Variational Inference for Cyclic Learning
Authors: Zhuojun Zou
Jie Hao
Venue: ICLR 2026 Poster (2026)
Keywords: Cyclic Learning
Self-supervised Learning
Primary area: learning theory

Abstract: Cyclic learning has emerged as a powerful paradigm for weakly-supervised learning. It involves training with pairs of inverse tasks and leverages cycle-consistency in the design of loss functions. However, its potential remains underexplored, as current methods are often narrowly focused on domain-specific implementations.
In this work, we develop generalized solutions for both pairwise cycle-consistent tasks and self-cycle-consistent tasks. By formulating cross-domain mappings as conditional probability functions, we reformulate the cycle-consistency objective as an evidence lower bound optimization problem via variational inference. Based on this formulation, we further propose two training strategies for arbitrary cyclic learning tasks: single-step optimization and alternating optimization.
Our framework demonstrates broad applicability across diverse tasks. In unpaired image translation, it offers a theoretical justification for CycleGAN and yields CycleGN—a competitive GAN-free alternative. 
In unsupervised tracking, following our conceptual design, CycleTrack and CycleTrack-EM achieve state-of-the-art results on multiple benchmarks.
This work establishes the theoretical foundations of cyclic learning and offers a general paradigm for future research.
The source codes for CycleGN and CycleTrack are publicly available.

Published as a conference paper at ICLR 2026
VARIATIONAL INFERENCE FOR CYCLIC LEARNING
Zhuojun Zou', .Je Haol.2
"Institute of Automation, Chinese Academy of Sciences, Beijing, China GGunggdong Institute of Artificial Intelligence and Advanced Computing, Guangzhou, China 2zouzhuojun2018,, gie.hao/ aat.aaa...........moooo.m ac.cn
ABSTRACT
Cyclic learning has emerged powerful paradigm for weakly-supervised learn- ing. It involves training with pairs of inverse tasks and leverages cycle-consisteney in the design of loss functions. However, its potential remains underexplored, current methods are often narrowly focused on comain-specifee implementations. In this work, develop generalized solutions for both pairwise cycle-consistent tasks and self-cycle-consistent tasks. By formulating cross-domain mappings as conditional probability functions, reformulate the cycle-consistency objec- tive as an evidence lower bound optimization problem via variational inference. Based on this formulation, we further propose two training strategies for arbi- trary cyclic learning tasks: single-step optimization and alternating optimization. Our framework demonstrates broad applicability across diverse tasks. In unpaired image translation, it offers a theoretical justification for CycleGAN and yields Cy- cleGN-a competitive GAN-free alternative. In unsupervised tracking, following conceptual design, CycleTrack and CycleTrack-EM, achieve state-of-the-an results on multiple benchmarks. This work establishes the theoretical foundations of cyclic learning and offers general paradigm for future research. The source codes for CycleGN and CCcle'Trace are publicly available.
INTRODUCTION
The need for labeled data is now one of the biggest obstacles in machine learning research, where supervised learning's reliance on manual labeling introduces both scalability issues and quality con- trol challenges. To address this, researchers have turned self-supervised training, the core idea of which is to generate supervisory signals from unlabeled data for training. Self-consistency-bar -bassd supersupe learning has already demonstrated strong capabilities the field of representation learning (Zhang et al.) 2016)] He et al. [0222] Mikolov et al. 2013 Devlin et al. 2019 Chen & He 202T). A series of studies have now shifted focus cooss- self-supervised learning con-
structed via cyclic consistency (Xu et al. 2023 Yuan et al. 2020 Dwibedi al. 2019 Wang al. 2024 Kulkarni et al. 2019).
This type of approach involves designing pair of inverse tasks and constructing the training pro- cess by leveraging the property that data points should return to their origin after cyclic processing. This not only eliminates the reliance on manual annotations but also preserves task-specific semantic constraints. As shown in Fig. [ this framework has been applied to various tasks (Zhu et al. [017]]
Wang et al., 2024 2019b Dwibedi et al. 2019). A well-known example is CycleGAN (Zhu al. 2017) (Fig. a)), wh which jointly optimizes two tasks by combining cycle consistency loss and adver- sarial loss, leading its widespread adoption various weakly supervised visual tasks (Almahairi et al. 2018 Yang et al.] 2020 Kwon & Park 2019). In contrast, a different approach is employed in the visual grounding (Referring Expression Comprehension) and image caption (Referring Expres- (F)..Db)).
sion Generation) loop (Fig. ()). where both CyCO (Wang al., (0244) and SC-Tune (Yue et al.) 2024) adopt alternating training strategies for the two tasks, showcasing the cross-modal adaptation capability. In CyCO, they first conduct cyclic training using only the cross-entropy loss with image captioning as the objective, followed by another training batch that utilizes only the bounding box losses (Rezatofighi et al.) 2019 Girshick 2015) for visual grounding. However, current approaches face two key limitations: First. task-specific designs hinder cross-domain generalization (c.g., the loss of CycleGAN cannot be directly applied to the video alignment task). Second, many methods

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Monet Photos
Referring Expression Comprehension
Forward Tracking
Text: man in white hat and (dd jadeet country sking
Bounding Boc 22.
Photos Monet
Backward Tracking
Reforring Expression Generation
(a) Image-to-Image Translation
(b) REC and REG
(c) Visual Object Tracking
Figure 1:
Tasks forming cyclic learning. (a) Image-to-image translation: forms cycles through
paired style transformations (e.g., photo<>painting). (b) Referring expression comprehension & referring expression generation: construct cycles by bridging positional descriptions and appearance descriptions of identical objects. (c) Visual object tracking: forms cycles via brwward trajectory consistency.
still rely on pseudo-labels (e.g.. unsupervised visual tracking approaches (Zheng et al. [2021] Wang al., 2019a; [Shen et al., 2022) require initial trajectories from base trackers). To address these limitations, we propose a probabilistic modeling approach to enable universal cyclic learning across all applicable tasks.
Building upon the constraint of cycle consistency, this work establishes unified probabilistic frame- work for both paired cyclic tasks (bidirectional mapping A-B and B-+) and self-cyclic tasks (A-B and B-AA mapped by the same function). Methodologically. this framework is inspired by the
(EM) algorithm (Neal & Hinton| 1998), leveraging as a foun- dational variational method for iterative training. By introducing latent variable it transforms the maximization of log-likelihood into the maximization of an evidence lower bound, and then approximates the optimum stepwise through the Expectation step (E-step) and Maximization step (M-step). This method has stood the test of time and remains highly influential across various fields this day (Sun & Yang, 2020, Bao et 2024 Qu et al. 2019). Another canonical application is the Variational Autoencoder (VAE) (Kingma et al. 2013), which assumes that the latent variables corresponding to the data follow prior distribution. Through variational inference, derives reconstruction loss and a Kullback-Leibler divergence (Kullback & Leibler [951) loss, ultimately training a decoder capable of generating new data samples from the prior distribution. In contrast, our framework aims to deliver theoretically rigorous and computationally efficient solutions for broad range of cyclic learning problems.
