Identifying the underlying time-delayed latent causal processes in sequential
data is vital for grasping temporal dynamics and making downstream reasoning.
While some recent methods can robustly identify these latent causal variables,
they rely on strict assumptions about the invertible generation process from
latent variables to observed data. However, these assumptions are often hard to
satisfy in real-world applications containing information loss. For instance,
the visual perception process translates a 3D space into 2D images, or the
phenomenon of persistence of vision incorporates historical data into current
perceptions. To address this challenge, we establish an identifiability theory
that allows for the recovery of independent latent components even when they
come from a nonlinear and non-invertible mix. Using this theory as a
foundation, we propose a principled approach, CaRiNG, to learn the CAusal
RepresentatIon of Non-invertible Generative temporal data with identifiability
guarantees. Specifically, we utilize temporal context to recover lost latent
information and apply the conditions in our theory to guide the training
process. Through experiments conducted on synthetic datasets, we validate that
our CaRiNG method reliably identifies the causal process, even when the
generation process is non-invertible. Moreover, we demonstrate that our
approach considerably improves temporal understanding and reasoning in
practical applications.

利用非可逆生成时序数据的 CAusal RepresentatIon 的 CaRiNG 方法可可靠地识别因果关系过程，提高实际应用中的时间理解和推理能力。

CaRiNG：非可逆生成过程下的学习时序因果表示

CaRiNG: Learning Temporal Causal Representation under Non-Invertible  Generation Process

Learning representations that generalize to novel compositions of known
concepts is crucial for bridging the gap between human and machine perception.
One prominent effort is learning object-centric representations, which are
widely conjectured to enable compositional generalization. Yet, it remains
unclear when this conjecture will be true, as a principled theoretical or
empirical understanding of compositional generalization is lacking. In this
work, we investigate when compositional generalization is guaranteed for
object-centric representations through the lens of identifiability theory. We
show that autoencoders that satisfy structural assumptions on the decoder and
enforce encoder-decoder consistency will learn object-centric representations
that provably generalize compositionally. We validate our theoretical result
and highlight the practical relevance of our assumptions through experiments on
synthetic image data.

通过可识别性理论的视角，我们研究了何时可以保证物体中心表示在组合泛化中保证可补全一致性，通过合成图像数据的实验验证了我们的理论结果和假设的实践相关性。

可证明的物体为中心学习的组合概括

Provable Compositional Generalization for Object-Centric Learning

We consider the identifiability theory of probabilistic models and establish
sufficient conditions under which the representations learned by a very broad
family of conditional energy-based models are unique in function space, up to a
simple transformation. In our model family, the energy function is the
dot-product between two feature extractors, one for the dependent variable, and
one for the conditioning variable. We show that under mild conditions, the
features are unique up to scaling and permutation. Our results extend recent
developments in nonlinear ICA, and in fact, they lead to an important
generalization of ICA models. In particular, we show that our model can be used
for the estimation of the components in the framework of Independently
Modulated Component Analysis (IMCA), a new generalization of nonlinear ICA that
relaxes the independence assumption. A thorough empirical study shows that
representations learned by our model from real-world image datasets are
identifiable, and improve performance in transfer learning and semi-supervised
learning tasks.

本研究针对概率模型的可辨识性理论，通过一种广泛的条件能量模型建立充分条件，使得学习到的表示在函数空间上是唯一的，从而可以用于在非线性 ICA 框架下的组件估计，同时提高了图像数据集在迁移学习和半监督学习任务中的性能。