SlowGuess/NeurIPS_2023_OCR huggingface dataset:
However, in practice, causal parts and non-causal-part could be still closely related. For example, waterbirds are typically paired with water backgrounds in the training set. To further reduce the potential hidden effects of non-causal parts, we introduce invariant learning [28, 70, 6], which first introduce a generative model to do interventions and then encourages hash codes to be sufficiently invariant to different non-causal parts.
In detail, a generative model  $G(\cdot ,\cdot)$  is first learnt to reconstruct original images using both causal and non-causal features. To optimize the generative model, the reconstruction loss in a mini-batch is written in the formulation of:
$$
\mathcal {L} _ {R E} = \mathbb {E} _ {\boldsymbol {x} _ {i} \in \mathcal {B}} \| \boldsymbol {x} - G \left(g ^ {c} \left(F (\boldsymbol {x} _ {i})\right), g ^ {n} \left(F (\boldsymbol {x} _ {i})\right)\right) \| _ {2} ^ {2}. \tag {12}
$$
With the well-trained model, we can simulate the intervention by utilizing different non-causal features. Here, we first generate synthetic images using  $\pmb{f}_i^c$  and  $\pmb{f}_k^n$ :
$$
\boldsymbol {x} _ {i} ^ {+ m} = \boldsymbol {x} _ {i} \left| d o \left(\boldsymbol {f} _ {m}\right) = G \left(\boldsymbol {f} _ {i} ^ {c}, \boldsymbol {f} _ {m} ^ {n}\right), \right. \tag {13}
$$
where  $do(\pmb{f}_m^n)$  denotes to impose non-causal features from a different sample  $\pmb{x}_m^n$  in  $\pmb{B}$ . Then we feed the synthetic sample into the hashing network to generate hash codes,  $\pmb{b}_i^{+m} = \psi(g^c(F(\pmb{x}_i^{+m})))$  and then minimize the variance under different intervention. The objective can be written as:
$$
\mathcal {L} _ {V} = \mathbb {E} _ {\boldsymbol {x} _ {i} \in \mathcal {B}} \left[ \operatorname {V a r} _ {m} \left(\boldsymbol {b} _ {i} ^ {+ m}\right) \right] = \mathbb {E} _ {\boldsymbol {x} _ {i}, \boldsymbol {x} _ {m} \in \mathcal {B}} \left\| \boldsymbol {b} _ {i} ^ {+ m} - \bar {\boldsymbol {b}} _ {i} \right\| ^ {2}, \tag {14}
$$
where  $\bar{b}_i = \mathbb{E}_{\boldsymbol{x}_m\in \mathcal{B}}[\boldsymbol {b}_i^{+m}]$  is the mean of synthetic hash codes. With effective invariant learning, we can generate domain-invariant binary codes for effective cross-domain retrieval.
Algorithm 1 Training Algorithm of IDEA
Require: Source data  $\mathcal{D}^s$ , target data  $\mathcal{D}^s$ , code length  $L$ ;
Ensure: The hashing network  $\psi(g^c(F(\cdot)))$ ;
1: Warm up our backbone by minimizing  $\mathcal{L}_D$  and  $\mathcal{L}_{RE}$
2: repeat
3: Sample a mini-batch  $B^{s}$  and  $B^{t}$  from  $\mathcal{D}^s$  and  $D^{t}$ , respectively;
4: Generate two augmented views for each sample;
5: Calculate positive set by Eqn. 8;
6: Generate synthetic samples under intervention by Eqn. 13;
7: Calculate the final loss objective in Eqn. 15;
8: Reverse the gradients  $T^n$ ;
9: Update parameters by gradient descent;
10: until convergence
Table 1: MAP performances on two bench-marking datasets with 64-bit hash codes.
