composition
The Best Mattress Toppers I've Tried (2026): Supportive, Plush, Memory Foam
I Tested the Best Mattress Toppers for a Good Night's Sleep These toppers will transform your mattress into exactly what you need, whether that's a super-plush pillow top, memory foam, or targeted back support. My hunt for the best mattress toppers has taught me how transformative they can be. It started years before now, when I was throwing my back out nightly on a thin futon mattress in my fresh-out-of-college days. I tried a few cheap sheets of foam that barely helped with my back pain . I gave up for a while and instead switched to a too-soft mattress (equally problematic), until finally finding the right combo: a firm, supportive mattress with a nice mattress topper on top to support my problem areas and side-sleeper shoulder pain. These toppers can alleviate your aches, sink you into insanely comfortable memory foam, and even pack supportive coils like a mattress. My favorite toppers range from soft wool layers and memory foam to firm and even hybrid toppers (yes, you can get mattress toppers with springs in them) to find the best option for you and your mattress. Curious what you should get? Read on to find my best mattress toppers for everything from back pain issues, college students, and more. All prices below are for queen-size toppers. What Is a Mattress Topper?
François Pachet on music generation with AI
Dr François Pachet is an AI researcher and musician, and one of the most influential figures in AI and music. His innovative contributions have defined the field over the past decades through creative systems such as the Continuator, and Flow Machines, among others. After leading the Spotify Creator Technology Research Lab and the Sony Computer Science Lab, he went on to create his own companies: Imagine All The People and Ynosound. In the context of IJCAI2025, he spoke about what deep learning changed, and what still remains wide open. He explains why tools like Suno and Udio--ChatGPT-like platforms for music generation--can produce astonishing results that still feel unsatisfying; why the next step for music generation requires combining sampling with search; and why the most important problems in artistic domains are, by nature, ill-defined--because there is no loss function to determine what is "good". Above all, he defends the importance of researcher autonomy: work on the questions that genuinely fascinate you, even when they fall outside prevailing trends--perhaps especially then. Thank you for joining me for this interview. Could you begin by telling us when was your first IJCAI and a memory related to it? I think the first IJCAI I attended was in Montreal in '95. I was there for a couple of workshops, one of them was about music and AI, and the other one I think was on advisor systems, something like that. And I remember there was a French colleague who was there also, at the time he was doing his PhD. And there was this researcher called Herbert Simon, who is a Nobel Prize pioneer of AI. I remember having chatted a little bit with this French guy who was very bold, and he just went up to Simon, said "Hey," and he started a conversation with him. And I was very impressed by the fact that you could meet those kinds of guys informally in a corridor or something at this conference.
A Sieve-Accelerated Quadrature Method for Exact Privacy Accounting in the 2020 U.S. Decennial Census
Su, Buxin, Su, Weijie, Wang, Chendi
In 2020, the U.S. Census Bureau adopted differential privacy for the Decennial Census by injecting integer-valued Gaussian noise into published census tabulations. Exactly evaluating the privacy guarantees of these data releases would enable the Bureau to determine the absolute minimum noise required to satisfy a given privacy budget, preventing the injection of unnecessary excess noise and thereby substantially enhancing the statistical utility of the data for downstream applications such as federal funding allocation and political redistricting. In this paper, we introduce a computationally efficient and mathematically rigorous quadrature method to evaluate the exact privacy profile of practical, large-scale census releases under the composition of heterogeneous discrete Gaussian mechanisms. Mathematically, this problem reduces to evaluating the tail probabilities of high-dimensional convolutions of integer-valued random variables sampled from heterogeneous discrete Gaussian distributions under exceptionally stringent numerical error tolerances (e.g., $10^{-35}$). By recasting the exact privacy accounting as a numerical integration problem via the discrete Fourier transform, we explicitly exploit the exponential convergence of the trapezoidal rule for complex analytic, periodic characteristic functions. Furthermore, to overcome the computational bottleneck of evaluating highly oscillatory integrands in high dimensions, we develop a sieve algorithm that identifies and prunes negligible quadrature nodes, accelerating the computation by three orders of magnitude. Taken together, these numerical innovations enable the first exact, assumption-free privacy accounting for the 2020 Census Demographic and Housing Characteristics File, achieving a 1,824-fold speedup over prior methods while maintaining census-mandated error tolerances.
