# Dimensionality Reduction & Visualization Embeddings

> One thread of 9 from the "embedding" map, covering the 9 papers in it. The other threads are not represented here.
>
> Every quotation was copied word for word from the paper's own text, and
> checked against that text. Quotes marked *inferred* failed that check and
> must be re-checked before use. Quotes marked *not re-checked* have not been
> matched against the paper's text as it now stands, so they carry no current
> verification either. Lines labelled *the tool's reading* are
> model judgment, not quotation, and carry no verification.
>
> **This is a scaffold, not prose.** The citations, quotes and structure are
> real; the argument is yours to write.

> Connects to: Latent Representation & Generative Spaces.

Rooted in classical techniques like t-SNE for visualizing learned representations (2013-2014), evolved toward unified manifold approximation methods (UMAP) with theoretical grounding (2018), increasingly used for interpretability and exploration of learned feature spaces.


**DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition** (2013) \cite{donahue2013decaf}

What it did: Establish embedding as visualization tool for features  *(the tool's reading)*

DeCAF uses t-SNE to embed high-dimensional feature vectors into low-dimensional space for analysis. The embedding technique itself is not novel but serves as an existing tool to validate the semantic quality of learned features.  *(the tool's reading)*

> “we run the t-SNE algorithm […] to find a 2-dimensional embedding of the high-dimensional feature space, and plot them as points colored depending on their semantic category in a particular hierarchy.”
>
> ✓ verified: found word for word in the paper's own text


**Stochastic Backpropagation and Approximate Inference in Deep Generative Models** (2014) \cite{rezende2014stochastic}

What it did: Shift embedding to latent space of generative models  *(the tool's reading)*

Stochastic Backpropagation demonstrates that deep latent Gaussian models can produce meaningful 2D embeddings through their recognition network. The embedding now comes from projecting data through the model's learned latent variables rather than post-hoc visualization.  *(the tool's reading)*

> “We project the MNIST data set to a 2-dimensional latent space and use this 2D embedding as a visualisation of the data – an embedding for MNIST is shown in figure […]. The classes separate into different regions, suggesting that such embeddings can be useful in understanding the structure of high-dimensional data sets.”
>
> ✓ verified: found word for word in the paper's own text


**Unsupervised Domain Adaptation with Residual Transfer Networks** (2016) \cite{long2016unsupervised}

What it did: Extend embedding to kernel spaces for domain adaptation  *(the tool's reading)*

Unsupervised Domain Adaptation advances embedding by mapping multi-layer features into reproducing kernel Hilbert spaces for distribution matching. This unified approach uses tensor product fusion and single MMD penalty instead of embedding layers separately.  *(the tool's reading)*

> “We fuse features of multiple layers with tensor product and embed them into reproducing kernel Hilbert spaces to match distributions for feature adaptation.”
>
> ✓ verified: found word for word in the paper's own text


**Geometric Deep Learning: Going beyond Euclidean data** (2016) \cite{bronstein2016geometric}

> “However, a Riemannian manifold can be realized as a subset of a Euclidean space (in which case it is said to be embedded in that space) by using the structure of the Euclidean space to induce a Riemannian metric.”
>
> ✓ verified: found word for word in the paper's own text


**UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction** (2018) \cite{mcinnes2018umap}

What it did: Provide theoretical foundation for general-purpose reduction  *(the tool's reading)*

UMAP reframes embedding as optimizing low-dimensional point positions from fuzzy simplicial complexes with theoretical grounding. The technique removes computational restrictions on embedding dimension, enabling broader applicability than prior methods.  *(the tool's reading)*

> “we can use a spectral layout to initialize the embedding.”
>
> ✓ verified: found word for word in the paper's own text


**Data re-uploading for a universal quantum classifier** (2019) \cite{perezsalinas2019data}

> “However, if more layers are applied, each one will perform a different rotation, and many different rotations together have the capability of enabling a feature map. Data embedded in this feature space can be easily separated into classes employing the regions on the Bloch sphere.”
>
> ✓ verified: found word for word in the paper's own text


**Definitions, methods, and applications in interpretable machine learning** (2019) \cite{murdoch2019definitions}

> “For example, in natural language processing, documents are embedded into vectors using tf-idf […] and in computer vision mathematical transformations have been developed to produce useful representations of images […].”
>
> ✓ verified: found word for word in the paper's own text


**What Makes for Good Views for Contrastive Learning?** (2020) \cite{tian2020what}

> “(a) Schematic of multiview contrastive representation learning, where an image is split into two views, and passed through two encoders to learn an embedding where the views are close relative to views from other images.”
>
> ✓ verified: found word for word in the paper's own text


**Unsupervised Learning of Visual Features by Contrasting Cluster Assignments** (2020) \cite{caron2020unsupervised}

> “The feature is then projected to the unit sphere, i.e., 𝐳_nt = f_θ(𝐱_nt) / f_θ(𝐱_nt)_2.”
>
> ✓ verified: found word for word in the paper's own text


_[Your synthesis: what it enabled, what it left unsolved.]_


## Where this thread connects

Each crossing is where one line of work fed another. These are the tool's reading of
the corpus, not quotations.

- **Dimensionality Reduction & Visualization Embeddings** → **Latent Representation & Generative Spaces** (2018): Manifold learning alignment