Office-Home	Office31
Methods	P2R	C2R	R2A	R2P	R2C	A2R	A2D	A2W	W2D	D2A	W2A	D2W	Avg
Unsupervised Hashing Methods
SH [62]	15.03	8.77	12.87	16.13	8.24	13.71	12.02	9.83	34.72	11.28	9.85	34.37	15.57
ITQ [17]	26.81	14.83	25.37	28.19	14.92	25.88	29.55	28.53	58.00	26.83	25.09	58.89	30.24
DSH [34]	8.49	5.47	9.67	8.26	5.28	9.69	16.66	15.09	39.24	16.33	13.58	41.07	15.74
LSH [16]	12.24	6.94	11.45	13.45	7.24	11.49	16.04	15.35	38.80	13.60	14.67	43.99	17.11
SGH [24]	24.51	13.62	22.53	25.73	13.51	22.93	24.98	22.47	53.94	22.17	20.52	56.36	26.94
OCH [35]	18.65	10.27	17.54	20.15	10.05	18.09	24.86	22.49	51.03	22.45	20.79	53.64	24.17
Transfer Hashing Methods
ITQ+ [79]	17.61	9.55	14.25	-	-	-	17.99	15.00	42.29	-	-	-	19.45
LapITQ+ [79]	16.89	10.37	13.56	-	-	-	19.96	18.24	43.32	-	-	-	20.39
GTH-g [74]	20.00	10.99	18.28	21.95	11.68	19.05	23.08	21.20	49.38	19.52	17.41	50.14	23.56
DAPH [21]	27.20	15.29	27.35	28.19	15.29	26.37	32.80	28.66	60.71	28.66	27.59	64.11	31.85
PWCF [22]	34.03	24.22	28.95	34.44	18.42	34.57	39.78	34.86	67.94	35.12	35.01	72.91	38.35
DHLing [22]	48.47	30.81	38.68	45.24	25.15	43.30	41.96	45.10	75.23	42.89	41.74	79.91	46.54
PEACE [58]	53.04	38.72	42.68	54.39	28.36	45.97	46.69	48.89	78.82	46.91	46.95	83.18	51.22
Ours	59.18	45.71	49.64	61.84	32.77	51.19	48.70	54.43	84.97	53.53	53.71	88.69	57.03
4.6 Summary
Finally, we summarize our framework with the following overall training objective as:
$$
\mathcal {L} = \mathcal {L} _ {D} + \mathcal {L} _ {C L} + \mathcal {L} _ {R E} + \mathcal {L} _ {V}. \tag {15}
$$
Moreover, the derivation of  $sign(\cdot)$  is zero for any non-zero value, and therefore it is difficult to compatible with the gradient propagation. To tackle this challenges, we adopt  $tanh(\cdot)$  to replace  $sign(\cdot)$  during optimization, which produces approximate hash codes  $\pmb{v} = \tanh(\psi(g^c(F(\pmb{x})))$  for training. Our model is first warmed up by the disentanglement module optimized by the reconstruction loss. Then we optimize the whole network with mini-batch stochastic gradient descent and the detailed progress of our IDEA can be found in Algorithm 1.
Baselines. We adopt a variety of state-of-the-art approaches for performance comparison, including six unsupervised hashing approaches (i.e., SH [62], ITQ [17], DSH [34], LSH [16], SGH [24], OCH [35]) and seven transfer hashing approaches (i.e., ITQ+ [79], LapITQ+ [79], GTH-g [74], DAPH [21], PWCF [22], DHLing [64], and PEACE [58]). Some results of ITQ+ and LapITQ+ are omitted because prior information is not accessible for sample pair construction.
Datasets. Experiments are conducted on different benchmark datasets: (1) Office-Home dataset [57]: This dataset contains examples from four domains (Ar, Cl, Pr, Re), each with 65 object categories. Two domains are selected as the source and target, resulting in six transferable image retrieval tasks
Table 2: MAP performances on the Digits dataset with 64-bit hash codes.
MNIST2USPS	USPS2MNIST
Code Length	16	32	48	64	96	128	16	32	48	64	96	128	Avg
Unsupervised Hashing Methods
SH [62]	15.56	13.67	13.80	13.45	13.35	12.95	15.59	14.35	14.22	13.57	12.92	12.96	13.87
ITQ [17]	13.05	15.57	18.54	20.12	23.12	23.89	13.69	17.51	20.40	20.30	22.79	24.59	19.46
DSH [34]	20.60	22.21	23.68	24.28	25.73	26.50	19.54	21.22	22.89	23.79	25.91	26.46	23.57
LSH [16]	12.40	13.54	15.89	16.01	18.54	20.44	12.76	14.86	14.77	16.89	16.32	19.67	16.01
SGH [24]	14.24	16.69	18.72	19.70	21.00	21.95	13.26	17.71	18.22	19.01	21.69	22.09	18.69
OCH [35]	13.73	17.22	19.59	20.18	20.66	23.34	15.51	17.75	18.97	21.50	21.27	23.68	19.45
Transfer Hashing Methods
ITQ+ [79]	22.84	21.20	20.68	19.15	17.99	18.52	-	-	-	-	-	-	20.06
LapITQ+ [79]	24.26	24.03	23.76	24.59	23.33	22.73	-	-	-	-	-	-	23.78
GTH-g [74]	20.45	17.64	16.60	17.25	17.26	17.06	15.17	14.07	15.02	15.01	14.80	17.34	16.47
DAPH [21]	25.13	27.10	26.10	28.51	30.53	30.70	26.60	26.43	27.27	27.99	30.19	31.40	28.16
PWCF [22]	47.47	51.99	51.44	51.75	50.89	59.35	47.14	50.86	52.06	52.18	57.14	58.96	52.60
DHLing [22]	49.24	54.90	56.30	58.28	58.80	59.14	50.14	51.35	53.67	58.65	58.42	59.17	55.67
PEACE [58]	52.87	59.72	60.69	62.84	65.13	68.16	53.97	54.82	58.69	60.91	62.65	65.70	60.51
Ours	58.89	64.48	65.72	67.48	70.24	74.34	60.99	61.47	65.45	67.97	69.72	72.31	66.59
Figure 3: We use 128-bit Precision-Recall curves to evaluate the performance of our method on the Office-31 and Office-Home datasets.
