Latent Space Optimization

Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can be significantly reduced. This is achieved by associating label prediction with the O(1) complexity closest cluster center search in a vector system used as target for latent space configuration (LSC). The proposed method only requires finding indexes of several largest and lowest values in the embedding vector making it extremely computationally efficient. We show that the proposed method does not change NN training accuracy computational results. We also measure the time required by different computational stages of NN inference and label prediction on multiple datasets. The experiments show that the proposed method allows to achieve up to 11.6 times overall acceleration over conventional methods. Furthermore, the proposed method has unique properties which allow to predict the existence of new classes.

Graph-based surrogate models provide fast alternatives to high-fidelity CFD solvers, but their opaque latent spaces and limited controllability restrict use in safety-critical settings. A key failure mode in oscillatory flows is phase drift, where predictions remain qualitatively correct but gradually lose temporal alignment with observations, limiting use in digital twins and closed-loop control. Correcting this through retraining is expensive and impractical during deployment. We ask whether phase drift can instead be corrected post hoc by manipulating the latent space of a frozen surrogate. We propose a phase-steering framework for pretrained graph-based CFD models that combines the right representation with the right intervention mechanism. To obtain disentangled representation for effective steering, we use sparse autoencoders (SAEs) on frozen MeshGraphNet embeddings. To steer dynamics, we move beyond static per-feature interventions such as scaling or clamping, and introduce a temporally coherent, phase-aware method. Specifically, we identify oscillatory feature pairs with Hilbert analysis, project spatial fields into low-rank temporal coefficients via SVD, and apply smooth time-varying rotations to advance or delay periodic modes while preserving amplitude-phase structure. Using a representation-agnostic setup, we compare SAE-based steering with PCA and raw embedding spaces under the same intervention pipeline. Results show that sparse, disentangled representations outperform dense or entangled ones, while static interventions fail in this dynamical setting. Overall, this work shows that latent-space steering can be extended from semantic domains to time-dependent physical systems when interventions respect the underlying dynamics, and that the same sparse features used for interpretability can also serve as physically meaningful control axes.

Molecular discovery is increasingly framed as an inverse design problem: identifying molecular structures that satisfy desired property profiles under feasibility constraints. While recent generative models provide continuous latent representations of chemical space, targeted optimization within these representations often leads to degraded validity, loss of structural fidelity, or unstable behavior. We introduce MoltenFlow, a modular framework that combines property-organized latent representations with flow-matching generative priors and gradient-based guidance. This formulation supports both conditioned generation and local optimization within a single latent-space framework. We show that guided latent flows enable efficient multi-objective molecular optimization under fixed oracle budgets with controllable trade-offs, while a learned flow prior improves unconditional generation quality.

We propose Q-BIOLAT, a framework for modeling and optimizing protein fitness landscapes in binary latent spaces. Starting from protein sequences, we leverage pretrained protein language models to obtain continuous embeddings, which are then transformed into compact binary latent representations. In this space, protein fitness is approximated using a quadratic unconstrained binary optimization (QUBO) model, enabling efficient combinatorial search via classical heuristics such as simulated annealing and genetic algorithms. On the ProteinGym benchmark, we demonstrate that Q-BIOLAT captures meaningful structure in protein fitness landscapes and enables the identification of high-fitness variants. Despite using a simple binarization scheme, our method consistently retrieves sequences whose nearest neighbors lie within the top fraction of the training fitness distribution, particularly under the strongest configurations. We further show that different optimization strategies exhibit distinct behaviors, with evolutionary search performing better in higher-dimensional latent spaces and local search remaining competitive in preserving realistic sequences. Beyond its empirical performance, Q-BIOLAT provides a natural bridge between protein representation learning and combinatorial optimization. By formulating protein fitness as a QUBO problem, our framework is directly compatible with emerging quantum annealing hardware, opening new directions for quantum-assisted protein engineering. Our implementation is publicly available at: https://github.com/HySonLab/Q-BIOLAT

We propose a robust and provably secure image steganography framework based on latent-space iterative optimization. Within this framework, the receiver treats the transmitted image as a fixed reference and iteratively refines a latent variable to minimize the reconstruction error, thereby improving message extraction accuracy. Unlike prior methods, our approach preserves the provable security of the embedding while markedly enhancing robustness under various compression and image processing scenarios. On benchmark datasets, the experimental results demonstrate that the proposed iterative optimization not only improves robustness against image compression while preserving provable security, but can also be applied as an independent module to further reinforce robustness in other provably secure steganographic schemes. This highlights the practicality and promise of latent-space optimization for building reliable, robust, and secure steganographic systems.

Latent-space Bayesian optimization (LSBO) extends Bayesian optimization to structured domains, such as molecular design, by searching in the continuous latent space of a generative model. However, most LSBO methods assume a fixed objective, whereas real design campaigns often face temporal drift (e.g., evolving preferences or shifting targets). Bringing time-varying BO into LSBO is nontrivial: drift can affect not only the surrogate, but also the latent search space geometry induced by the representation. We propose Time-Aware Latent-space Bayesian Optimization (TALBO), which incorporates time in both the surrogate and the learned generative representation via a GP-prior variational autoencoder, yielding a latent space aligned as objectives evolve. To evaluate timevarying LSBO systematically, we adapt widely used molecular design tasks to drifting multi-property objectives and introduce metrics tailored to changing targets. Across these benchmarks, TALBO consistently outperforms strong LSBO baselines and remains robust across drift speeds and design choices, while remaining competitive under actually time-invariant objectives.

