Several power-law critical properties involving different statistics in natural languages -- reminiscent of scaling properties of physical systems at or near phase transitions -- have been documented for decades. The recent rise of large language models (LLMs) has added further evidence and excitement by providing intriguing similarities with notions in physics such as scaling laws and emergent abilities. However, specific instances of classes of generative language models that exhibit phase transitions, as understood by the statistical physics community, are lacking. In this work, inspired by the one-dimensional Potts model in statistical physics we construct a simple probabilistic language model that falls under the class of context sensitive grammars (CSG), and numerically demonstrate an unambiguous phase transition in the framework of a natural language model. We explicitly show that a precisely defined order parameter -- that captures symbol frequency biases in the sentences generated by the language model -- changes from strictly 0 to a strictly nonzero value (in the infinite-length limit of sentences), implying a mathematical singularity arising when tuning the parameter of the stochastic language model we consider. Furthermore, we identify the phase transition as a variant of the Berezinskii-Kosterlitz-Thouless (BKT) transition, which is known to exhibit critical properties not only at the transition point but also in the entire phase. This finding leads to the possibility that critical properties in natural languages may not require careful fine-tuning nor self-organized criticality, but is generically explained by the underlying connection between language structures and the BKT phases.

An experienced human Observer reading a document -- such as a crime report -- creates a succinct plot-like $\textit{``Working Memory''}$ comprising different actors, their prototypical roles and states at any point, their evolution over time based on their interactions, and even a map of missing Semantic parts anticipating them in the future. $\textit{An equivalent AI Observer currently does not exist}$. We introduce the $\textbf{[G]}$enerative $\textbf{[S]}$emantic $\textbf{[W]}$orkspace (GSW) -- comprising an $\textit{``Operator''}$ and a $\textit{``Reconciler''}$ -- that leverages advancements in LLMs to create a generative-style Semantic framework, as opposed to a traditionally predefined set of lexicon labels. Given a text segment $C_n$ that describes an ongoing situation, the $\textit{Operator}$ instantiates actor-centric Semantic maps (termed ``Workspace instance'' $\mathcal{W}_n$). The $\textit{Reconciler}$ resolves differences between $\mathcal{W}_n$ and a ``Working memory'' $\mathcal{M}_n^*$ to generate the updated $\mathcal{M}_{n+1}^*$. GSW outperforms well-known baselines on several tasks ($\sim 94\%$ vs. FST, GLEN, BertSRL - multi-sentence Semantics extraction, $\sim 15\%$ vs. NLI-BERT, $\sim 35\%$ vs. QA). By mirroring the real Observer, GSW provides the first step towards Spatial Computing assistants capable of understanding individual intentions and predicting future behavior.

DNA sequence alignment involves assigning short DNA reads to the most probable locations on an extensive reference genome. This process is crucial for various genomic analyses, including variant calling, transcriptomics, and epigenomics. Conventional methods, refined over decades, tackle this challenge in two steps: genome indexing followed by efficient search to locate likely positions for given reads. Building on the success of Large Language Models (LLM) in encoding text into embeddings, where the distance metric captures semantic similarity, recent efforts have explored whether the same Transformer architecture can produce numerical representations for DNA sequences. Such models have shown early promise in tasks involving classification of short DNA sequences, such as the detection of coding vs non-coding regions, as well as the identification of enhancer and promoter sequences. Performance at sequence classification tasks does not, however, translate to sequence alignment, where it is necessary to conduct a genome-wide search to successfully align every read. We address this open problem by framing it as an Embed-Search-Align task. In this framework, a novel encoder model DNA-ESA generates representations of reads and fragments of the reference, which are projected into a shared vector space where the read-fragment distance is used as surrogate for alignment. In particular, DNA-ESA introduces: (1) Contrastive loss for self-supervised training of DNA sequence representations, facilitating rich sequence-level embeddings, and (2) a DNA vector store to enable search across fragments on a global scale. DNA-ESA is >97% accurate when aligning 250-length reads onto a human reference genome of 3 gigabases (single-haploid), far exceeds the performance of 6 recent DNA-Transformer model baselines and shows task transfer across chromosomes and species.

We present the interpretable meta neural ordinary differential equation (iMODE) method to rapidly learn generalizable (i.e., not parameter-specific) dynamics from trajectories of multiple dynamical systems that vary in their physical parameters. The iMODE method learns meta-knowledge, the functional variations of the force field of dynamical system instances without knowing the physical parameters, by adopting a bi-level optimization framework: an outer level capturing the common force field form among studied dynamical system instances and an inner level adapting to individual system instances. A priori physical knowledge can be conveniently embedded in the neural network architecture as inductive bias, such as conservative force field and Euclidean symmetry. With the learned meta-knowledge, iMODE can model an unseen system within seconds, and inversely reveal knowledge on the physical parameters of a system, or as a Neural Gauge to "measure" the physical parameters of an unseen system with observed trajectories. We test the validity of the iMODE method on bistable, double pendulum, Van der Pol, Slinky, and reaction-diffusion systems.

Soft deployable structures - unlike conventional piecewise rigid deployables based on hinges and springs - can assume intricate 3-D shapes, thereby enabling transformative technologies in soft robotics, shape-morphing architecture, and pop-up manufacturing. Their virtually infinite degrees of freedom allow precise control over the final shape. The same enabling high dimensionality, however, poses a challenge for solving the inverse design problem involving this class of structures: to achieve desired 3D structures it typically requires manufacturing technologies with extensive local actuation and control during fabrication, and a trial and error search over a large design space. We address both of these shortcomings by first developing a simplified planar fabrication approach that combines two ingredients: strain mismatch between two layers of a composite shell and kirigami cuts that relieves localized stress. In principle, it is possible to generate targeted 3-D shapes by designing the appropriate kirigami cuts and selecting the right amount of prestretch, thereby eliminating the need for local control. Second, we formulate a data-driven physics-guided framework that reduces the dimensionality of the inverse design problem using autoencoders and efficiently searches through the ``latent" parameter space in an active learning approach. We demonstrate the effectiveness of the rapid design procedure via a range of target shapes, such as peanuts, pringles, flowers, and pyramids. Tabletop experiments are conducted to fabricate the target shapes. Experimental results and numerical predictions from our framework are found to be in good agreement.