Specifically, we formalize cycle consistency by treating intermediate data points as latent variables, with cross-task transitions as learnable distributions. Within this framework, we propose: (i) universal single-step loss derived via variational inference that enforces cycle consistency for end- to-end training, and (ii) an EM-based method that alternately updates model parameters two tasks when KI. divergence approximation is infeasible. To validate the universality and effectiveness of our method, we conduct experiments in two distinct tasks: for image translation, our approach not only reveals the working mechanism of CycleGAN al. 2017) but also achieves bidirectional style mappings without GANs through the EM method. In object tracking, our model effectively captures dynamic target appearance variations via self-cyclic constraints, significantly improving unsupervised tracking robustness. The proposed probabilistic framework provides a unified solution for diverse cyclic learning scenarios. Our main contributions are:
We regard the intermediate points tion-sstrrtin//noo-temnnal points) in cyclic learning as latent variables, thereby establishing the first variational probabilistic framework that uni- fies both paired and self-cyclic tasks through variational inference.
We derive two theoretically grounded optimizers for general cyclic learning: (i) a single- step variational loss thus enabling stable and efficient training with explicit distributions, and (fi) a KL-free, EM-based algorithm compatible with complex distributions.
In unpaired image translation, we theoretically explain the success of CycleGAN and pro- pose a GAN-free, EM-based alternative. In visual tracking, we introduce CycleTrack (single-step) and Cycle Track-EM (EM- based, which achieve ofate-of-the -fr unsupervised performance.
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2 VARIATIONAL INFERENCE FOR CYCLIC LEARNING
2.1 METHODOLOGY
Fundamentally, the generation problem involves learning function f that maps data points from the input space to the output space, I.c., f: X - y. For example, in image captioning, X' is a collection of natural images where data point x is photo of a horse, and y the set of all grammatically E ) for x would be natural language description of the horse. The goal of a generative model is to learn this mapping f, such that for an input from the domain X, the output ((x) appears "real" and follows a specific distribution in the codomain ) Although the generative function itself is not an explicit probabilistic model, it implicitly encodes the dynamic process of probabilistic transition.
correct sentences. The corresponding
We now examine a special case from a theoretical perspective: when y = =x( is invertible. In this scenario, defines bijective mapping, and there exists unique inverse function x = (y). which is a necessary condition to guarantee cycle consistency. When a specific observed value is given, it must have been produced by unique x ff). Probabilistically, this implies that under the condition y = { the distribution of X' is deterministic-all probability mass is concentrated the single point x. Thus, the conditional probability density function p(xly) becomes Dirac function:
p(xly) 8(x (y))
(1)
Let g()) denote (-) with o and 0 being the parameters to be learned for ʃ and respectively, then the conditional probability can be expressed as:
(x 8(x (o));; Po(ylx) = 5(y fo(x)).
Based on the above transformation relationships, cyclic learning can be formulated probabilistically to optimize the mapping functions. Specifically, for cycle that starts from a data point and returns itself, we aim to maximize the log- likeliieohood, i.e., max log po (x). By introducing the variational distribution q (y x), we obtain:
log log)o(x) - / / (y1x) log
Pa (x. dy = Bro log po (x. y) g (y
+
(3)
Po (y(y)x)
where DKL denotes the Kullback-Leibler divergence. Here, parameterizes only the conditional distribution pa yx)),,, which is usually implemented as a neural network. The joint distribution po(x.y) y) is defined by (xly) and the prior p(y), while the posterior po is the conditional distribution of y given x and is not directly parameterized. The first term corresponds to the so- called Evidence Lower Bound (ELBO), which admits the following decomposition:
(x) = / to (y xx) log (xly)dy - (xo((o
(4)
where f go (y(x) log po po (xly)ds represents the reconstruction expectation, while (gox)(v))))ll( enforces distributional alignment between (y(x)) and the prior p(y). One may simultaneously consider the symmetric case starting from data point y and completing the cycle back to y. for which the ELBO is given by:
Co (x,
= [o (x ( x IP()))
(5)
+ (1 (y Dx (go(al)) p(=)).
Here, we use x, y to denote data generic sense, while x, refer to specific data instances. The gap between the maximum log- likeeiihoood and its evidence lower bound is:
DKL (v((() (pp (ylx)) + DxL (xxx)x(x)))lllxxxxxxx))))
(6)
The maximization of (x. inherently minimizes two KL divergence terms. Through this pro- cess, the variational distributions 4s (y(x) and qo (xly) are regularized to align with the prior dis- tributions p(y) and p(x), respectively, while also being implicitly encouraged to approximate the derelederived posteriors (y|x)) and (xly). This dual regularization reflects the core objective of cyclic learning: to learn pair of stochastic mappings that jointly consistent with both the marginal structure of the data and the cyclic reconstruction constraint, thereby forming a probabilis- tically coherent bidirectional translation between the two domains.
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Cycle consistency of x nrt
Blas of domain y D
L Friezze
Compute x
Loss
Compute
Y for
Loss
D
Inner Logs
fxx)
= 9o(9)
2
Outer Loop
goly
y = fo(8)
Bias of domain X
Cycle consistency of D
① Compute Y
fu
Loop
3 Freeze
+
D
Loss
Compute
(a) Single-step approach
(b) E-M approach
Figure 2: General solution for cyclic learning. (a) Single-step joint optimization. iteration optimization.
(b) Dual EM-
This probabilistic formulation shares conceptual roots with both variational autoencoders (Kingma et al. 2013) and the expectation ineccation-maxxiizzttonn algorithm (Neal & Hinton 1998). In fact, the two specific learning strategies we introduce next can be seen as their direct analogues: one follows VAE-style joint optimization, and the other adopts EM-style iterative optimization. What dis- Rather
tinguishes our framework from the previous methods is the role of the latent variable than being free latent variable used solely model the distribution x, here y is real observed variable from domain V. It carries its own structure and constraints, and must satisfy the marginal prior p(y) estimated from data. The learning objective is not merely to reconstruct x, but learn bidirectional mappings that are probabilistically consistent with both domains, forming cycle that respects the intrinsic properties yf
Returning to the perspective of mapping functions, for the first term in Eq. we have:
/ 4o (y(x) log (xly)dy f 5(y [xx()) log 0(x (o (y) log 5(x go (x)()))))
(7)
Then, for a distance function Deye (x, x) that zero iff x = and positive otherwise, maximizing the expected log-likelihood reduces minimizing Deye: arg max (x1s)) [log Po (x 0,6
arg max log 8(x. (o(ff = arg min Daye (x, go (x))).
