Investigating the Invertibility of Multimodal Latent Spaces: Limitations of Optimization-Based Methods

Siwoo Park

REVIEW 5 major objections 5 minor 34 references

Investigating the Invertibility of Multimodal Latent Spaces: Limitations of Optimization-Based Methods

T0 review · 5 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Task-specific models hit text targets but can't invert latent spaces.

desk verdict A well-documented negative result that overreaches: the experiments show naive inversion fails, not that latent spaces are non-invertible. read the letter →

arxiv 2507.23010 v1 pith:FURGR5AG submitted 2025-07-30 cs.LG cs.AIcs.CVcs.SDeess.AS

Siwoo Park This is my paper · ORCID

classification cs.LGcs.AIcs.CVcs.SDeess.AS

keywords multimodallatentspacesnetworkinversionoptimization-basedtext-to-imagespeechrecognitionspaceinterpretabilitytask-specificmodelsinverseproblemsindeeplearning

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tests whether multimodal latent spaces of task-specific models can be run backwards by optimization: starting from a desired output and adjusting the input to produce it. It proposes a general inversion objective and applies it in both directions across text-image (BLIP, Flux.1-dev) and text-audio (Whisper-Large-V3, Chatterbox-TTS) models. The central claim is that although optimization can force outputs to match a text target (a caption, a transcription), the perceptual quality of the reconstructions stays chaotic, and inferred text embeddings do not align with semantically meaningful vocabulary tokens. The conclusion is that latent spaces optimized purely for forward tasks do not inherently support robust and interpretable inverse mappings, which matters because invertibility would let practitioners interrogate and reuse these models.

What carries the argument

The carrying mechanism is an optimization-based network-inversion objective: fix the model $f$, treat a raw input $x$ (pixel image, log-mel spectrogram, or token/pooled text embedding) as the parameter, and minimize a loss $L(f(x), y)$ between the model output and a target $y$ with Adam or AdamW and gradients from autograd. For generative-model inversion, the same objective is paired with cosine-similarity matching of the optimized embedding against the model's vocabulary tokens to test whether the latent point is semantically interpretable. This framework lets the paper test invertibility bidirectionally: discriminative models pushed into generation, and generative models pushed into classification.

What would settle it

One concrete test: optimize a text-to-image model's text embedding with the same objective but add a perceptual prior or use a diffusion-based inversion method, then ask human raters whether the generated images match the target; if coherent images appear while nearest-token cosine similarity stays near chance, the paper's conclusion that the latent space lacks interpretable inverse structure is falsified. A second observation-level check is whether the reported token similarities exceed the chance similarity of random embeddings to vocabulary tokens.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is that task-specific multimodal encoders and decoders can be steered toward inverse goals—a captioning model can be made to produce an image its own captioner reads as "a red apple on a wooden table," and a speech recognizer can be made to transcribe an optimized spectrogram as the same phrase—but the resulting image or audio is perceptually incoherent noise. When the direction is reversed, optimizing text embeddings of a text-to-image or text-to-speech model to reproduce a target output yields embeddings whose nearest vocabulary tokens have only low cosine similarity (roughly 0.06–0.08 for token embeddings, up to about 0.15 for the pooled embedding), placing them near random semantic identities. The paper reads this as evidence that forward-task optimization does not endow latent spaces with the structure needed for interpretable inversion.

Load-bearing premise

The conclusion depends on assuming that unconstrained gradient descent with cross-entropy, MSE, or mel-spectrogram loss is a fair test of whether these latent spaces support inverse mappings; if a better inversion method recovered coherent inputs, the central claim would collapse.

