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Data-driven techniques have emerged as a promising alternative to traditional numerical methods for solving PDEs. For time-dependent PDEs, many approaches are Markovian -- the evolution of the trained system only depends on the current state, and not the past states. In this work, we investigate the benefits of using memory for modeling time-dependent PDEs: that is, when past states are explicitly used to predict the future. Motivated by the Mori-Zwanzig theory of model reduction, we theoretically exhibit examples of simple (even linear) PDEs, in which a solution that uses memory is arbitrarily better than a Markovian solution. Additionally, we introduce Memory Neural Operator (MemNO), a neural operator architecture that combines recent state space models (specifically, S4) and Fourier Neural Operators (FNOs) to effectively model memory. We empirically demonstrate that when the PDEs are supplied in low resolution or contain observation noise at train and test time, MemNO significantly outperforms the baselines without memory -- with up to 6x reduction in test error. Furthermore, we show that this benefit is particularly pronounced when the PDE solutions have significant high-frequency Fourier modes (e.g., low-viscosity fluid dynamics) and we construct a challenging benchmark dataset consisting of such PDEs. 

The BigCode community, an open-scientific collaboration working on the responsible development of Large Language Models for Code (Code LLMs), introduces StarCoder and StarCoderBase: 15.5B parameter models with 8K context length, infilling capabilities and fast large-batch inference enabled by multi-query attention. StarCoderBase is trained on 1 trillion tokens sourced from The Stack, a large collection of permissively licensed GitHub repositories with inspection tools and an opt-out process. We fine-tuned StarCoderBase on 35B Python tokens, resulting in the creation of StarCoder. We perform the most comprehensive evaluation of Code LLMs to date and show that StarCoderBase outperforms every open Code LLM that supports multiple programming languages and matches or outperforms the OpenAI code-cushman-001 model. Furthermore, StarCoder outperforms every model that is fine-tuned on Python, can be prompted to achieve 40% pass@1 on HumanEval, and still retains its performance on other programming languages. We take several important steps towards a safe open-access model release, including an improved PII redaction pipeline and a novel attribution tracing tool, and make the StarCoder models publicly available under a more commercially viable version of the Open Responsible AI Model license. 

Abstract Despite the f₀(980) hadron having been discovered half a century ago, the question about its quark content has not been settled: it might be an ordinary quark-antiquark ($${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$) meson, a tetraquark ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}q\overline{q}$) exotic state, a kaon-antikaon ($${{\rm{K}}}\overline{{{\rm{K}}}}$$ $K\overline{K}$) molecule, or a quark-antiquark-gluon ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$ $q\overline{q}g$) hybrid. This paper reports strong evidence that the f₀(980) state is an ordinary$${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$meson, inferred from the scaling of elliptic anisotropies (v₂) with the number of constituent quarks (n_q), as empirically established using conventional hadrons in relativistic heavy ion collisions. The f₀(980) state is reconstructed via its dominant decay channel f₀(980) →π⁺π⁻, in proton-lead collisions recorded by the CMS experiment at the LHC, and itsv₂is measured as a function of transverse momentum (p_T). It is found that then_q= 2 ($${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$state) hypothesis is favored overn_q= 4 ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}q\overline{q}$or$${{\rm{K}}}\overline{{{\rm{K}}}}$$ $K\overline{K}$states) by 7.7, 6.3, or 3.1 standard deviations in thep_T< 10, 8, or 6 GeV/cranges, respectively, and overn_q= 3 ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$ $q\overline{q}g$hybrid state) by 3.5 standard deviations in thep_T< 8 GeV/crange. This result represents the first determination of the quark content of the f₀(980) state, made possible by using a novel approach, and paves the way for similar studies of other exotic hadron candidates. 

A first search for beyond the standard model physics in jet multiplicity patterns of multilepton events is presented, using a data sample corresponding to an integrated luminosity of $138{\mathrm{fb}}^{-1}$of 13 TeV proton-proton collisions recorded by the CMS detector at the LHC. The search uses observed jet multiplicity distributions in one-, two-, and four-lepton events to explore possible enhancements in jet production rate in three-lepton events with and without bottom quarks. The data are found to be consistent with the standard model expectation. The results are interpreted in terms of supersymmetric production of electroweak chargino-neutralino superpartners with cascade decays terminating in prompt hadronic $R$-parity violating interactions. 

A search for the rare decay $D^0\to {\mu }^{+}{\mu }^{-}$is reported using proton-proton collision events at $\sqrt{s}=13.6\mathrm{TeV}$collected by the CMS detector in 2022–2023, corresponding to an integrated luminosity of $64.5{\mathrm{fb}}^{-1}$. This is the first analysis to use a newly developed inclusive dimuon trigger, expanding the scope of the CMS flavor physics program. The search uses $D^0$mesons obtained from $D^{*+}\to D^0{\pi }^{+}$decays. No significant excess is observed. A limit on the branching fraction of $\mathcal{B}(D^0\to {\mu }^{+}{\mu }^{-})<2.4\times {10}^{-9}$at 95% confidence level is set. This is the most stringent upper limit set on any flavor changing neutral current decay in the charm sector. 

A<sc>bstract</sc> A search for a heavy pseudoscalar Higgs boson, A, decaying to a 125 GeV Higgs boson h and a Z boson is presented. The h boson is identified via its decay to a pair of tau leptons, while the Z boson is identified via its decay to a pair of electrons or muons. The search targets the production of the A boson via the gluon-gluon fusion process, gg → A, and in association with bottom quarks,$$\text{b}\overline{\text{b}}\text{A }$$. The analysis uses a data sample corresponding to an integrated luminosity of 138 fb⁻¹collected with the CMS detector at the CERN LHC in proton-proton collisions at a centre-of-mass energy of$$\sqrt{s}=13$$TeV. Constraints are set on the product of the cross sections of the A production mechanisms and the A → Zh decay branching fraction. The observed (expected) upper limit at 95% confidence level ranges from 0.049 (0.060) pb to 1.02 (0.79) pb for the gg → A process and from 0.053 (0.059) pb to 0.79 (0.61) pb for the$$\text{b}\overline{\text{b}}\text{A }$$process in the probed range of the A boson mass,m_A, from 225 GeV to 1 TeV. The results of the search are used to constrain parameters within the$${\text{M}}_{\text{h},\text{EFT}}^{125}$$benchmark scenario of the minimal supersymmetric extension of the standard model. Values of tanβbelow 2.2 are excluded in this scenario at 95% confidence level for allm_Avalues in the range from 225 to 350 GeV.