0.6
0.6
Here the cocee-oonsistency loss Deye serves as a specifc proxy for the probabilistic expectation, directly minimizing the discrepancy between go (x)) and
Under the deterministic mapping assumption, where go (ylx) collapses to a Dirac delta - (x))), the second term in Eq. reddues
f 5(y fx)) log
5(y fo(x)) dy log lofo(((()))) + constant. p(y)
D Dxz(gs(yix)llld
where the constant arises from the ill-defined log 5(0) and can be ignored in optimization. Thus, maximizing the negative KL divergence is equivalent to maximizing log (x),, i.e., encouraging mapped output (x) ) to lie in regions where the prior p(y) high.
In practice, p(y) may not be explicitly modeled, especially when y resides in a complex domain. In such cases, we can replace log (x)( with a distance function Dsim (f)() (x)x))) )) that measures how well the generated sample fits the target domain V. This leads to the following equivalence:
arg max +
D Dx x) [p(r)) = arg max log (epp(f(())) = arg min D.im (x). (10)
classic choice for D Dsim is the Wasserstein distance (Vaserstein 1969 which provides
ingful geometric discrepancy measure. Combining Eq. with Eq. 8 and Eq. I0 the overall optimization objective for the deterministic cyclic mapping can be approximated
arg max la (x) ze arg min (Deye (x, go (x)())) Deam (fo,
(11)
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Note that (x) requires joint optimization of 8 and o. which may not achieve exact equality in Eq. I due to differing gradient behaviors across distance metrics. Nevertheless, since both D Deye and D proxy methods, minimizing Daye + Diim to approximate max (x,s(x) x) is not detrimental to training. The core design principle requires the loss function to incorporate:
The similarity between & and (measured by Daye)
. The degree to which y belongs to y (measured by Dsim)
For eyclic tasks, models may converge to local optima of either min Deye or min D Daim- This neces- sitates task-specific balancing between these two approximating terms.
By integrating Eq. with Eq. IT we arrive at the two-way cycle-consistent loss:
C(x,y) y) = D (x, (f (x))) + D (ff(x)))) + D (y, (oo + D (y),,,, (12)
which corresponds to the direct optimization scheme shown in F(g.
The variational interpretation in Eq. suggests natural alternating optimization strategy. By treat- ing the two mappings as coupled latent-variable models, we can view the learning process as jointly maximizing log po (x) and log (y). where each benefits from the other's intermediate outputs. This motivates an EM-based procedure that iterates between two complementary stages: fixing one mapping to infer pseudo-labels for the other.
Concretely, as illustrated in Fig. b)), the Eg-Mo stage first uses the current forward mapping fo to generate = (x) from a sampled batch of x (E-step), then updates the backward mapping ge by minimizing the cycle loss Deye (x, go (})) (M-step). Symmetrically, the E- stage samples y. produces & = go (y), and updates fo via Deye(y, fx)). This alternating scheme promotes stable convergence by progressively aligning both mappings with the cyclic consistency constraint.
From a probabilistic perspec- tive, in the M stage, as- sume the current forward map- ping fo is sufficiently accu-
Algorithm 1 An EM approach for cycle- tasks.
Input: Dataset X = (x' j y {
1:
while not converge do
rate, i.e., (x(x)x) approximates the true posterior p(y]x). Un- der this assumption, the E, step (sampling x and generat- ing = f((x)) effectively en- forces (y)())))))l())))
2:
while insufficient loss decrease do
3:
Sample batch of datapoints X" {x} from X
4:
Get pseudo-labels ý = L (x) for each x E 2' VA Eg
5:
Update 0 via L())- = Digg (x, (8)) A Mg
6:
end while
= O. which implies (y(x) = p(y])). The subsequent Ma 9:
7:
while insufficient loss decrease do
8:
Sample batch of datapoints y" {y} from y
Get pseudo-labels & = go(y) ) for each y E )' \ Esp
step then updates 0 by maximiz- ing (riv) po ( (x])]] driv- ing f toward lower bound de- termined by the approximation quality of Ta-
10:
Update e via L(Ø) D (y, (x))) \A Ms
11:
end while
12:
end while
Output: Generative models g-(-) and fø(-).
Symmetrically, in the Mg stage, we assume go is sufficiently accurate, such that po (xly) effec- tively represents the true conditional distribution p(xly). The Eg step (sampling y and generating x = go ())) then enforces DKL. (go (xlx))p(x())) = 0, and the M, step updates & by maximizing (xy [log P ( (y)x)] Algorithm summarizes the complete procedure, but with the tone of genera- tive models.
In the standard EM algorithm. the E-step fixes parameters find the latent distribution q(z) that tightens the ELBO, typically by computing the posterior p(z x, 0). The M-step then fixes g(z) and updates 0 to maximize the expected complete-data coordinate ascent, alternately optimizing O and qzz). Our method employs a different variational inference workflow since we focus on learning mappings p(xly) and p(y|x) rather than data dis- tributions. When optimizing Pa (xly), the E-step fixes 0 and finds the optimal qo ()(x)x) - this is accomplished by the Eg stage, which updates 6 to better approximate the posterior. The M-step then maximizes the expected log- likelihoooo under this qo (y(x) corresponding to the Ea stage, which updates using the generated lsbels-labels. The same logic applies to p (y |x). Parameters 0 and & are alternately updated while keeping the other fixed. For clarity, we define fixing network
ligliikllihod.. This process can be viewed as
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The correspondence between com- ponents in Eg 12 and those in CycleGAN.
Table 1:
Table 2: The correspondence between steps in
Algo. | and those in CycleGN.
Components Eq
Components CycleGAN
Steps Algo
Steps in CycleGN
ogg (x, (o (x))
Exmpaata be (fa()) - x|]x]
D (xa(). V)
(fa x,))
Ea
fa(x)
eug (v. To (as (1)1)
Pyropaet by fo (9s (rr) xllx)
Mg
Update via Luyo (go)
Fampaara (lls x|[x]
Dam (90 (3))
Cawd Lae, Dx )/
Fg
go(y)
M
Update via Coy((fa) By- on (ll)(( x
parameters and sampling data as the E-step, and maximizing distribution functions as the M-step, labeled as Eg-M, and Ey-Ma based on the optimized parameters. Essentially, Eg-Mø serves as the E-step for po (xly) while Eg-Ma acts as its M-step. Thus, our method also implements coordinate ascent, alternately optimizing model parameters and parameterized distribution functions.