Editorial extensions

If this is right

Optimization can satisfy text-side targets (captions or transcriptions) without producing perceptually coherent images or audio, so textual agreement is not evidence of true inversion.
Generative models' text latents lie near low-similarity vocabulary neighborhoods under this protocol, so interpreting optimized embeddings as discrete tokens is unreliable.
Discriminative multimodal models do not acquire implicit generative capacity just because gradients flow to their inputs.
The paper's conclusion motivates designing latent spaces explicitly constrained for invertibility, for example with reconstruction priors or cycle-consistency, rather than optimizing forward performance alone.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The result is protocol-conditional: the paper uses unconstrained gradient descent on raw inputs with no priors, regularizers, or established inversion techniques, so the claim "these latent spaces are not invertible" is really "these latent spaces were not invertible under this optimization recipe"; a stronger optimizer or a prior (diffusion guidance, perceptual losses, projection to the data mani
A testable extension: run the same inversion objectives with a perceptual or adversarial loss and measure both human-judged coherence and nearest-token cosine score; if those jump, the low token similarities reported here are artifacts of objective choice rather than latent-space structure.
The near-chance cosine similarities may partly reflect tokenizer vocabulary size and embedding anisotropy, so the paper's interpretability claim would be strengthened by comparing against chance-level similarity for randomly sampled embeddings.
Adversarial examples show that forward-trained latent spaces can be controlled in a shallow, non-semantic way, so the paper's finding draws a line between adversarial controllability and semantic invertibility.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Siwoo,

Quick take: this is an honest empirical report, but the central claim doesn't follow from the experiments. What the paper actually shows is that unconstrained gradient descent on raw inputs produces perceptually meaningless outputs for BLIP, Flux.1-dev, Whisper, and Chatterbox. That is consistent with what adversarial-example and network-inversion papers have demonstrated for years—and the paper cites those lines. The specific measurements are new, but the interpretation (that the latent spaces themselves lack invertible structure) is an overgeneralization from a single, prior-free optimization recipe.

What's genuinely useful: the paper documents step-by-step optimization trajectories for each model, with figures and tables that let you watch the progress. For BLIP and Whisper, the optimizations converge to inputs that the models transcribe or caption as the exact target text. That is a clean demonstration of the known phenomenon: you can satisfy a discriminative model's output without producing anything a human would recognize. The token-similarity tables for Flux and Chatterbox are also informative, showing that optimized embeddings stay far from any vocabulary token.

The soft spots are load-bearing. The protocol uses no priors, no regularizers, and no established inversion techniques—single-step Flux sampling, Griffin-Lim for audio, and no comparison to any baseline. With high-dimensional inputs, unconstrained optimization is expected to land in adversarial, out-of-distribution regions. So the failure is a property of the optimizer and objective, not a demonstrated property of the latent space. The low cosine similarities to tokens are unsurprising: nothing in the objective pushes embeddings toward the token manifold. The quantitative metrics are weak: PESQ around 1.0 is at the floor, and BERTScore is constant across steps, so it is not measuring anything meaningful. No code, seeds, or hyperparameters are provided, and there are no statistical tests.

The paper would be more honest if it said 'naive inversion fails for these models' rather than 'multimodal latent spaces do not inherently possess the structure required for robust and interpretable inverse mappings.' That abstract-level claim is unsupported.

Who should read this? Someone thinking about trying gradient descent inversion on a new model might find the qualitative figures a useful caution. But researchers in inversion or adversarial robustness will learn little new. I would not cite it.

Recommendation: reject in current form. If the authors add proper baselines (perceptual losses, GAN priors, diffusion inversion), scope the claims to the specific protocol, and release code, it could become a modest empirical note. As is, it does not deserve referee time.

Referee Report

5 major / 5 minor

Summary. The paper investigates whether multimodal latent spaces of task-specific models (BLIP, Flux.1-dev, Whisper-Large-V3, Chatterbox-TTS) support inverse mappings obtained by optimization. The authors propose an optimization-based framework (Section 3, Eq. (2)) that performs gradient descent on raw inputs—images, log-mel spectrograms, or text embeddings—to match a target output, and apply it bidirectionally across text-image and text-audio pairs. They report that while optimization can force models to produce outputs that are textually aligned with targets (e.g., BLIP captions match the prompt; Whisper transcribes the target phrase), the resulting images and audio are perceptually incoherent, and the optimized text embeddings from Flux and Chatterbox do not align with meaningful vocabulary tokens. The paper concludes that multimodal latent spaces do not inherently possess the structure required for robust and interpretable inverse mappings.

