Existing gradient-based optimization methods update parameters locally, in a direction that minimizes the loss function. We study a different approach, symmetry teleportation, that allows parameters to travel a large distance on the loss level set, in order to improve the convergence speed in subsequent steps. Teleportation exploits symmetries in the loss landscape of optimization problems. We derive loss-invariant group actions for test functions in optimization and multi-layer neural networks, and prove a necessary condition for teleportation to improve convergence rate. We also show that our algorithm is closely related to second order methods. Experimentally, we show that teleportation improves the convergence speed of gradient descent and AdaGrad for several optimization problems including test functions, multi-layer regressions, and MNIST classification.

Artificial intelligence (AI) is used in numerous fields of science, yet the initial research questions and targets are still almost always provided by human researchers. AI-generated creative ideas in science are rare and often vague, so that it remains a human task to execute them. Automating idea generation and implementation in one coherent system would significantly shift the role of humans in the scientific process. Here we present AI-Mandel, an LLM agent that can generate and implement ideas in quantum physics. AI-Mandel formulates ideas from the literature and uses a domain-specific AI tool to turn them into concrete experiment designs that can readily be implemented in laboratories. The generated ideas by AI-Mandel are often scientifically interesting - for two of them we have already written independent scientific follow-up papers. The ideas include new variations of quantum teleportation, primitives of quantum networks in indefinite causal orders, and new concepts of geometric phases based on closed loops of quantum information transfer. AI-Mandel is a prototypical demonstration of an AI physicist that can generate and implement concrete, actionable ideas. Building such a system is not only useful to accelerate science, but it also reveals concrete open challenges on the path to human-level artificial scientists.

We extend Algorithm 1 to stochastic gradient descent (SGD). Algorithm 3 here modifies Algorithm 1 to allow transformations on both parameters and data. In this section, we derive the group actions for the test functions and multi-layer neural networks. More details about group theory can be found in textbooks such as Lang (2002). B.1 Continuous symmetry in test functions B.1.1 Ellipse Consider the following loss function with a 2 R However, we will only use the 2 variable version in the experiments.

We also show that our algorithm is closely related to second order methods.

We extend Algorithm 1 to stochastic gradient descent (SGD). Algorithm 3 here modifies Algorithm 1 to allow transformations on both parameters and data. In this section, we derive the group actions for the test functions and multi-layer neural networks. More details about group theory can be found in textbooks such as Lang (2002). B.1 Continuous symmetry in test functions B.1.1 Ellipse Consider the following loss function with a 2 R However, we will only use the 2 variable version in the experiments.

Verification of the integrity of deep learning inference is crucial for understanding whether a model is being applied correctly. However, such verification typically requires access to model weights and (potentially sensitive or private) training data. So-called Zero-knowledge Succinct Non-Interactive Arguments of Knowledge (ZK-SNARKs) would appear to provide the capability to verify model inference without access to such sensitive data. However, applying ZK-SNARKs to modern neural networks, such as transformers and large vision models, introduces significant computational overhead. We present TeleSparse, a ZK-friendly post-processing mechanisms to produce practical solutions to this problem. TeleSparse tackles two fundamental challenges inherent in applying ZK-SNARKs to modern neural networks: (1) Reducing circuit constraints: Over-parameterized models result in numerous constraints for ZK-SNARK verification, driving up memory and proof generation costs. We address this by applying sparsification to neural network models, enhancing proof efficiency without compromising accuracy or security. (2) Minimizing the size of lookup tables required for non-linear functions, by optimizing activation ranges through neural teleportation, a novel adaptation for narrowing activation functions' range. TeleSparse reduces prover memory usage by 67% and proof generation time by 46% on the same model, with an accuracy trade-off of approximately 1%. We implement our framework using the Halo2 proving system and demonstrate its effectiveness across multiple architectures (Vision-transformer, ResNet, MobileNet) and datasets (ImageNet,CIFAR-10,CIFAR-100). This work opens new directions for ZK-friendly model design, moving toward scalable, resource-efficient verifiable deep learning.

We present a lattice-based scheme for homomorphic evaluation of quantum programs and proofs that remains secure against quantum adversaries. Classical homomorphic encryption is lifted to the quantum setting by replacing composite-order groups with Module Learning-With-Errors (MLWE) lattices and by generalizing polynomial functors to bounded natural super functors (BNSFs). A secret depolarizing BNSF mask hides amplitudes, while each quantum state is stored as an MLWE ciphertext pair. We formalize security with the qIND-CPA game that allows coherent access to the encryption oracle and give a four-hybrid reduction to decisional MLWE. The design also covers practical issues usually left open. A typed QC-bridge keeps classical bits produced by measurements encrypted yet still usable as controls, with weak-measurement semantics for expectation-value workloads. Encrypted Pauli twirls add circuit privacy. If a fixed knowledge base is needed, its axioms are shipped as MLWE "capsules"; the evaluator can use them but cannot read them. A rho-calculus driver schedules encrypted tasks across several QPUs and records an auditable trace on an RChain-style ledger. Performance analysis shows that the extra lattice arithmetic fits inside today's QPU idle windows: a 100-qubit, depth-10^3 teleportation-based proof runs in about 10 ms, the public key (seed only) is 32 bytes, and even a CCA-level key stays below 300 kB. A photonic Dirac-3 prototype that executes homomorphic teleportation plus knowledge-base-relative amplitude checks appears feasible with current hardware. These results indicate that fully homomorphic, knowledge-base-aware quantum reasoning is compatible with near-term quantum clouds and standard post-quantum security assumptions.

We analyze a learning-to-optimize (L2O) algorithm that exploits parameter space symmetry to enhance optimization efficiency. Prior work has shown that jointly learning symmetry transformations and local updates improves meta-optimizer performance. Supporting this, our theoretical analysis demonstrates that even without identifying the optimal group element, the method locally resembles Newton's method. We further provide an example where the algorithm provably learns the correct symmetry transformation during training. To empirically evaluate L2O with teleportation, we introduce a benchmark, analyze its success and failure cases, and show that enhancements like momentum further improve performance. Our results highlight the potential of leveraging neural network parameter space symmetry to advance meta-optimization.

Multi-task learning (MTL) is a widely explored paradigm that enables the simultaneous learning of multiple tasks using a single model. Despite numerous solutions, the key issues of optimization conflict and task imbalance remain under-addressed, limiting performance. Unlike existing optimization-based approaches that typically reweight task losses or gradients to mitigate conflicts or promote progress, we propose a novel approach based on Continual Optimization with Symmetry Teleportation (COST). During MTL optimization, when an optimization conflict arises, we seek an alternative loss-equivalent point on the loss landscape to reduce conflict. Specifically, we utilize a low-rank adapter (LoRA) to facilitate this practical teleportation by designing convergent, loss-invariant objectives. Additionally, we introduce a historical trajectory reuse strategy to continually leverage the benefits of advanced optimizers. Extensive experiments on multiple mainstream datasets demonstrate the effectiveness of our approach. COST is a plug-and-play solution that enhances a wide range of existing MTL methods. When integrated with state-of-the-art methods, COST achieves superior performance.