This approach eliminates the need to define Diim as Eq. 12] thus avoiding both training instability caused by metric inaccuracies or ill-defined data distributions. A key question then arises: how does the EM iteration ensure that ý = fo (x) E ) The answer stems from its alternating optimization nature: in the second M-step, enforce ý (ge (y)( to approximate y, thereby guaranteeing that the output of f-(-) falls within V. By symmetry, this also ensures & = go(y) E X.
2.2 APPLICATION ON UNPAIRED IMAGE TRANSLATION
We use CyclcGAN et al. 2017) as an example and conduct experiments on the unpaired image- to-image translation task. For two distinct image domains X' and V, the objective of CycleGAN is find pair of mapping functions, denoted as fo + y and go : y - X. The method employs a end-to-end training strategy for network training, with the proposed loss function as follows:
L(J0.90 90, Dx. Dy)= = LGAN(fe: Dy, x,)) + LoAN(go, Dx V/ X) + Leye(So go),
(13)
where LGAN denotes the adversarial loss and Leys represents the cycle consistency loss. Dx and Dy the discriminators for domains X' and y respectively, which engage in adversarial training with the generators ge and fe. Laye consists of both forward and backward cycle consistency losses:
Laye go) Ex-pesta (x) (olgo (lll (xx(x))
x[[1] + Ey-pasta (go - ylla).
(14)
Under our framework, the corresponding components of the loss function be mapped onto those in [2] as summarized in Tab. [ LGAN encourages the generated distribution to resemble the target distribution, while Loye ensures cycle consistency. The adversarial training of a GAN discriminator is intrinsically linked to minimizing the Shasen-Shannon (JS) divergence (Lin 2002) between the generated and real data distributions (Goodfellow et al. 2014). As the IS divergence variant of the KI. divergence, the adversarial loss can be viewed as an indirect means of optimizing a divergence related to DKL- By integrating these components, becomes evident that Eq, [3] is specific instantiation of our general formulation in Eq. 12 This connection provides a theoretical explanation for the effectiveness of CycleGAN.
symmetric
Based on Algo. D propose eyclic learning approach that alternately optimizes the forward and backward tasks. The detailed procedure is summarized Tab. 2 with iterations continuing until convergence is achieved. Unlike CycleGAN, our method eliminates adversarial discriminators entirely and is thus named CycleGN.
2.3 EXPERIMENTS
CycleGN and CycleGAN (Zhu et al., 2017) adopt the same generator architecture as pix2pix (Isola et al. 2017). The unpaired training and test images are sourced from the Cityscapes dataset (Cordis ctt al. 2016). CycleGN alternates between training Eg-Ma and Eg every 200 samples, with total of 100 training epochs. All other training configurations are identical to CycleGAN. We com- pare our approach against several methods that employ different loss functions for cyclic learning, including CoGAN (Liu & Tuzel 2016), BiGAN/ALI (Dumoulin et al.) 2016 Donahue al.) 2016 SimGAN (Shrivastava et al. (017). and the feature loss combined with GAN (Shrivastava et al. 2007 Zhu et al. 2017). We evaluate method on the Cityscapes dataset for both labels-to-photo

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Table 3: FCN-scores of -photo for dif- ferent methods on Cityscapes.
Classification photo labels on Cityscapes.
Table 4:
performance of
Persixel nec.
Per-class acc.
Persixel acc.
Per-clas sec.
Class
Loss
GAN
IOU
Loss
GAN
IOU
CoGAN
0.40
0.10
0.06
CoGAN
0.45
0.11
0.08
BIGAN/ALI
0.19
0.06
0.02
BIGANIALI
0.41
0.13
0.07
SimGAN
0.20
0.10
0.04
SimGAN
0.47
0.11
0.07
Feat. loss GAN
0.06
0.04
0.01
Feat, loss GAN
0.50
0.10
0.06
CycleGAN CycleGN (ours)
0.52
0.17
0.11
CycleGAN
0.58
0.22
0.16
0.52
0.14
0.10
CycleGN (ours)
0.51
0.16
0.10
and photo-to-labels translation tasks. Tab. 3 and compare CycleGN with CycleGAN and other loss configurations. The successes achieved by CycleGAN on this pair of cyclic tasks demonstrate the feasibility of the single-step optimization paradigm. Moreover, our proposed application of Cy- cleGN based on the EM method achieves better accuracy than other loss functions, trailing only marginally behind CycleGAN. Notably, CycleGN achieves competitive generation results without any adversarial structure, simply by pushing the generative network's 's outputs closer to target domain instances.
EXTENDING TO SELF-CYCLIC LEARNING
3.1 METHODOLOGY
Loss
Cycle consistency: Degel
Bias of domain: Dam
8ofx, 4:3
Single-Step Approach
step
E-M Approach
M stop
shared mapping function in Ω
step:
M step: Compute
de
Compute
Loss
D
Figure 3: General solution for self-cyclic learning.
We consider special case with single-task learning as illustrated in Fig. 3 where for any X, Q and any x E X. y E V, the symmetry 0 o holds. When fo go. triv- ial solution (x)) = x would be (x(x = However, since y = (x) must belong to y not X' in cyclic learning, go (x) cannot directly equal Thus, we reformulate the opti- mization objective of cyclical learn- ing as go(go x. X', )), X²) x, which corresponds to optimizing the conditional probability log po (x()),
Algorithm An EM approach for self-cyclic tasks.
Input: Dataset [ with X {
I: while not converge do
2: Random chosen sub-domains X, C Ω
3: Sample batch of datapoints X' = [x} from X'
4: E-step: Stop Gradient
5: Get pseudo-labels ý go (x, X, X2))) for each E X
6: M-step: Learning Procedure
7: Update 0 via L()) Deye (x, go (,.
8: end while
Output: Generative model g+
yielding the evidence lower bound:
le (x X') Egg (x))) [log pe (xly, ),, X)] Dr (go (y) x, xxxx)))))(()
(15)
For self-cyclic tasks, either the backward forward components in the asymmetric task loss in Eq. 12 can be removed, leading to the following loss function:
[(x) Deye (x. go (x. X. R.))), X)) + Deim (go(x, X,)))
(16)

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This loss function guides the model y go(;; 1, -))) toward through sim preventing conver- gence to the local optimum go (x, x. = x.
The EM algorithm remains applicable to self-cyclic learning. As outlined in Algo. 2 the E-step minimizes D Dr (y)(y)x, X, pp (y H.. ).)), while the M-step maximizes the ex expected log- likelihood arg max E Ep- (r1x..X.3) [log po (xly, y 2 The KL divergence term in Eq. 15 is omitted in M-step as reduces to constant in this case. Note that fo = 9a enables joint optimization of bidirectional tasks in EM process, contrasting with the Eg-Ma Ex-Ma alternating sequence in Algo.