(P2R, C2R, R2A, R2P, R2C, A2R). (2) Office-31 dataset [42]: This widely used benchmark dataset contains over 4000 examples classified into 31 classes, which are from three domains (Am, We, Ds). We randomly select two domains as the source and target, resulting in six transferable image retrieval tasks (A2D, A2W, W2D, D2A, W2A, D2W). (3) Digits dataset: We focus on MNIST [26] and USPS [23], each containing ten handwritten digits. Each sample is re-scaled to  $16 \times 16$ . We select one dataset as the source and the other as the target, resulting in two transferable image retrieval tasks (MNIST2USPS and USPS2MNIST).
Implementation Details & Evaluation metrics. We perform experiments on an A100-40GB GPU.  $10\%$  of the target examples are used as test queries and the remaining target and source samples are viewed as the training set. As for the database, source domain data is adopted in cross-domain retrieval while target domain data is adopted in single-domain retrieval. The hashing network is optimized using mini-batch SGD with momentum. The batch size is set to 36 and the learning rate is fixed as 0.001. We evaluate the retrieval performance using four common metrics: mean average precision (MAP), precision-recall curve, top-N accuracy curve, and top-N recall curve. MAP is the primary metric for evaluating retrieval accuracy, while the precision-recall curve provides an overall performance indicator at different recall levels. The top-N accuracy curve shows the accuracy for different numbers of retrieval instances. As the key metrics, MAP and precision-recall curve can reflect the overall performance of our model in retrieval tasks. We also analyze the top-N accuracy and recall curves to evaluate the performance at different number of retrieved results. These comprehensive evaluations allow us to have an in-depth understanding of the model's retrieval ability.
5.2 Empirical Results
Performance Comparison. We present the results of our experiments on several benchmark datasets in Tables 1 and Table 2, where we report the mean average precision (MAP) scores achieved by our IDEA and other state-of-the-art methods. Our analysis of the results leads to the following conclusions. On the Office-Home and Office31 datasets, our IDEA achieves an outstanding average MAP score of 57.03, which significantly outperforms the second-best method, PEACE, with an average MAP score of 51.22. Furthermore, IDEA achieves the highest MAP scores across all query types, including P2R, C2R, R2A, R2P, R2C, A2R, A2D, A2W, W2D, D2A, W2A, and D2W. On the
Figure 4: Visualization of 128-bit hash codes on MNIST dataset in left three columns; Sensitivity analysis results of our proposed IDEA on Office-Home and Office-31 datasets are shown in right two columns on three cross-domain retrieval tasks.
Digits dataset, IDEA consistently achieves the highest MAP scores for all hash code lengths, ranging from 16 to 128 bits. This demonstrates the consistency of our method across different code lengths. For instance, on the MNIST2USPS task, IDEA achieves an average MAP score of 74.34 for 128-bit codes, which is significantly higher than the second-best method, PEACE, with an average MAP score of 68.16. Overall, our experimental results demonstrate that the proposed IDEA is effective and outperforms state-of-the-art methods on various benchmark datasets. These findings highlight the potential of our method for practical applications in cross-domain image retrieval tasks. We present the recall-precision curves of four compared approaches (PWCF, DHLing, PEACE, and IDEA) on two cross-domain retrieval tasks in Figure 3. Furthermore, in most cases, the curve of IDEA is higher than that of the other three baselines, indicating that the binary codes generated by IDEA works better for the hash table lookup strategy.