Variational Bayes (VB) inference algorithm is used widely to estimate both the parameters and the unobserved hidden variables in generative statistical models. The algorithm -- inspired by variational methods used in computational physics -- is iterative and can get easily stuck in local minima, even when classical techniques, such as deterministic annealing (DA), are used. We study a variational Bayes (VB) inference algorithm based on a non-traditional quantum annealing approach -- referred to as quantum annealing variational Bayes (QAVB) inference -- and show that there is indeed a quantum advantage to QAVB over its classical counterparts. In particular, we show that such better performance is rooted in key concepts from quantum mechanics: (i) the ground state of the Hamiltonian of a quantum system -- defined from the given variational Bayes (VB) problem -- corresponds to an optimal solution for the minimization problem of the variational free energy at very low temperatures; (ii) such a ground state can be achieved by a technique paralleling the quantum annealing process; and (iii) starting from this ground state, the optimal solution to the VB problem can be achieved by increasing the heat bath temperature to unity, and thereby avoiding local minima introduced by spontaneous symmetry breaking observed in classical physics based VB algorithms. We also show that the update equations of QAVB can be potentially implemented using $\lceil \log K \rceil$ qubits and $\mathcal{O} (K)$ operations per step. Thus, QAVB can match the time complexity of existing VB algorithms, while delivering higher performance.

The paradigm of variational quantum classifiers (VQCs) encodes \textit{classical information} as quantum states, followed by quantum processing and then measurements to generate classical predictions. VQCs are promising candidates for efficient utilization of a near-term quantum device: classifiers involving $M$-dimensional datasets can be implemented with only $\lceil \log_2 M \rceil$ qubits by using an amplitude encoding. A general framework for designing and training VQCs, however, has not been proposed, and a fundamental understanding of its power and analytical relationships with classical classifiers are not well understood. An encouraging specific embodiment of VQCs, quantum circuit learning (QCL), utilizes an ansatz: it expresses the quantum evolution operator as a circuit with a predetermined topology and parametrized gates; training involves learning the gate parameters through optimization. In this letter, we first address the open questions about VQCs and then show that they, including QCL, fit inside the well-known kernel method. Based on such correspondence, we devise a design framework of efficient ansatz-independent VQCs, which we call the unitary kernel method (UKM): it directly optimizes the unitary evolution operator in a VQC. Thus, we show that the performance of QCL is bounded from above by the UKM. Next, we propose a variational circuit realization (VCR) for designing efficient quantum circuits for a given unitary operator. By combining the UKM with the VCR, we establish an efficient framework for constructing high-performing circuits. We finally benchmark the relatively superior performance of the UKM and the VCR via extensive numerical simulations on multiple datasets.

Despite significant recent progress, machine vision systems lag considerably behind their biological counterparts in performance, scalability, and robustness. A distinctive hallmark of the brain is its ability to automatically discover and model objects, at multiscale resolutions, from repeated exposures to unlabeled contextual data and then to be able to robustly detect the learned objects under various nonideal circumstances, such as partial occlusion and different view angles. Replication of such capabilities in a machine would require three key ingredients: (i) access to large-scale perceptual data of the kind that humans experience, (ii) flexible representations of objects, and (iii) an efficient unsupervised learning algorithm. The Internet fortunately provides unprecedented access to vast amounts of visual data. This paper leverages the availability of such data to develop a scalable framework for unsupervised learning of object prototypes--brain-inspired flexible, scale, and shift invariant representations of deformable objects (e.g., humans, motorcycles, cars, airplanes) comprised of parts, their different configurations and views, and their spatial relationships. Computationally, the object prototypes are represented as geometric associative networks using probabilistic constructs such as Markov random fields. We apply our framework to various datasets and show that our approach is computationally scalable and can construct accurate and operational part-aware object models much more efficiently than in much of the recent computer vision literature. We also present efficient algorithms for detection and localization in new scenes of objects and their partial views.

Artificial neural networks are comprised of an interconnected collection of certain nonlinear devices; examples of commonly used devices include linear threshold elements, sigmoidal elements and radial-basis elements. We employ results from harmonic analysis and the theory of rational approximation to obtain almost tight lower bounds on the size (i.e.

An artificial neural network (ANN) is commonly modeled by a threshold circuit, a network of interconnected processing units called linear threshold gates. The depth of a network represents the number of unit delays or the time for parallel computation. The SIze of a circuit is the number of gates and measures the amount of hardware. It was known that traditional logic circuits consisting of only unbounded fan-in AND, OR, NOT gates would require at least O(log n/log log n) depth to compute common arithmetic functions such as the product or the quotient of two n-bit numbers, unless we allow the size (and fan-in) to increase exponentially (in n). We show in this paper that ANNs can be much more powerful than traditional logic circuits. In particular, we prove that that iterated addition can be computed by depth-2 ANN, and multiplication and division can be computed by depth-3 ANNs with polynomial size and polynomially bounded integer weights, respectively. Moreover, it follows from known lower bound results that these ANNs are optimal in depth. We also indicate that these techniques can be applied to construct polynomial-size depth-3 ANN for powering, and depth-4 ANN for mUltiple product.