LLMMeets Diffusion: AHybrid Framework for Crystal Material Generation
Recent advances in generative modeling have shown significant promise in designing novel periodic crystal structures. Existing approaches typically rely on either large language models (LLMs) or equivariant denoising models, each with complementary strengths: LLMs excel at handling discrete atomic types but often struggle with continuous features such as atomic positions and lattice parameters, while denoising models are effective at modeling continuous variables but encounter difficulties in generating accurate atomic compositions. To bridge this gap, we propose CrysLLMGen, a hybrid framework that integrates an LLM with a diffusion model to leverage their complementary strengths for crystal material generation. During sampling, CrysLLMGen first employs a fine-tuned LLM to produce an intermediate representation of atom types, atomic coordinates, and lattice structure. While retaining the predicted atom types, it passes the atomic coordinates and lattice structure to a pre-trained equivariant diffusion model for refinement. Our framework outperforms state-of-the-art generative models across several benchmark tasks and datasets. Specifically, CrysLLMGen not only achieves a balanced performance in terms of structural and compositional validity but also generates more stable and novel materials compared to LLM-based and denoisingbased models Furthermore, CrysLLMGen exhibits strong conditional generation capabilities, effectively producing materials that satisfy user-defined constraints.
MACS: Multi-Agent Reinforcement Learning for Optimization of Crystal Structures
Geometry optimization of atomic structures is a common and crucial task in computational chemistry and materials design. Following the learning to optimize paradigm, we propose a new multi-agent reinforcement learning method called Multi-Agent Crystal Structure optimization (MACS) to address periodic crystal structure optimization. MACS treats geometry optimization as a partially observable Markov game in which atoms are agents that adjust their positions to collectively discover a stable configuration. We train MACS across various compositions of reported crystalline materials to obtain a policy that successfully optimizes structures from the training compositions as well as structures of larger sizes and unseen compositions, confirming its excellent scalability and zero-shot transferability. We benchmark our approach against a broad range of state-of-theart optimization methods and demonstrate that MACS optimizes periodic crystal structures significantly faster, with fewer energy calculations, and the lowest failure rate. Code is available at https://github.com/lrcfmd/macs.
LoRAShop: Training-Free Multi-Concept Image Generation and Editing with Rectified Flow Transformers
We introduce LoRAShop, the first framework for multi-concept image editing with LoRA models. LoRAShop builds on a key observation about the feature interaction patterns inside Flux-style diffusion transformers: concept-specific transformer features activate spatially coherent regions early in the denoising process. We harness this observation to derive a disentangled latent mask for each concept in a prior forward pass and blend the corresponding LoRA weights only within regions bounding the concepts to be personalized.
Differentially Private Gomory-Hu Trees
Given an undirected, weighted n-vertex graph G = (V,E,w), a Gomory-Hu tree T is a weighted tree on V that preserves the Min-s-t-Cut between any pair of vertices s,t V. Finding cuts in graphs is a key primitive in problems such as bipartite matching, spectral and correlation clustering, and community detection. We design a differentially private (DP) algorithm that computes an approximate Gomory-Hu tree. Our algorithm is ε-DP, runs in polynomial time, and can be used to compute s-tcuts that are O(n/ε)-additive approximations of the Min-s-t-Cuts in Gfor all distinct s,t V with high probability. Our error bound is essentially optimal, since [29] showed that privately outputting a single Min-s-t-Cut requires Ω(n) additive error even with (ε,δ)-DP and allowing for multiplicative error. Prior to our work, the best additive error bounds for approximate all-pairs Min-s-t-Cuts were O(n3/2/ε)for ε-DP [47] and O( mn/ε)for (ε,δ)-DP [66], both achieved by DP algorithms that preserve all cuts in the graph. To achieve our result, we develop an ε-DP algorithm for the Minimum Isolating Cuts problem with near-linear error, and introduce a novel privacy composition technique combining elements of both parallel and basic composition to handle'bounded overlap' computational branches in recursive algorithms, which maybe of independent interest.