3.2 APPLICATION ON UNSUPERVISED VISUAL TRACKING
Visual object tracking is classic self cycle-consistent task, with its cyclic structure illustrated in Fig. [c). Based the paradigm proposed in this work, can design two self self-supervised schemes.
For video sequence, let X' and y be the selected template and search frames, with x as a random object box in X. Then, the loss function of the tracker 7 can be derived from Eq. T6
L(T, x) La(x.x(x..... T(Txx X, y), )/ x)) - Xx,)).
(17)
s.l. y = arg maxyEROx, (yU
where La the bounding-box loss, IoU represents the Intersection over Union between two bound- ing boxes, and BOXy is detector- generated bounding-bow set in frame V The correspondence between this loss function and Eq I6 is as follows:
Deyo go (0 x2 x)) (X,)
D Damm (ox (x)))) = L, (T(x,XX)))
Using Algo. as reference, we also propose EM variant that bypasses y distribution estimation, where the expectation step computes ÿ T T(x, X,)), and the maximization step updates by optimizing the objective L (x, T )())
Since current trackers fail to achieve differentiable head-to-tail connections, we are compelled to develop CycleTrack from scratch. We map template boxes to positional tokens via MLP, then concatenate them with uncropped frame tokens as input. The main architecture combines a vanilla VIT (Dosovitskiy et al. 2021) encoder, STARK's feature enhancer Yan al.) (021), and parallel FCOS heads (Tian et al. 2019) that generate confidence-weighted box outputs. The tracker can be formally expressed y Tx(x, X)) For clarity, refer the single-step trained tracker as CycleTrack and the EM-trained tracker as CycleTrack-EMM.
3.3
EXPERIMENTS
Table Comparison with leading unsupervised trackers LaSOT and TrackingNet.
Table 6: Comparison with leading strictly- unsupervised trackers two datasets.
LaSOT
TrackingNet
LaSOT
TrackingNel
Method
AUC
Precision
AUC
Precision
Method
AUC
Precision
AUC
Precision
ResPUL.
54.6
48.5
ResPUL
54.6
48.5
LUDT+
30.5
28.8
49.5
LUDT
26.2
23.4
54.3
46.9
USOT*
35.8
34.0
61.5
56.6
USOT
33.7
32.3
59.9
55.1
off
46.8
44.8
64.9
58.5
ULAASTooff
42.9
40.5
ULASTT
47.1
45.1
65.4
ULASST-o
43.3
40.7
CycleTrack
$1.0
49.7
75.9
71.5
CycleTrack
45.0
42.2
65.6
59.0
CycleTrack-FM
57.9
CycleTrack-FM
In CycleTrack and CycleTrack-EM, L, adopts the weighted LI and GloU(Rezatofighi et al. 2019
losses consistent with STARK STARK(Yan et al., 202I). The DETA SitectorrOuyang--Zhaan et al. 2022 produces detections on Mralkl et al., 2018). GOT- GOT-1Ok (uuann et al. (019), and La- SOT al. 22019,, combined with CocO et al. 2014) for unsupervised training. Optical flow labels are generated by ARFlow et al.) 2020) on YouTube- veee-voSXuuu et al. 2018). ImageNet- ViD(Deng et al. 2009), GOT-10k, and LaSOT, serving the strietly unsupervised set. We conduct
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Real Photo
Reconstructed
Photo
Fake Photo
Real Labels
Reconstructed
Labols
Fake Labels
Gy
CycleTiack (full supervised)
GroundTruth
#000
PO4DO
150000
#2000
MOOD1
N0400
POBDO
A180-
42000
(a) Failure cases in CycleGN
(b) Failure cases in CycleTrack- EM
Figure 4: Failure cases in cyclic learning. (a) CycleGN failures in photo++map translation: While reconstructed images closely resemble real images, the generated fake images exhibit significant quality degradation. (b) Mislocalizations in CycleTraack-Ni) (highlighted by yellow boxes): Target objects are confused with other salient objects or visually similar distractors.
comparisons with leading unsupervised trackers, including ResPUL et al. 202T), LUDT al. 202T), USOT et al., 202T). ULeST((hen et al.) 2022). We evaluate our unsuper- vised object tracking methods on LaSOT and TrackingNet, demonstrating significant advantages over existing approaches. Unlike conventional methods requiring pseudo-labels for image cropping, tracker directly implements the proposed cyclic learning paradigm through full-image process- ing. Experimental results in Tab. 5 and show our single-step and EM-based training approaches achieve state-of-the-ar performance in both unsupervised pervised
and strictly unsu- settings, outperforming the second-best methods by considerable margins. Additionally, framework naturally supports semi-supervised training (see Appendix for more details).
4 FURTHER ANALYSIS AND DISCUSSION
This section outlines the primary concerns of cyclic learning in applied contexts.
1. Is the mapping learned by cyclic learning always what we need?
Not necessarily. We observe that cyclic learning models can learn incorrect mappings across paired domains. As shown in Fig. 4 although the reconstructed photos can closely match the real pho- tos (and similarly for the reconstructed maps and the real maps), the intermediate fake images re- main unsatisfactory. In visual tracking. CycleTrack occasionally locates incorrect objects in search frames. Owing to the annotation bias of the detector, the tracker can still probabilistically re-localize the target even when initialized with random objects. This may cause the tracker to degenerate into a basic object detector.
We attribute these failure cases primarily the inherent limitations of cyclic learning itself. Without paired annotations, the models only learn some mapping between domains X' and y that satisfies cycle consistency but does not guarantee that the learned mapping is exactly what we intend. Intro- ducing additional constraints beyond cycle consistency may help mitigate this issue.
Additionally, the EM method has intrinsic risk of converging to local optima. During training, ge may gradually adapt to two distinct modes: go (a) = x and (y) = This means it simultancously leams mappings from A - X' and y - B, both of which can be achieved with single set of parameters 0, where A = {a'} and B = [b'} represent domains that emerge local optima. Correspondingly, fo learns the mappings X + A and B + y. As a result, we obtain a pair of bidirectional mappings: X' ++ A and B ++ V, which deviate from the intended behavior X' ++ V. Once a steady state where both cycles are satisfied is reached, the assumption p(y[x) = qo (ylx) ) in an inner loop never be achieved.