Significance. If the central claim were established, the paper would contribute to the literature on interpretability, network inversion, and multimodal representation learning, and its use of several widely used public models is timely. However, the evidence presented is anecdotal and methodologically insufficient. The paper does not compare against established inversion techniques, does not report multiple runs, seeds, or hyperparameters, and the quantitative metrics (PESQ, BERTScore, CLIPScore) are not linked to the perceptual and semantic conclusions. The main observation—that naive unconstrained optimization finds out-of-distribution inputs—is already well known from the adversarial-example literature. The paper's strength is that it documents these failures on modern multimodal systems, but as it stands the results do not support the strong claim that the latent spaces themselves are non-invertible.

major comments (5)

[Section 3 and Section 4] The inversion objective in Eq. (2) is solved by unconstrained gradient descent on raw inputs with no prior, regularizer, or in-distribution projection. The failure of this specific protocol does not establish that the latent space is inherently non-invertible; it is well known from the adversarial-example literature (Refs. [2], [7], [29]) that unconstrained optimization finds out-of-distribution solutions that satisfy the model output without semantic meaning. To support the central claim, the paper must compare against established inversion techniques (e.g., natural-image priors, GAN or diffusion priors, projected gradient descent onto token embeddings, vocoder-based audio reconstruction) and show that these also fail to produce meaningful inversions.
[Section 4.1.2 and Section 4.2.2, Tables 5-6 and 8-11] The token-interpretability analysis computes cosine similarity between optimized continuous embeddings and vocabulary embeddings, but the optimization objective contains no term that encourages the optimized embedding to lie near the token manifold. Low cosine similarities are therefore an expected consequence of the protocol, not evidence that the latent space is semantically non-invertible. A meaningful test would either optimize in the discrete token space (e.g., with a Gumbel-softmax or projection step) or compare against the cosine-similarity distribution obtained from in-distribution prompt embeddings that are known to work in the forward model.
[Section 4.1.2] The Flux.1-dev experiments rely on single-step inference from a 4-bit quantized model, and the paper states this is done 'for computational efficiency' without justifying that single-step inference is a faithful proxy for the generative model. Rectified flow models like Flux typically require multiple denoising steps, and optimizing against a single-step output may exploit approximation error rather than the true text-to-image mapping. This is load-bearing because the paper's conclusion about Flux rests on embeddings optimized against this approximate forward pass. At minimum, the authors should verify their findings with multi-step inference or a higher-precision model.
[Section 5, Tables 13-15] The quantitative metrics do not support the paper's qualitative conclusions. PESQ values in Table 14 are essentially constant near 1.0 (the minimum of the scale), and BERTScore in Table 15 is identical across all optimization steps for each category, indicating that the metric is insensitive to the optimization progress. CLIPScore in Table 13 decreases for some categories. No error bars, multiple seeds, statistical tests, or comparison baselines are provided. The paper claims these results 'consistently validate the hypothesis,' but the numbers as reported are at best uninformative and at worst contradict the narrative of progressive convergence.
[Section 6.3] The broad conclusion that task-specific classification models 'show no capacity for generative tasks' is an overgeneralization from two models (BLIP and Whisper) and one optimization recipe each. The same applies to the statement that reconstructed embeddings 'consistently do not align with the model's own discrete vocabulary tokens,' which is based solely on the cosine-similarity analysis discussed above. The claims should be restricted to the specific protocol and models tested, or be supported by evidence that alternative, more powerful inversion methods also fail.

minor comments (5)