AdaPrivate-TS: Private Thompson Sampling for Contextual Bandits with Privacy Amplification
Riyazat, Mohammadreza, Ukwatta, Eranga
We present AdaPrivate-TS, a differentially private contextual bandit algorithm that combines Thompson Sampling with batched zCDP composition. Our key insight is that differential privacy noise inflates the posterior covariance in a structured way: adding Gaussian noise $N(0,σ^2 I)$ to $b$ yields sampling covariance $v^2 A^{-1} + σ^2 A^{-2}$, which Thompson Sampling interprets as increased uncertainty rather than pure corruption. Under event-level privacy (protecting individual interactions) with stochastic contexts, we prove that the privacy cost is only $O(\sqrt{d}\,\log T/\sqrtρ)$, logarithmic in $T$, because parallel composition amortizes noise across batches. Additionally, we explore privacy amplification via Poisson subsampling, which can reduce effective noise at stringent privacy budgets. Experiments on synthetic and real-world datasets demonstrate: (1) AdaPrivate-TS achieves 93-99% of non-private performance at $\varepsilon \in [0.5, 5]$, outperforming UCB by 0.5-3.7% and up to 18% with tuned adaptive exploration at extreme $\varepsilon$; (2) privacy amplification provides additional 2-5% gains at low $\varepsilon$; (3) on MovieLens and Jester, AdaPrivate-TS achieves the best overall performance among event-level baselines, dominating at $\varepsilon \geq 2$; (4) under DP-SVD private features, TS's advantage over UCB grows to +11%, confirming noise-as-uncertainty is not limited to reward privacy. We provide rigorous proofs for privacy guarantees under interactive zCDP composition and comprehensive evaluation including convergence curves, 12-seed CIs, and DP-SVD feature ablation.
Disentangled Representation Learning via Modular Compositional Bias
Recent disentangled representation learning (DRL) methods heavily rely on factorspecific strategies--either learning objectives for attributes or model architectures for objects--to embed inductive biases. Such divergent approaches result in significant overhead when novel factors of variation do not align with prior assumptions, such as statistical independence or spatial exclusivity, or when multiple factors coexist, as practitioners must redesign architectures or objectives. To address this, we propose a compositional bias, a modular inductive bias decoupled from both objectives and architectures. Our key insight is that different factors obey distinct "recombination rules" in the data distribution: global attributes are mutually exclusive, e.g., a face has one nose, while objects share a common support (any subset of objects can co-exist). We therefore randomly remix latents according to factor-specific rules, i.e., a mixing strategy, and force the encoder to discover whichever factor structure the mixing strategy reflects through two complementary objectives: (i) a prior loss that ensures every remix decodes into a realistic image, and (ii) the compositional consistency loss introduced by Wiedemer et al. [50], which aligns each composite image with its corresponding composite latent. Under this general framework, simply adjusting the mixing strategy enables disentanglement of attributes, objects, and even both, without modifying the objectives or architectures. Extensive experiments demonstrate that our method shows competitive performance in both attribute and object disentanglement, and uniquely achieves joint disentanglement of global style and objects.
Composing Linear Layers from Irreducibles
Contemporary large models often exhibit behaviors suggesting the presence of low-level primitives that compose into modules with richer functionality, but these fundamental building blocks remain poorly understood. We investigate this compositional structure in linear layers by asking: can we identify/synthesize linear transformations from a minimal set of geometric primitives? Using Clifford algebra, we show that linear layers can be expressed as compositions of bivectors--geometric objects encoding oriented planes--and introduce a differentiable algorithm that decomposes them into products of rotors. This construction uses only O log2 d parameters, versus O(d2) required by dense matrices. Applied to the key, query, and value projections in LLM attention layers, rotor-based layers match the performance of strong baselines such as block-Hadamard and low-rank approximations. Our findings provide an algebraic perspective on how these geometric primitives can compose into higher-level functions within deep models.