2. Which is better single-step training or EM training?
In image translation, the single-step CycleGAN outperforms the EM-based CycleGN. Conversely, in visual tracking, the EM-based method CycleTrack Track- surpasses its single-step loss variant, Cycle- Track. Besides, as introduced in the opening section, image generation (Ksnn & Park 2019

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60
0.8
0.8
50
AUC LaSOT
AUC on LaSOT
0.6
Train loU
0.6
40
Train
0.4
-30
Train loU
AUC on LaSOT
0.2
20
100
200
300
400
500
0
100
200
300
400
500
(a) Train Cycle'Track via Daye
(b)
Train Cycle'Track-Bi via Dog oye
Figure 5: Ablation on Daim removal (E-step removal): (a) Train tracker solely with Deyci (b) Freeze forward process via E-step, then train tracker with D Deye:
Yang et al. 2020) tend to favor single-step optimization, whereas the REC-REG cycle Yue et al, 2024 Wang al., 2024) exhibits preference for EM optimization. We argue that the choice be- tween these two methods primarily depends on whether Dx is well approximated. Both methods must employ the cycle-consistency loss Deyer which can be disregarded in this comparison. The accuracy of Deim in measuring the KL divergence between sample and target distributions critically influences convergence behavior, For instance, while EM methods may introduce training instability, the GAN discriminator provides a robust 1 surrogate that makes single-step optimization prefer- able. In contrast, aligning with the nearest detection box in Cycle is unreliable, because targets may remain completely undetected. This leads to poor Dsim estimation, explaining CycleTrack s inferior performance compared to CycleTrack-
An alternative perspective that, compared to paired eyclic tasks, self-cyclic tasks allow for more stable EM training by eliminating the need to wait for one EM process to converge before initiating the next. We provide a more detailed analysis of the applicable scenarios in Appendix C
Can we rely solely on the cycle-consistency loss?
Using only the Daye loss in single-step optimization is mathematically equivalent to removing the E-step in the EM algorithm by eliminating the ttop-gradient operation, which introduces a key lim- itation: the generated ý often fails to adhere to the target domain distribution due the lack of explicit constraints. In our implementation. we disable the E-step by removing the forward-process freezing operation in CycleTrrack-NN clearly trivial solutions compared to the complete EM training procedure. This behavior parallels the significant performance deterioration observed in CycleGAN when removing adversarial loss while retaining only the cycle-consistency loss. This validates the necessity of both the Dsim loss for single-step step methods and the E-step for EM algorithms.
As evidenced
Fig. [ this ablated model converges to
CONCLUSION
This work introduces novel probabilistic framework that unifies cycle-consistent learning through variational modeling. By formulating cyclic tasks within a general theoretical foundation, we es- tablish principled connections between previously disparate approaches. The framework naturally gives rise to two complementary optimization strategies VAE-style single-step method for effi- cient training, and EM variant that operates without KI. divergence estimation. Together, these contributions provide both theoretical coherence and practical flexibility for cycle-consistent learn- ing across tasks. In image translation, our framework theoretically explains CycleGAN's success as variational approximation of cycle-consistent learning, while enabling GAN-free alternatives via EM optimization. In object tracking, self-cyclic constraints enable dynamic modeling of target ap- pearance variations, allowing both single-step and EM-based trackers achieve robust unsupervised performance. We hope this work will inspire future research directions in cyclic learning.
ACKNOWLEDGMENTS
This work supported by the Guangdong S&T Program under Grant No. 202480101040005.
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A EXTENDED INFERENCES
A.1 FROM MAXIMIZING LOG-LIKELIHOOD TO MAXIMIZING ELBO
Here, we derive Eq.
in detail:
/ 2 (y(x lo (x)dy
log pa (x)
/ (x(xxx) log po(x. y)
po(y(x) dy
f (x(x)) (x)x))) log
(x. y)
go(y(x) (y(x)x)
dy
(18)
(y(yxx) x)
= / (x(xx) log
px(
dy + I /00 (x)()i)) log
go go(y)x) dy
4s (F/x)
(y(x)
log po (x.
= (r
(y(x)x)
with
log Px(x. y)
(x) (s/x)
(x/x)
96 (y/x))
- g00 (1/xx) log po (x(x)y)p(y) dy
(v(x)x)
(19)
/ (x()))) log (x +
go log p(y) (x(x) dy
(x1x0 [log (oog))(x(y)) - Drr (y/x))(()))))
The above derivation yields decomposition of the log-likelihood log px()) into lower bound. Starting from the log-marginal likelihood, Eq. 18 introduces variational distribution Io (y x) and decomposes log (x into the sum of two expectation terms: the first term is the evidence lower bound (x), and the second term is the KL divergence between the variational distribution (y(x)) and the true posterior po (y x)). Eq. 19 further expands the ELBO term (x) into its standard form: the difference between a reconstruction expectation term and a KL divergence term.
A.2 ANOTHER CONSTRAINT: FEATURE CONSISTENCY
The feature consistency assumes that corresponding data points from the two domains can overlap when mapped to the same space, or that paired data samples share domain-invariant features. In essence, this serves way to constrain by aligning and y f(x) in a particular feature space, thereby replacing or enhancing the role of D x) x)))p(()) in single-step optimization. The dif- ference between feature consistency and cycle consistency in constraining the range of lies in their metrics: the former is represented by D (y, x) while the latter is approximated by Dsim (y, Since additional reasonable constraints are introduced, the mapping quality may improve men- tioned in the main text, but Dsim (y, x) may also lack proper definition in practical applications as is the case with Dsi (y,)).
For instance, Wang et al. (009b)) models the relationship between forward and backward pixels as a self-cycle-consistent task, performing cyclic training across multiple frames with one-step training pattern. In Eq. 16 D Deye is expressed in this work as the requirement for pixel alignment within the cycle formed by different frames, while Daim enforces feature consistency for the object across frames, serving a self-supervised representation learning method which aims to learn frame-level embeddings by temporally aligning video sequences. This task is formulated as self-consistent task. The method enforces Deye by constructing bidirectional mappings between video frames. Meanwhile, Dx is implicitly satisfied as the same encoder maps inputs into the embedding space. Additionally, the mapping process in the embedding space inherently enforces a feature consistency constraint. Since feature consistency falls outside the scope of this work, provide only brief introduction here.
replacement for the KL divergence. Dwwbeddi et al. (2019) proposes
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Predicted Search Box
Search Patches
Template Patches
Box Head
MLP
Linear Projection
Patch Embedding
Feature Enhancement
Object Query Token
Bounding Box Token
Transformer Encoder
Transformer Encoder
Feature Enhancement
Linear Projection
MLP
Loss
Box Head
Search Patches
Template Patches
Template
Predicted Template Box
a Semplate-Search Tracking
(b) Search-Template Tracking
Figure 6: The structure of CycleTrack.
Table The performance of different optimization methods in image translation tasks.
Per-pixel accuracy
Per-class accuracy
Class IOU
Loss
Labels Photo
D + D
0.41
0.07
0.03
D3 D2
0.39
0.05
0.02
D.E" D.t
D.
D.
0.51
0.13
0.10
CycleGN
0.52
0.14
0.10
CycleGAN Zhu et al
2017)
0.52
0.17
0.11
Photo Labels
D. DJ
0.10
0.06
0.02
DE D2
0.32
0.09
0.05
D. CycleGN
D
D.
D
0.52
0.16
0.11
0.51
0.16
0.10
CycleGAN et al.
2017)
0.58
0,22
0.16
B EXTENDED EXPERIMENTS
B. SEVERAL VARIANTS OF SINGLE-STER LOSS
This paper focuses the joint optimization of max mlax)oogpo( (lo We show that optimizing only a single direction, specifically maximizing p(x) alone or p(y) alone, influences performance in both forward and backward tasks. Tab. summarizes the results, where D + D sim and D + +D correspond to maximizing lox)(x) and logp(y) respectively. Another variant involves rotated optimization of log p(x) and log p(y), denoted in the table D& + D. 2 DY D D Unlike Algo. [ this approach switches objectives every mini-batch without awaiting convergence between EM cycles. While this configuration demonstrates inferior performance CycleGAN on both tasks, it remains viable. We argue that under constrained training conditions, splitting Eq. 12 into dual cyclic objectives with rotated training provides feasible alternative.
B.2 FULLY- SUPERVISED AND SEMI-SUPERVISED EXPERIMENTS OF CYCLETRACK
CycleTrack was evaluated under identical settings to STARK for supervised training. In the semi- supervised setup, only the annotation of the target in the first frame of each sequence was available.
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Table 8: Comparison between fully-supervised and semi-supervised CycleTrack with state-of-the- art supervisd trackers on LaSOT and TrackingNet.
LaSOT
TrackingNet
Method
AUC
Precision
AUC
Precision
Bhht al.
2019
56.9
56.7
74.0
68.7
STARK Yan al. 2021)
67.1
82.0
Mixformer-22K Cui
et al.
2022
69.2
74.7
83.1
81.6
OSTrack(Yc Ye ct at. 2022
69.1
75.2
83.1
82.0
GRM Gao al. 2023
69.9
75.8
84.0
83.3
CycleTrar Track (lully)
70.1
82.9
81.0
CycleTrack-EN (semi)
63.6
66.7
80.6
78.3
Since the similarity loss Diim (5. )) cannot be defined in search frames under this configuration, the single-step optimization method becomes inapplicable. Therefore, we exclusively employed the EM approach for semi-supervised training. As shown in Tab. g CycleTraak achieves comparable performance leading two-frame trackers, demonstrating that our assembled network possesses the fundamental capabilities expected of competent tracker. Notably, the semi-supervised CycleTrack- EM delivers remarkably strong performance, showing minimal degradation compared to its fully- supervised counterpart and even surpassing the fully-supervised DiMP. These results validate the effectiveness of our proposed training methodology.
C EXTENDED DISCUSSIONS
Given that the single-step approach is more conceptually straightforward and has achieved remark- able success in CycleGAN-related applications, while the EM-based method is less prevalent, provide the following recommendations for its applicable scenarios:
i. Scenarios without D estimation.
GANs serve as an effective estimator of DKL, L. but they are not universally suitable for all tasks. In practice, apart from GANs, few methods reliably approximate KL divergence. While image- based domain adaptation largely adopts CycleGAN and uses GANs as the estimator, other modali- ties attempting use single-step losses have generally achieved suboptimal results. This has com- pelled some studies to resort to alternatives such as feature consistency Adopting EM-based methods may offer a new perspective for addressing problems in non-GAN scenarios.
in Appendix A.2).
ii. Scenarios where convergence to local optima can be avoided.
a). Semi-supervised settings with limited annotated data:
Even a small amount of annotated data can prevent domains X' and y from forming independent cycles. In such configurations, domains X' and ) are necessarily connected. Even if the network tends to generate simpler outputs, the locally optimal domains B and will remain closer to the true domains X' and
b). When fa and go are already capable of generating outputs in the target domain: In this case, although the network lacks direct mapping ability between domains, has acquired the capacity to generate results in domain ) through other upstream tasks (even if not starting from domain X'). EM training then acts as fine-tuning on pre-trained network, significantly reducing the possibility of the network freely diverging other domains.
c). When no alternative domains are available to the generative function-i.ee in strictly bijective scenarios: While training CrckeTrack, observed that for any output quadruple beyond object bounding boxes, there are hardly any other mcaningful or structured combinations that can satisfy cycle consistency. This makes producing object bounding descriptions the most straightforward choice for the network.
iii. Scenarios that call for quick and simple trial.
In practice, EM training involves only the reconstruction loss D Deyes which is generally the simplest loss to design across tasks and modalities. In contrast, designing and optimizing Daim is consid-
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Ground Truth
CycleTrack (full supervised)
CyckeTrack (semi-supervised)
CycleTrack
CycleTrack-EMM EM
(a) Visualization tracking results by different CycleTrack variants on LaSOT.
Real Photo
Reconstructed Photo
Fake Photo
Real Labels
Reconstructed Labels
Fake Labels
(b) Visualization of labels translation results by CycleGN Cityscape.
erably more challenging. Another key consideration lies the structural constraints imposed by single-step loss training: for fo and ge to be trained end-to-end, they must form fully differen- tiable pipeline. Satisfying this requirement often places strong constraints on the architecture of both hooworks-sometimsss even necessitating customized designs, as encountered in our work on CycleTracch In contrast, the EM approach imposes no structural constraints on fo and ge, since the two networks are trained separately. This enables the use of cinfeefeerntiiabee operations during training.