Qualitative Results. Here we provide a qualitative analysis of the model. Specifically, we use t-SNE visualization to display the hash codes learned by IDEA, PEACE, and DHLing (see the three subfigures on the left side of Figure 4). When compared to the PEACE and DHLing baseline methods, our IDEA-generated hash codes show more discriminative structures, with binary codes of different categories being better separated. These results indicate that the proposed method can produce hash codes with better discriminative power, which facilitates more effective image retrieval.
Parameter Sensitivity. In this part, we conduct sensitivity analysis for two important hyperparameters, which is shown in the right subplot of the Figure 4. We can observe that the MAP values for all three cross-domain retrieval tasks slightly decrease as the  $\beta$  parameter increases, indicating a negative impact on model performance. However, the decrease is not significant, allowing for an increase in  $\beta$  to balance loss terms without causing a significant reduction in model performance. Similarly, the MAP values increase and then decrease as  $\tau$  increases, demonstrating the potential for improved model performance. However, exceeding an optimal  $\tau$  range may have a negative impact on retrieval performance. Thus, determining the optimal  $\tau$  value through experimentation is necessary for achieving optimal retrieval performance in practical applications. In our experiments, we set  $\beta$  and  $\tau$  to 0.1 and 0.5, respectively.
Ablation Study. We have introduced several variants of our IDEA to investigate the impact of each components: (1) IDEA w/o  $\mathcal{L}_{RE}$  removes the original image reconstruction loss from the generated model, (2) IDEA w/o  $\mathcal{L}_{CL}$  removes the consistency learning loss, (3) IDEA w/o  $\mathcal{L}_V$  removes the hash code variance under intervention, and (4) IDEA w/o  $\mathcal{L}_{MI}$  removes the mutual information loss. By summarizing the
Table 3: Ablation Studies on six benchmark cross-domain retrieval tasks.
Dataset	Office-Home	Office31	Digits
Method	C2R	R2A	A2D	A2W	U2M	M2U
IDEA w/o LRE	44.02	47.29	47.05	53.11	64.80	64.49
IDEA w/o CL	42.11	45.97	45.36	51.17	64.25	63.76
IDEA w/o LV	45.10	49.09	48.21	53.96	57.34	66.97
IDEA w/o LMI	44.89	48.92	48.05	53.79	67.12	66.85
Ours	45.71	49.64	48.70	54.43	67.97	67.48
results of these model variants in Table 3. We conclude, the ablation experiments show that removing any of the four components (i.e.,  $\mathcal{L}_{RE}$ ,  $\mathcal{L}_{CL}$ ,  $\mathcal{L}_V$ ,  $\mathcal{L}_{MI}$ ) leads to a drop in performance on all datasets and tasks. Notably,  $\mathcal{L}_{RE}$  and  $\mathcal{L}_{CL}$  have the most significant impact. Our IDEA achieves the best or comparable performance on all datasets and tasks, demonstrating its effectiveness in learning disentangled representations for domain generalization. Specifically, it achieves the highest MAP on Office-Home and Digits datasets and the highest accuracy on the A2W task of the Office31 dataset, outperforming the ablated variants.
This work studies the problem of domain adaptive retrieval and proposes a novel method named IDEA to solve the problem. Our IDEA first disentangle causal and non-causal features within each image, guided by the principles of the information bottleneck. Moreover, these causal features are used to generate discriminative binary codes through consistency learning across both source and target domains. To generate domain-invariant binary codes, we simulates the intervention of various non-causal effects and encourage the invariance of hash codes. Extensive experiments on benchmark datasets validate the superiority of IDEA.
Broader Impacts and Limitations. This work improves the performance cross-domain retrieval, which can benefit real-world search engineers. Moreover, our work provides a new direction of incorporating invariant learning into cross-domain retrieval problems. One limitation of our work is that IDEA cannot tackle the open-set scenarios where target samples may come from unseen classes and we would extend our IDEA to more generalization scenarios in our future works. In particular, more advanced techniques such as modes in AICG and multimodal large-scale learning can be incorporated into our IDEA to improve the generalizability in a wider range of scenarios. In addition, we would explore more detailed visualization and interpretability analysis of invariant learning in the scope of cross-modal retrieval.