Symbolic Regression (SR) tries to reveal the hidden equations behind observed data. However, most methods search within a discrete equation space, where the structural modifications of equations rarely align with their numerical behavior, leaving fitting error feedback too noisy to guide exploration. To address this challenge, we propose GenSR, a generative latent space-based SR framework following the map construction -> coarse localization -> fine search'' paradigm. Specifically, GenSR first pretrains a dual-branch Conditional Variational Autoencoder (CVAE) to reparameterize symbolic equations into a generative latent space with symbolic continuity and local numerical smoothness. This space can be regarded as a well-structured map'' of the equation space, providing directional signals for search. At inference, the CVAE coarsely localizes the input data to promising regions in the latent space. Then, a modified CMA-ES refines the candidate region, leveraging smooth latent gradients. From a Bayesian perspective, GenSR reframes the SR task as maximizing the conditional distribution $p(\mathrm{Equ.} \mid \mathrm{Num.})$, with CVAE training achieving this objective through the Evidence Lower Bound (ELBO). This new perspective provides a theoretical guarantee for the effectiveness of GenSR. Extensive experiments show that GenSR jointly optimizes predictive accuracy, expression simplicity, and computational efficiency, while remaining robust under noise.

Despite the strong performance of large language models (LLMs) across diverse tasks, their susceptibility to adversarial attacks and unsafe content generation remains a significant obstacle to deployment, particularly in high-stakes settings. Addressing this challenge requires safety mechanisms that are both practically effective and theoretically grounded. In this paper, we introduce BarrierSteer, a novel inference-time framework that improves response safety by embedding learned nonlinear safety constraints directly into the model's latent representation space. BarrierSteer treats hidden-state safety classifiers as Control Barrier Functions (CBFs), enabling constraint-guided steering of unsafe latent trajectories during generation. By composing multiple safety constraints through efficient constraint merging without modifying the underlying LLM parameters, BarrierSteer preserves model utility. We provide theoretical results showing that applying CBFs in the latent space yields a principled, modular, and computationally efficient approach for steering with respect to learned safety constraints, with guarantees conditional on the learned barriers capturing the intended safety property. Our extensive experimental results across multiple model families and datasets demonstrate that BarrierSteer substantially reduces adversarial attack success rates and unsafe generations, outperforming the existing method. The code is available in our GitHub repository.

Long-range geophysical forecasts are fundamentally limited by chaotic dynamics and numerical errors. While data assimilation can mitigate these issues, classical variational smoothers require computationally expensive tangent-linear and adjoint models. Conversely, recent efficient latent filtering methods often enforce weak trajectory-level constraints and assume fixed observation grids. To bridge this gap, we propose Latent Ensemble Variational Data Assimilation (LEVDA), an ensemble-space variational smoother that operates in the low-dimensional latent space of a pretrained differentiable neural dynamics surrogate. By performing four-dimensional ensemble-variational (4DEnVar) optimization within an ensemble subspace, LEVDA jointly assimilates states and unknown parameters without the need for adjoint code or auxiliary observation-to-latent encoders. Leveraging the fully differentiable, continuous-in-time-and-space nature of the surrogate, LEVDA naturally accommodates highly irregular sampling at arbitrary spatiotemporal locations. Across three challenging geophysical benchmarks, LEVDA matches or outperforms state-of-the-art latent filtering baselines under severe observational sparsity while providing more reliable uncertainty quantification. Simultaneously, it achieves substantially improved assimilation accuracy and computational efficiency compared to full-state 4DEnVar.

This study investigates the impact of regularization of latent spaces through truncation on the quality of generated test inputs for deep learning classifiers. We evaluate this effect using style-based GANs, a state-of-the-art generative approach, and assess quality along three dimensions: validity, diversity, and fault detection. We evaluate our approach on the boundary testing of deep learning image classifiers across three datasets, MNIST, Fashion MNIST, and CIFAR-10. We compare two truncation strategies: latent code mixing with binary search optimization and random latent truncation for generative exploration. Our experiments show that the latent code-mixing approach yields a higher fault detection rate than random truncation, while also improving both diversity and validity.

Bayesian optimisation (BO) enables sample-efficient global optimisation of expensive black-box functions but remains challenging in high dimensions. We investigate nonlinear dimensionality reduction to a sequence of low-dimensional latent-space BO (LSBO) problems. Early LSBO used linear random and supervised embeddings; building on Grosnit et al., we employ variational autoencoders (VAEs), deep metric loss for structured latent manifolds, and retraining to adapt the encoder-decoder pair to newly sampled regions. We couple LSBO with sequential domain reduction (SDR) directly in latent space (SDR-LSBO), narrowing search domains as evidence accumulates. Implemented in GPU-accelerated BoTorch with Mat'ern-5/2 Gaussian-process surrogates, our methods improve benchmark optimisation quality, and retraining can enhance BO performance. Comparisons with adaptive supervised linear random embeddings demonstrate the effectiveness of VAE-based BO for nonlinear low-dimensional structures. We analyse BO-VAE with a fixed pretrained representation, decomposing ambient-space simple regret into latent BO error and a fixed VAE-induced representation gap. Under a PAC-Bayes-certified reconstruction condition and standard fixed-prior assumptions for expected improvement with a Mat'ern-5/2 kernel, latent BO error vanishes as the evaluation budget increases, whereas the representation gap remains fixed and may impose a non-vanishing error floor. Visualisations empirically assess accessibility of the ambient optimum through the learned decoder. To our knowledge, this is the first study combining SDR with VAE-based LSBO. Our analysis clarifies metric shaping and retraining choices critical for scalable latent-space BO. For reproducibility, source code is available at https://github.com/L-Lok/Nonlinear-Dimensionality-Reduction-Techniques-for-Bayesian-Optimization.git.