18


Reviews:
[{"review_id": "YSmWdo0wia", "reviewer": "Reviewer_uEwd", "summary": "This paper presents a general framework for training cyclic learning models, built on single-step and alternating optimization strategies. The framework's broad utility is shown in two areas: for unpaired image translation, it not only provides a theoretical basis for CycleGAN but also produces CycleGN and CycleTrack, a competitive model that doesn't require GANs. Overall, this work lays the theoretical groundwork for cyclic learning and offers a universal approach for subsequent research.", "questions": "**Q1** : The connection between the proposed EM-style framework and the classical EM algorithm remains unclear.  \n    In the traditional EM formulation, the objective is to maximize the data likelihood.  \n    Could the authors clarify how optimizing the cycle-consistency loss ($D_{cyc}$) in their setting corresponds to maximizing the likelihood?  \n    Is it correct to interpret the cycle loss as a *surrogate reconstruction objective* that implicitly optimizes the likelihood function, similar to the role of the reconstruction term in variational inference?\n\n    \n **Q2** :    Given the absence of explicit $D_{KL}$ control in the EM method, are there any theoretical or empirical evaluations confirming that the generated distributions $\\mathcal{X}$ and $\\mathcal{Y}$ approach the true priors, rather than merely achieving a cyclically consistent but unrealistic local optimum?\n    \n\n**Q3** :   Given the observed instability of results across different tasks, could the authors identify specific problem types or conditions under which the proposed EM-based framework is expected to outperform standard GAN-based models?  \n    What are the authors’ insights regarding the comparative advantages of their approach?  \n    In other words, what would constitute the \\textit{ideal use case} where this framework would be preferable to a conventional GAN setup?", "limitations": "", "rating": 4, "confidence": 4, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "The paper presents a method (CycleGN) that avoids the bottleneck of the previously proposed cycle methods, like unstable adversarial optimization (GAN-style). This enables competitive results without explicitly using discriminators. The paper is well-structured and easy to follow.", "weaknesses": "1) The performance of the *CycleGN EM-based* approach was found to be *inconsistent across tasks* - showing stable results in some settings but degraded performance in others compared to CycleGAN (single-step with GAN).  This indicates that method still lack a unified mechanism to fully remove the D_{KL} surrogate across different problem domains.\n\n  \n2) A issue remains where models can achieve nearly perfect while the *intermediate translation remains unrealistic. This is an intrinsic limitation of cyclic training.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "axbSaylRkP", "reviewer": "Reviewer_dfXf", "summary": "This paper proposes a unified probabilistic framework to generalize cyclic learning, moving beyond the ad-hoc, task-specific implementations that currently dominate the field. The authors identify that while cycle-consistency is a powerful tool for weakly-supervised learning, it lacks a common theoretical foundation. To address this, they reformulate the cycle-consistency objective as a variational inference (VI) problem. The core of their approach is to model the cross-domain mappings (e.g., $A \\rightarrow B$ and $B \\rightarrow A$) as conditional probability functions and treat the intermediate generated data as latent variables. This allows them to re-cast the training objective as the optimization of an Evidence Lower Bound (ELBO) on the data log-likelihood.\n\nFrom this single theoretical framework, the authors derive two distinct and general optimization strategies. The first is a \"VAE-style\" single-step loss that optimizes the full objective at once, which the authors show provides a new theoretical justification for the success of architectures like CycleGAN. The second is an \"EM-style\" alternating optimization algorithm that iteratively updates the forward and backward mappings, avoiding the need for an explicit KL divergence approximation (like a GAN's discriminator). The framework's effectiveness is demonstrated on two very different tasks: unpaired image translation, where their proposed GAN-free \"CycleGN\" is competitive with CycleGAN, and unsupervised visual object tracking, where their \"CycleTrack\" and \"CycleTrack-EM\" models establish a new state-of-the-art on multiple benchmarks.", "questions": "Regarding the CycleGN failure case in Figure 4a (where reconstruction is good but intermediate images are poor), could you elaborate on the cause? Is this a local optimum that is inherent to the alternating EM optimization, or does this failure mode confirm that the EM approach is more vulnerable to \"cheating\" precisely because it lacks the explicit $D_{sim}$ (distributional) constraint on the latent variable that the single-step method has?\n\nThe claim that CycleGN is a general, competitive alternative to CycleGAN would be significantly strengthened by testing it on more unstructured translation tasks (e.g., horse $\\leftrightarrow$ zebra, style transfer). Have you performed experiments on such tasks? How does the EM-style approach perform in these more unconstrained settings where the GAN-based $D_{sim}$ term is known to be critical?", "limitations": "", "rating": 8, "confidence": 2, "soundness": 4, "presentation": 4, "contribution": 3, "strengths": "- Novel Theoretical Contribution: Its primary strength is the novel and elegant reformulation of cycle-consistency as a variational inference (VI) problem. This connects a widely-used heuristic to fundamental probabilistic principles (like ELBO maximization, VAEs, and the EM algorithm) for the first time.\n\n- Generalization: The framework is highly general, providing a unified theory for both paired cyclic tasks (like image translation) and self-cyclic tasks (like video tracking), which were previously treated with separate, task-specific methods.", "weaknesses": "- Analysis of EM-Style Failure Modes: The paper honestly presents failure cases (Fig. 4a) where the EM-based CycleGN achieves good cycle-reconstruction but produces poor-quality intermediate \"fake\" images. This suggests the model has learned an \"incorrect mapping\" that satisfies $g(f(x)) \\approx x$ but where $f(x)$ is not a faithful member of the target domain $Y$. This is a crucial finding and a known risk of EM-style approaches converging to a local optimum. The paper would be improved by a deeper analysis of why this happens in the VI framework. Is it an inherent instability of the alternating optimization? Or does it confirm that the EM approach, by \"lacking explicit constraints on latent variables\" (Section 2.1), is more vulnerable to this specific failure mode than the single-step method, which explicitly constrains the intermediate variable with $D_{sim}$?\n\n- Limited Scope of Image Translation Experiments: The validation of CycleGN is performed only on the Cityscapes (labels $\\leftrightarrow$ photo) dataset. This is a highly structured translation task. The original CycleGAN paper demonstrated its robustness on much more \"unstructured\" and challenging tasks, such as horse $\\rightarrow$ zebra or style transfer (Monet $\\rightarrow$ photo). To compellingly claim CycleGN is a general, competitive alternative to CycleGAN, it should be tested on these more diverse and difficult translation tasks. It is possible the EM-style approach works well for structured tasks but struggles with more unconstrained mappings where a GAN's distributional matching is essential.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "XA25CLIpyd", "reviewer": "Reviewer_w19x", "summary": "This paper has a good intuition to use the latent variables bridging the two domains. They summarize the success of CycleGan by modeling the two terms of reconstruction and distribution alignment and propose several multi-variants like “CycleGN” (GAN-free)  and CycleTrack / CycleTrack-EM and achieve SOTA on unsupervised visual tracking tasks.", "questions": "Questions:\n\n\n1  What are the abbreviations IoU for in Eq. (17)? Should it be argmax based on the results in the table 3-4?\n\n\n2 Could you explain in more detail when your method will be successful? Will your methods be useful to the questions like domain adaptations in different modalities?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "Sterngeths:\n\n\nThe paper establishes a framework to broad the cyclin-style loss functions in computer vision tasks. The paper has a clear concept by understanding the cycle term as reconstruction and the GAM term as the KL surrogate for making single-step optimization. Their proposed methods help address the failure conditions for the CycleGAN and are useful in the visual tracking tasks.", "weaknesses": "Weakness:\n\n\n1 Overall the math deductions are good, but there are many typos and rigor issues, e.g.: In eq.3, where does the p_{data} come from?; Extra parenthesis in Eq. (16); what are the abbreviations IoU for in Eq. (17)? Should it be argmax based on the results in the table 3-4?\n\n\n2 Figure 2 and Figure 3 are not clear enough to be understood. \n\n\n3 CycleGN is close but generally behind CycleGAN in the more challenging direction (photo→labels), suggesting that the Dsim/EM recipe doesn’t yet match a well-trained discriminator as a KL surrogate.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)