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ddpm的重参数化技巧
DDPM（Diffusion Deep Probabilistic Model）是一种生成模型，用于建模高维数据的分布。
在DDPM中，重参数化技巧被应用于训练模型和生成样本。
在DDPM中，重参数化技巧的主要目的是使梯度可以通过随机采样进行有效的反向传播。
具体而言，重参数化技巧将模型中的随机变量重新参数化为一个确定性函数（通常是通过变量的均值和标准差进行参数化）。
这样一来，在模型训练过程中，可以通过采样一个固定的噪声向量来生成样本，而不需要进行不可导的随机采样操作。
通过重参数化技巧，可以将采样过程的随机性从模型中分离出来，使得模型在前向计算和反向传播中都保持可微分。
这样，可以使用基于梯度的优化算法（如反向传播和随机梯度下降）来训练DDPM模型。
重参数化技巧的一种常见形式是使用扰动抽样（Perturbation Sampling）。
在这种方法中，模型中的随机变量由一个固定的噪声向量和参数化函数来生成。
通过学习生成函数的参数，可以控制噪声向量对生成样本的影响，从而调整模型的输出分布。
总的来说，重参数化技巧是在生成模型中的一种常用技术，通过将随机性与模型的确定性部分分离，使得模型在训练和采样过程中都能保持可微分性。
这为使用梯度优化算法进行模型训练和生成样本提供了便利。
模型超参数英文标准格式在机器学习和深度学习中，超参数（Hyperparameters）是模型训练过程中设置的参数，其值在训练之前需要手动进行选择或调整。
以下是超参数的英文标准格式：
1. Learning rate：学习率
2. Batch size：批量大小
3. Number of epochs：训练轮数
4. Hidden layer size：隐藏层大小
5. Dropout rate：随机失活率
6. Regularization strength：正则化强度
7. Number of layers：层数
8. Activation function：激活函数
9. Optimization algorithm：优化算法
10. Weight initialization：权重初始化
11. Learning rate decay：学习率衰减
12. Momentum：动量
13. Loss function：损失函数
这些是一些常见的超参数，其英文标准格式在机器学习和深度学习的文献和实践中被广泛使用。
请注意，具体的超参数名称和格式可能会因不同的算法、库或框架而有所变化，但上述列出的超参数是相对通用的，适用于大多数机器学习和深度学习任务。
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The camcorder also records in A VCHD, ideal for quality video for HDTV and Blu-ray disc burning. Additionally, the camcorder can shoot MP4 HD video, which is ideal for sharing over the internet at up to 28Mbps. Having the ability to switch between all three of three formats makes this camcorder an ideal tool that is versatile for creating content to live in a number of different environments.Carl Zeiss ® Vario Sonnar T* lens w/ 12x optical zoomThe HDR-CX900 comes equipped with a newly developed Carl Zeiss ® Vario-Sonnar T* lens that has cleared a series of tough performance tests. 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There’s nothing else like it in the industry.Optical SteadyShot™ Image Stabilization with Intelligent Active Mode is an advanced optical image stabilization technology that corrects camera shake to capture scenes with phenomenal smoothness and stability. Intelligent Active Mode analyzes video frames and provides compensation with assistance from the new BIONZ® X image processing engine. Whether recording movies while strolling on vacation, shooting while chasing a child, or zooming in to capture faraway subjects, Handycam’s simple solution smoothly reproduces the scene with a higher level of stability.High contrast 0.39" OLED EVF for eye-level framingThe HDR-CX900 employs high contrast a 0.39” OLED Tru-Finder EVF which reproduces rich color and deep black. A new optical design of the EVF, using four dual-surface aspherical lenses, allows for a 33-degree wide angle view that is amazing clear through the edge of the view finder. Large 3.5" Xtra Fine LCD™ (921K)The 3.5” (16:9) Xtra Fine LCD™ screen (921K) displays sharp, bright, vivid images, letting you compose a shot more easily -- even outdoors, while enabling you to change settings to best represent the scene.Simple connectivity to smartphones via Wi-Fi®/NFCConnectivity with smartphones for One-touch sharing/One-touch remote has been simplified with Wi-Fi®/NFC control. In addition to Wi-Fi® support for connecting to smartphones, the HDR-CX900 also supports NFC (near field communication) providing “touch connection” convenience when transferring images to Android™ smartphones and tablets. Users need only touch devices to connect; no complex set-up is required. Moreover, when using Smart Remote Control — a feature that allows shutter release to be controlled by a smartphone — connection between HDR-CX900 and the smartphone can be established by simply touching devices.Specifications1. Requires NFC-compatible mobile device. Check device’s user manual for compatibility.© 2014 Sony Electronics Inc. All rights reserved. Reproduction in whole or in part without written permission is prohibited. Sony, Exmor R, BIONZ and the Sony logo are trademarks of Sony Corporation. All other trademarks are trademarks of their respective owners. Features and specifications subject to change without notice. / UPC:027********* / Updated: January 3, 2014。