[Throughout] There are numerous typos and formatting issues, including 'Quantitatve' in the Section 5.2 heading, 'classifer' in Section 4.1.2, 'T ext-Image' in Section 4, and inconsistent capitalization in the abstract ('multimodal' after a period).
[Section 4.2.2, Tables 8-11] The row for 'step 750' appears twice in each of Tables 8-11, and the row for 'step 1000' appears only in Table 11. This appears to be a copy-and-paste error that should be corrected.
[Section 4.1.2 and Section 4.2.2] The paper does not report the learning rate, optimizer settings, number of optimization runs, random seeds, or other hyperparameters needed to reproduce the experiments. These details are essential for any optimization-based study.
[Section 4.2.1] The Whisper experiment optimizes a log-mel spectrogram and then reconstructs audio with Griffin-Lim, which is a lossy and often poor-quality reconstruction even for natural speech. The poor perceptual quality of the reconstructed audio may be entirely due to the Griffin-Lim inversion, not the latent space. This confound should be explicitly acknowledged or avoided by using a learned vocoder.
[Section 5.3] PESQ is designed for evaluating telephone-band speech codecs and is not an appropriate metric for assessing the perceptual quality of synthesized speech or noise. The authors should justify the metric choice or use a more suitable evaluation (e.g., MOS prediction or a neural speech quality model).

Circularity Check

2 steps flagged · score 6.0 of 10

Central negative claims are built into the unconstrained optimization protocol: low token similarity and chaotic perceptual quality are consequences of the chosen objectives, not independent properties of the latent spaces.

fitted input called prediction [Section 4.1.2 (Tables 5-6) and Section 4.2.2 (Tables 8-11)]
"Our objective function for this task is formulated as J(x) = L(f(x), y), where x represents the text embeddings (both the token embeddings and the pooled prompt embeddings), y is the target image, and L denotes a suitable loss function. ... We computed cosine similarity for each embedding against every token within its corresponding tokenizer's vocabulary. The tokens with the highest similarity scores are summarized in Table 5 and Table 6."

The optimized x is produced by minimizing a reconstruction loss only; no term in J(x) encourages the continuous embedding to lie near a discrete vocabulary token. The paper's own measure of 'semantic interpretability' is cosine similarity to vocabulary tokens, so low cosine similarity is a mathematical consequence of unconstrained optimization in a high-dimensional space, not an empirical property of the latent space. The 'prediction' that reconstructed embeddings do not align with vocabulary tokens is therefore forced by the definition of the optimization objective and the evaluation metric; it would occur for any continuous space without a token-alignment constraint, independent of invertibility.
fitted input called prediction [Section 4.1.1 (Figures 1-4), Section 4.2.1 (Figures 13-17; Table 7), interpreted in Sections 6.2-6.3]
"This optimization aims to minimize the cross-entropy loss with AdamW optimizer between the text transcribed by the model and the target text. ... The reconstructed audio is a strong indicator that the model completely lacks the implicit generative potential required to synthesize coherent audio, despite its remarkable discriminative capabilities for transcription. ... Task-specific classification models (e.g., image captioning, speech recognition) show no capacity for generative tasks, never successfully manipulating their input to achieve a perceptually meaningful output."

The raw input (pixel image or log-mel spectrogram) is fitted to a text/transcription objective, with no perceptual-coherence prior, no in-distribution constraint, and (for audio) a lossy Griffin-Lim reconstruction added after optimization. Under such an unconstrained inversion objective, out-of-distribution, noise-like solutions are the expected result whenever many inputs satisfy the text loss. The paper then labels this protocol artifact as evidence that task-specific classification models 'show no capacity for generative tasks' and that latent spaces 'do not inherently possess the structure required for robust and interpretable inverse mappings.' The negative finding is entailed by the choice of objective function, not discovered about the latent spaces.