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A The Upper Bound of Mutual Information
We define:
$$
\hat {I} \left(\boldsymbol {F} ^ {n}, \boldsymbol {Y}\right) = \mathbb {E} _ {p \left(\boldsymbol {F} ^ {n}, \boldsymbol {Y}\right)} \left[ \log p (\boldsymbol {y} \mid \boldsymbol {f} ^ {n}) \right] - \mathbb {E} _ {p \left(\boldsymbol {F} ^ {n}\right)} \mathbb {E} _ {p (\boldsymbol {Y})} \left[ \log p (\boldsymbol {y} \mid \boldsymbol {f} ^ {n}) \right] \tag {16}
$$
Then, we show that  $\hat{I}(\pmb{F}^n, \pmb{Y})$  is an upper bound of  $I(\pmb{F}^n, \pmb{Y})$ . In formulation, we calculate their difference as follows:
$$
\begin{array}{l} \hat {I} (\boldsymbol {F} ^ {n}, \boldsymbol {Y}) - I (\boldsymbol {F} ^ {n}, \boldsymbol {Y}) \\ = \mathbb {E} _ {p (\boldsymbol {F} ^ {n}, \boldsymbol {Y})} [ \log p (\boldsymbol {y} \mid \boldsymbol {f} ^ {n}) ] - \mathbb {E} _ {p (\boldsymbol {F} ^ {n})} \mathbb {E} _ {p (\boldsymbol {Y})} [ \log p (\boldsymbol {y} \mid \boldsymbol {f} ^ {n}) ] \\ - \mathbb {E} _ {p (\boldsymbol {F} ^ {n}, \boldsymbol {Y})} [ \log p (\boldsymbol {y} \mid \boldsymbol {f} ^ {n}) - \log p (\boldsymbol {y}) ] \\ = \mathbb {E} _ {p (\boldsymbol {F} ^ {n}, \boldsymbol {Y})} [ \log p (\boldsymbol {y}) ] - \mathbb {E} _ {p (\boldsymbol {F} ^ {n})} \mathbb {E} _ {p (\boldsymbol {y})} [ \log p (\boldsymbol {y} \mid \boldsymbol {f} ^ {n}) ] \tag {17} \\ = \mathbb {E} _ {p (\boldsymbol {Y})} \left[ \log p (\boldsymbol {y}) - \mathbb {E} _ {p (\boldsymbol {F} ^ {n})} \left[ \log p (\boldsymbol {y} \mid \boldsymbol {f} ^ {n}) \right] \right] \\ = \mathbb {E} _ {p (\boldsymbol {Y})} \left[ \log \left(\mathbb {E} _ {p (\boldsymbol {F} ^ {n})} [ p (\boldsymbol {y} | \boldsymbol {f} ^ {n}) ]\right) - \mathbb {E} _ {p (\boldsymbol {F} ^ {n})} [ \log p (\boldsymbol {y} | \boldsymbol {f} ^ {n}) ] \right] \\ \geq 0 \text {(J e s s e n ' s I n e q u a l i t y)}, \\ \end{array}
$$
where the last inequality holds due to Jensen's Inequality with a convex function  $\log (\cdot)$ .
These baselines for model comparison are introduced as below:
- SH [62] is based on the theory of graph Laplacian. The binary code of a new data point is efficiently computed by the spectral analysis, enabling the out-of-distribution extension for unseen samples.
- ITQ [17] is an uncomplicated and effective alternative minimization algorithm. It can be incorporated into both supervised and unsupervised learning processes.
- LSH [16] is an important method in compressing high-dimensional data. It aims to map similar data points into the same bucket.
- DSH [34] is a model variant of LSH, which generates multiple view of the data point for metric learning using random projections.
- SGH [24] aims to compress high-dimensional data in a bit-wise manner, which is efficient for large-scale semantic similarity learning.
- OCH [35] leverage the tensor product to generate an ordinal graph, which guides the learning to generate more related hash codes.
- ITQ+ [79] is the early effort to implement transfer learning for hashing study, which learns a slack mapping from the source domain and achieves domain alignment through the quantization loss.
-  $\mathrm{LapITQ + [79]}$  is an extension of  $\mathrm{ITQ + [79]}$  by transferring the geometric relationship in the source domain to generate high-quality hash codes.
- GTH-g [74] selects the best hash mapping for target data using source data following the principle of maximum likelihood estimation.
- DAPH [21] utilizes a domain-invariant feature projection to reduce the domain discrepancy.
- PWCF [22] leverages a Bayesian model to learn discriminative hash codes and then infer the similarity structure using histogram features.
- DHLing [64] utilizes learning to cluster to optimize hash code within a single domain and then reduces the domain shift using the memory bank.
- PEACE [58] learns the semantics on target data using pseudo-labeling techniques and then minimizes the domain shift using both implicit and explicit manners.
C The Details of Datasets
Three popular benchmarks, i.e., Office-Home dataset, Office-31 and Digits, are adopted for performance comparison. Their details are elaborated as follows: