0.937, 0.955]	0.987 [0.985, 0.989]

Appendix

Table 5: Greedy allocation relative to exact optima (mean over 100 held-out households per size, with 95% bootstrap intervals).

$n$	Strategy	Recall@20	NDCG@20	PUR	Min Util.	Gini	NSW	Items
2	A) Independent	0.292	0.292	0.187	11.37	0.072	12.96	20.0
2	B) Conflict resolution	0.252	0.263	0.142	8.92	0.105	10.82	15.1
2	C) Utilitarian	0.264	0.270	0.184	10.34	0.086	12.16	20.0
2	D) Max-Min	0.260	0.268	0.185	10.84	0.061	12.13	20.0
2	E) Nash	0.267	0.273	0.185	10.75	0.072	12.30	20.0
3	A) Independent	0.283	0.291	0.279	10.36	0.096	12.87	20.0

Appendix

Table 6: Household allocation across household sizes

n=2

–

6

(100 held-out households per size). CSR is 1.00 in every row. Items is the mean number of foods each member receives; strategies A and C–E always fill all

K=20

slots. Bootstrap confidence intervals are released with the code.

Member	Single-serving foods	Total	Shared dishes (utility) + individual foods	Total
1 (none)	Baby oatmeal cereal, sweetened tea, fruit yogurt, coffee cake, barbecue chicken, corn puffs	5.84	Bread 0.20, beans 0.14; oatmeal cereal, tea, fruit yogurt, coffee cake	4.28
2 (none)	Froot Loops, yeast doughnut, mozzarella, hamburger, cola, chocolate sandwich cookie	5.57	Bread 0.23, beans 0.16; Froot Loops, doughnut, mozzarella, hamburger	4.19
3 (none)	Low-fat fruit yogurt, whole milk, salted pretzels, cheese pizza, French fries, banana	4.74	Bread 0.22, beans 0.16; yogurt, whole milk, pretzels, cheese pizza	4.09
4 (hypertension)	Bacon, fried eggs, French dressing, tap water, toasted wheat bread, heavy cream	5.85	Bread 0.23, beans 0.17; bacon, fried eggs, French dressing, tap water	4.33
Complete meals: 0 of 4 (single-serving) vs. 4 of 4 (shared). Pantry used: 14.35% vs. 10.71%.

Appendix

Table 7: Worked example: one held-out NHANES household with learned utilities,

K=6

. Single-serving allocation gives each member six foods; structured shared allocation cooks white bread and pinto beans once for all members and adds four individual foods. Totals are bundle utilities on the min-max-normalized scale. Both shared dishes are safe for every member.

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