full rationale

There is no formal mathematical circularity, no load-bearing self-citation chain, and no imported uniqueness theorem; the reference list is entirely external, so patterns 3-5 do not apply. The circularity is methodological: the paper's two headline negative results are consequences of the optimization objectives it chose. For generative-model inversion, the objective J(x) contains only reconstruction loss; vocabulary alignment is then measured post hoc, so low cosine similarity is forced by the absence of any token-alignment term. For discriminative-model 'generation,' raw inputs are optimized against a text/transcription loss with no perceptual prior; the resulting noise-like images and audio are therefore artifacts of the unconstrained search, not evidence about latent-space invertibility. The abstract and Section 6.3 promote these protocol artifacts to a structural property of multimodal latent spaces. This is partial circularity: the predictions are built into the experimental definition, though the paper does contain independent empirical observations, such as that text-matching inverses can be found at all. Score 6 reflects that the central negative claims reduce by construction, while the paper retains independent empirical content in its reported optimization trajectories.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claim rests on hand-chosen optimization settings and several domain assumptions about how to interpret the inversion results. None of these assumptions are independently validated, and no new entities are introduced.

free parameters (4)

Optimization step counts = 10,000 (BLIP), 200 (Flux), 3,000 (Whisper), 1,000 (Chatterbox)
Chosen by hand without convergence criteria; results depend on these values.
Guidance scale and CFG string for Flux = 3.5 and empty string
Chosen by hand; affects the single-step inference used as the inversion target.
Token counts = 10 tokens (Flux), 23 tokens (Chatterbox)
Fixed by hand; the search space for inversion depends on these counts.
Single-step diffusion approximation = 1 step for optimization, 50 steps for evaluation
The inversion optimizes a one-step approximation of Flux, not the full generative process; this is a modeling choice that may explain the poor results.

assumptions (4)

domain assumption Unconstrained gradient descent in input space is a fair test of inverse mapping
The entire study evaluates invertibility by running raw gradient descent without priors or regularizers; no justification is given that this is representative of optimization-based inversion.
domain assumption Cosine similarity to nearest vocabulary token measures semantic interpretability
Tables 5-6 and 8-11 interpret low cosine similarity as a lack of semantic meaning, but this metric is never validated against human judgment or downstream tasks.
ad hoc to paper Single-step Flux inference approximates the generative model for inversion
The paper optimizes a one-step inference of Flux to save compute, then uses the optimized embeddings to draw conclusions about Flux's latent space. This approximation is not justified.
domain assumption Griffin-Lim reconstruction from a log-mel spectrogram gives perceptually meaningful audio
The paper reconstructs audio with Griffin-Lim and treats the noisy result as evidence that Whisper's latent space cannot generate coherent audio, but Griffin-Lim is known to produce poor-quality speech.

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Cite this review

Pith. "Pith review of Investigating the Invertibility of Multimodal Latent Spaces: Limitations of Optimization-Based Methods." pith.science (2026). https://pith.science/paper/FURGR5AG

@misc{pith2026250723010,
  author       = {Pith},
  title        = {Pith review of: Investigating the Invertibility of Multimodal Latent Spaces: Limitations of Optimization-Based Methods},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FURGR5AG}},
  note         = {Machine review of arXiv:2507.23010}
}

read the original abstract

This paper investigates the inverse capabilities and broader utility of multimodal latent spaces within task-specific AI (Artificial Intelligence) models. While these models excel at their designed forward tasks (e.g., text-to-image generation, audio-to-text transcription), their potential for inverse mappings remains largely unexplored. We propose an optimization-based framework to infer input characteristics from desired outputs, applying it bidirectionally across Text-Image (BLIP, Flux.1-dev) and Text-Audio (Whisper-Large-V3, Chatterbox-TTS) modalities. Our central hypothesis posits that while optimization can guide models towards inverse tasks, their multimodal latent spaces will not consistently support semantically meaningful and perceptually coherent inverse mappings. Experimental results consistently validate this hypothesis. We demonstrate that while optimization can force models to produce outputs that align textually with targets (e.g., a text-to-image model generating an image that an image captioning model describes correctly, or an ASR model transcribing optimized audio accurately), the perceptual quality of these inversions is chaotic and incoherent. Furthermore, when attempting to infer the original semantic input from generative models, the reconstructed latent space embeddings frequently lack semantic interpretability, aligning with nonsensical vocabulary tokens. These findings highlight a critical limitation. multimodal latent spaces, primarily optimized for specific forward tasks, do not inherently possess the structure required for robust and interpretable inverse mappings. Our work underscores the need for further research into developing truly semantically rich and invertible multimodal latent spaces.

Figures

Figures reproduced from arXiv: 2507.23010 by the authors.

**Figure 2.** Optimization results using Adam with base image initialization for [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Optimization results using AdamW with Gaussian noise initialization [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

Figures from the paper (26 more)

**Figure 4.** Figure 4: Optimization results using AdamW with base image initialization for [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]

**Figure 5.** Figure 5: Single-step Inference Optimization using AdamW with Gaussian noise [PITH_FULL_IMAGE:figures/full_fig_p010_5.png]

**Figure 6.** Figure 6: 50 Denoising Step Inference by Optimization results [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: t-SNE R 2 visualization of pooled embedding R 768 across training steps This figure presents a t-SNE projection of the pooled R 768 embeddings on R 2 , which captures their state at different stages of training. The dynamic shifts highlight the model’s learning traject…

**Figure 8.** Figure 8: step 0 [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

**Figure 9.** Figure 9: step 750 15 [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]

**Figure 10.** Figure 10: step 1500 [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]

**Figure 11.** Figure 11: step 2250 16 [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]

**Figure 12.** Figure 12: step 3000 17 [PITH_FULL_IMAGE:figures/full_fig_p017_12.png]

**Figure 13.** Figure 13: step 0 18 [PITH_FULL_IMAGE:figures/full_fig_p018_13.png]

**Figure 14.** Figure 14: step 750 [PITH_FULL_IMAGE:figures/full_fig_p019_14.png]

**Figure 15.** Figure 15: step 1500 [PITH_FULL_IMAGE:figures/full_fig_p019_15.png]

**Figure 16.** Figure 16: step 2250 19 [PITH_FULL_IMAGE:figures/full_fig_p019_16.png]

**Figure 17.** Figure 17: step 3000 20 [PITH_FULL_IMAGE:figures/full_fig_p020_17.png]

**Figure 18.** Figure 18: step 0 21 [PITH_FULL_IMAGE:figures/full_fig_p021_18.png]

**Figure 19.** Figure 19: step 250 [PITH_FULL_IMAGE:figures/full_fig_p022_19.png]

**Figure 20.** Figure 20: step 500 [PITH_FULL_IMAGE:figures/full_fig_p022_20.png]

**Figure 21.** Figure 21: step 750 22 [PITH_FULL_IMAGE:figures/full_fig_p022_21.png]

**Figure 22.** Figure 22: step 1000 [PITH_FULL_IMAGE:figures/full_fig_p023_22.png]

**Figure 23.** Figure 23: target 23 [PITH_FULL_IMAGE:figures/full_fig_p023_23.png]

**Figure 24.** Figure 24: step 0 [PITH_FULL_IMAGE:figures/full_fig_p024_24.png]

**Figure 25.** Figure 25: step 250 24 [PITH_FULL_IMAGE:figures/full_fig_p024_25.png]

**Figure 26.** Figure 26: step 500 [PITH_FULL_IMAGE:figures/full_fig_p025_26.png]

**Figure 27.** Figure 27: step 750 [PITH_FULL_IMAGE:figures/full_fig_p025_27.png]

**Figure 28.** Figure 28: step 1000 25 [PITH_FULL_IMAGE:figures/full_fig_p025_28.png]

**Figure 29.** Figure 29: target 26 [PITH_FULL_IMAGE:figures/full_fig_p026_29.png]

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