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It is ideal for companies facing thermal challenges with their products and companies that require very accurate thermal analysis of their PCB and enclosure designs.SOLIDWORKS Flow Simulation can be used to:• Dimension air conditioning and heating ducts with confidence, taking into account materials, isolation and thermal comfort.• Investigate and visualize airflow to optimize systems and air distribution.• Test products in an environment that is as realistic as possible.• Produce Predicted Mean Vote (PMV) and Predicted Percent Dissatisfied (PPD) HVAC results for supplying schools and government institutes.• Design better incubators by keeping specific comfort levels for the infant and simulating where support equipment should be placed.• Design better air conditioning installation kits for medical customers.• Simulate electronic cooling for LED lighting.• Validate and optimize designs using a multi-parametric Department of Energy (DOE) method.SOLIDWORKS FLOW SIMULATIONOur 3D EXPERIENCE® platform powers our brand applications, serving 12 industries, and provides a rich portfolio of industry solution experiences.Dassault Syst èmes, t he 3D EXPERIENCE® Company, provides business and people wit h virt ual universes t o imagine sust ainable innovat ions. It s world-leading solutions transform the way products are designed, produced, and supported. Dassault Systèmes’ collaborative solutions foster social innovation, expanding possibilities for the virtual world to improve the real world. The group brings value to over 220,000 customers of all sizes in all industries in more than 140 countries. For more information, visit .Europe/Middle East/Africa Dassault Systèmes10, rue Marcel Dassault CS 4050178946 Vélizy-Villacoublay Cedex France AmericasDassault Systèmes 175 Wyman StreetWaltham, Massachusetts 02451-1223USA Asia-PacificDassault Systèmes K.K.ThinkPark Tower2-1-1 Osaki, Shinagawa-ku,Tokyo 141-6020Japan©2018 D a s s a u l t S y s t èm e s . A l l r i g h t s r e s e r v e d . 3D E X P E R I E N C E ®, t h e C o m p a s s i c o n , t h e 3D S l o g o , C A T I A , S O L I D W O R K S , E N O V I A , D E L M I A , S I M U L I A , G E O V I A , E X A L E A D , 3D V I A , B I O V I A , N E T V I B E S , I F W E a n d 3D E X C I T E a r e c o m m e r c i a l t r a d e m a r k s o r r e g i s t e r e d t r a d e m a r k s o f D a s s a u l t S y s t èm e s , a F r e n c h “s o c i ét é e u r o p ée n n e ” (V e r s a i l l e s C o m m e r c i a l R e g i s t e r # B 322 306 440), o r i t s s u b s i d i a r i e s i n t h e U n i t e d S t a t e s a n d /o r o t h e r c o u n t r i e s . A l l o t h e r t r a d e m a r k s a r e o w n e d b y t h e i r r e s p e c t i v e o w n e r s . 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gpts制作标准
GPTs（Generative Pre-trained Transformers）是OpenAI推出的自定义GPT。
在制作GPTs时，需要遵循以下标准：
1. 明确目标：在开始制作GPTs之前，需要明确目标。
这包括确定要解决的问题、要实现的功能以及目标用户等。
2. 数据质量：用于训练GPTs的数据需要质量高，并且与目标任务相关。
数据清洗和预处理是确保数据质量的关键步骤，包括去除噪音、填充缺失值、处理异常值等。
3. 模型选择：选择适当的预训练模型是制作GPTs的重要步骤。
不同的模型具有不同的特点和适用范围，需要根据目标任务选择最合适的模型。
4. 训练过程：在训练GPTs时，需要合理设置超参数、选择适当的优化器和学习率等。
同时，训练过程中也需要对模型进行适当的调整和优化，以确保模型能够快速收敛并获得良好的性能。
5. 评估与调优：在训练完成后，需要对GPTs的性能进行评估。
这包括准确率、召回率、F1值等指标的评估。
根据评估结果，可以对GPTs进行进一步的调优和改进，以提高其性能。
6. 部署与监控：将训练好的GPTs部署到实际应用中时，需要考虑模型的运行效率和稳定性。
同时，需要定期对模型进行监控和维护，以确保其性能和准确性。
7. 隐私与安全：在制作和部署GPTs时，需要关注隐私和安全问题。
这包括数据隐私、模型安全、防止恶意使用等。
需要采取适当的措施来保护用户隐私和数据安全，并确保模型不会被恶意利用。
遵循这些标准，可以帮助您制作出高质量的GPTs，并在实际应用中获得良好的效果。
TGP11010MHz Pulse Generator with DelayThurlby Thandar Instruments Ltd. operates a policy of continuous development and re-serves the right to alter specifications without prior notice.Designed and built in the EEC by:Thurlby Thandar Instruments Ltd .Glebe Road,Huntingdon.Cambs.PE187DX England Tel:+44(0)1480412451Fax:+44(0)1480450409e-mail:sales@ Web:THURLBY THANDAR INSTRUMENTSTGP11010MHz Pulse GeneratorPERIOD PULSE WIDTHPULSE DELAYTTL OUTMAIN OUTSYNC OUTAMPLITUDE FUNCTION /MODEManual Trigger Run Triggered GatedTRIGGER INOPERATEOn Off10V Max.NormalComplement1V -10V 0.1V -1V50Ω100ns1ms100us 1s100ms 10ms 10us 1us 500ms50us500us50ns500ns 5US5ms50ms 500ms50us500us50ns500ns 5us 5ms50ms 111101010Square Double PulsePulseDelayed Pulse56432178910OverlapOverlapTHURLBY THANDAR INSTRUMENTSq 0.1Hz to 10MHz frequency rangeq 50ns minimum pulse width; fully variable pulse delay q Squarewave, double pulse and delayed pulse modes q Free-run, gated and triggered modesq50Ωoutput, variable 0.1V to 10V; TTL and sync outputsAn essential instrumentThe generation of pulses for the stimulus and control of electronic systems is beyond the capability of all but the most sophisticated of function gener-ators.The architecture of a dedicated pulse generator enables it to generate pulses of a set width regardless of the repetition rate offering duty cycles which can extend down to 1in 100million.In addition to continuous operation,single or multiple pulses can be gener-ated in response to trigger or gating signals with precisely defined timing relationships.A dedicated pulse-waveform output amplifier provides flat top pulses with fast rise and fall times at variable amplitude.Variable delayThe TGP110offers selectable delay between the sync output and pulse output.In triggered mode this also sets the delay between a trigger signal and the start of the pulse.Wide pulse rangeThe TGP110can generate pulse widths in the range 50ns to 5s.There are eight overlapping decade ranges with vernier control within each range.The period range is 100ns to 10s,equivalent to a repetition rate range of 10MHz to 0.1Hz.Delay is independently adjustable over the same range as pulse width.A complement switch inverts the mark-space polarity.Squarewave and double pulseIn square mode,squarewaves are generated at a frequency set by the pe-riod controls alone.This provides a convenient means of generating vari-able period edges where the pulse width is unimportant,for example.In double pulse mode,a second pulse is generated within every period at a set delay after the start of the first pulse.The delay is independently ad-justable.SPECIFICATIONSPERIOD,PULSE WIDTH,DELAYEach parameter is variable within 8 overlapping decade ranges with a vernier providing continuously variable control within each range.PERIOD Range:100nsec to 10sec (10MHz to 0·1Hz).Jitter:<0.1%.PULSE WIDTH Range:50nsec to 5sec Jitter:<0.1%.DELAY Range:50nsec to 5secTRIGGER,GATERUNNormal operational mode in which pulses are generated continuously at 0.1Hz to 10MHz.TRIGGEREDDC to 10MHz pulse train in synchronism with external trigger pulses; pulse width determined by pulse width controls. Trigger can be generated manually from front panel button.GATED0·1Hz to 10MHz pulse train, parameters set by period and pulse width con-trols, starts synchronously with leading edge of gate input. Last pulse is com-pleted at the end of gating period. Gating signal can be generated manually from front panel button.PULSE MODESNORMAL PULSEOne pulse is generated each period. The delay setting is ignored.SQUAREWAVE0·1Hz to 10MHz squarewave, frequency set by the period controls. Pulse width and delay settings ignored.Mark : Space ratio:1:1±10%.DOUBLE PULSEA second pulse is generated after a delay set by the delay controls; the delay is related to the leading edge of the first pulse.DELAYED PULSEA pulse is generated after a delay set by the delay controls; the delay is re-lated to rising edge of the trigger signal.INPUTSGATE/TRIG INPUT Frequency range:DC -10MHzSignal range:TTL threshold;max.input ±10V.Min. pulse width:>30nsec.Input Impedance:Typically 10k Ω.OUTPUTS50ΩOUTPUT Amplitude:Two switch selectable ranges of 0·1V -1·0V and1V -10V from 50Ω.(50mV to 500mV and 500mV to 5V into 50Ω).Adjustable within ranges by a single turn ver-nier.Rise/Fall Times:Typically 10nsec into 50Ωload.Maximum 15ns.Aberrations:Typically <5%for output set at >20%of range maxi-mum,into 50Ω.AUX OUTPUTDuplicates 50Ωoutput but at a fixed CMOS/TTL level.SYNC OUTPUT Amplitude:A positive going pulse at CMOS/TTL level.Timing:Leading edge starts >20nsec before the TTL/50Ωout-put transition.Duration:Typically PLEMENT SWITCHInverts the AUX and 50Ωoutputs.GENERALPower:230V or 115V AC nominal 50/60Hz,adjustable internally;operating range ±14%of nominal;20VA max.Size:140x 220x 230mm (HxWxD)Weight:1.6kg (3.5lb)Operating Range:+5°C to 40°C,20-80%RH.Storage Range:-40°C to 70°CSafety:Complies with EN61010-1.EMC:Complies with EN55081-1and EN50082-1.Note:This is a faxable data sheet,a colour brochure is also available.。
多模态机器学习的标签生成与迁移学习随着多模态数据的广泛应用，多模态机器学习的研究也越来越受到关注。
在多模态机器学习中，标签生成是一个重要的任务，它可以用来从多个模态中自动地生成标签。
而迁移学习则是指在一个任务上训练好的模型可以迁移到另一个任务上进行应用。
本文将探讨多模态机器学习中的标签生成与迁移学习，并讨论它们在实际应用中的挑战和解决方法。
首先，我们来介绍一下什么是多模态机器学习。
在传统的机器学习方法中，通常只使用单一模态数据进行训练和预测。
而在现实生活中，我们经常会遇到同时包含图像、文本、语音等不同类型数据的场景。
这些不同类型的数据相互之间存在着丰富而复杂的关联关系，通过同时使用这些数据进行训练和预测可以提高系统性能。
标签生成是指从原始输入数据中自动地提取出相应标签信息。
在单一模态场景下，通常可以通过监督式学习方法来实现标签生成任务。
然而，在多模态场景下，由于不同模态数据之间的差异性，传统的监督式学习方法可能无法直接应用。
因此，研究者们提出了一系列方法来解决多模态标签生成任务。
其中一种常用的方法是使用深度学习模型来学习多模态数据之间的关联关系。
通过将不同类型的数据输入到深度神经网络中，可以通过网络中间层的表示来捕捉到不同模态之间的关联信息。
然而，在多模态标签生成任务中还存在着一些挑战。
首先是数据异构性问题。
由于不同类型数据之间存在着差异性，因此如何将不同类型数据进行有效地融合是一个关键问题。
其次是标签稀疏性问题。
在多模态场景下，由于每种类型的数据都可能存在着缺失或噪声，因此如何有效地提取出准确且稳定的标签信息也是一个挑战。
为了解决这些挑战，研究者们提出了一系列方法和技术来改进多模态标签生成任务。
其中一种常用的方法是使用注意力机制来对不同类型数据进行加权融合。
通过对每个输入样本中每个模态进行注意力权重计算，并将其应用到深度神经网络中，可以更好地捕捉到不同模态之间的关联信息。
另一种方法是使用生成对抗网络（GAN）来进行多模态标签生成。
- 1 -NEOPAN 100 ACROS II is a medium-speed, ultrahigh-image- quality black-and-white negative film that boasts the world’s highest standard in grain quality among ISO-100 films, rich gradation and outstanding sharpness. These features make it an excellent choice for a wide range of photographic applica-tions, including portraits, landscape, architectural subjects, product photography, photomicrography, duplication work and astrophotography.● World’s Highest Standard in Grain QualityThrough the incorporation of Fujifilm’s new proprietary “Super Fine-Σ Grain Technology ”, this film delivers the world’s highest standard in grain quality among ISO-100 black-and-white films. Its fine grain, along with its superb grain alignment and rich gra-dation, makes possible smoother and sharper textural depiction, even in big enlargements.● Excellent Processing CharacteristicsBy incorporating the newly developed “P .I.D.C. (Precision Iodine Distribution Control) Technology”, NEOPAN 100 ACROS II pro-vides stable processing results not only during manual pro-cessing with all kinds of developers and fixers, but in every type of automatic processor as well.● Improved Reciprocity CharacteristicsThis film exhibits extremely minimal reduction in sensitivity even in extended, low-light exposures, thus producing excellent results in astronomical photography and night scenes, as well as archi-tecture and other subjects requiring long exposures.ISO100/21°Orthopanchromatic135……36-exp. (with patrone)Thickness: 0.134mmTAC (Cellulose Triacetate), Gray baseUse an exposure meter for exposure determination. If a meteris not available, refer to the following table. Light Conditions Seashore or SnowScenesunder Bright SunBright Sunlight Hazy SunlightCloudy BrightCloudy Day or Open ShadeLensAperture f/16 f/11 f/8f/8 f/5.6 ShutterSpeed(sec.)1/250 1/250 1/250 1/1251/125● Reciprocity CharacteristicsNo exposure compensation is required for exposures at shutter speeds of less than 120 seconds. However, for ex-posures of 120 seconds or longer, provide the compensation indicated below. Exposure Time (sec.) 120 - 1000 Exposure Corrections*+1/2* A “+” followed by a number indicates the required increase in lens opening.● The use of an exposure meter is recommended, especially for indoor photography due to the wide variation in brightness levels that may be encountered. Use of a tripod or other means of stabilizing the camera is recommended for expo-sures at shutter speeds of less than 1/100 secondFlash Exposure ● Shutter SpeedWhen electronic flash exposures are to be made, the shutter speed for cameras with a focal-plane shutter should be set in accordance with the camera instructions. In the case of lens-shutter cameras (such as compact cameras, certain medium-format cameras and studio cameras), the shutter speed can be varied. ● Lens ApertureThe following formula can be used to obtain satisfactory lens opening.NEOPAN 100 ACROS II (135)NEOPAN 100 ACROS II (135)AF3-0258E- 2 -LensAperture = (f-number)Electronic Flash Guide Number (at ISO 100)Electronic Flash-to-Subject Distance(meters or feet)● When an automatic electronic flash unit is employed, set the film speed at ISO 100. 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In such cases, use the safelight for as short a period as possible and only towards the end of the development period.(1) DevelopmentTo prevent the appearance of development marks and as-sure uniform finish, agitate the developer continuously for the first minute and for five seconds every minute thereafter.● Development Conditions (Small Tank Development) The following table shows development times and tempera-tures for each developer.When deep tanks are used, development times should be extended by 5 to 10%, compared to those used with small tanks.* EI (Exposure Index) is the exposure determination designator and thecamera or exposure meter ISO speed should be set to this value.** The (1:1) parenthesized ratio given in the foregoing table indicates thatone part water is to be added to one part developer.(2) Stop BathFor the stop bath a 1.5 % acetic acid solution is recommended. 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RESOLVING POWER7-3, Akasaka 9-chome, Minato-ku, Tokyo 107-0052, JapanRef.No. AF3-0258E (20.02-BX)- 4 -。
GENERATING PROSODY BY SUPERPOSING MULTI-PARAMETRICOVERLAPPING CONTOURSBleicke Holm and Gérard BaillyInstitut de la Communication Parlée-CNRS/INPG/U346,avenue Félix Viallet,38031Grenoble Cedex1,FranceABSTRACTWe present here a model for generating prosody by superposing overlapping multi-parametric contours.These contours are as-sociated with high-level communication tasks such as segmenta-tion,hierarchisation or emphasis of discourse units.We propose a analysis-by-synthesis scheme for automatically learning these contours and apply this new paradigm to the enunciation of math-ematical formulae and utterances carrying various attitudes.1.INTRODUCTIONIt is a commonly accepted that prosody takes part in the transmis-sion of linguistic information during the speech act.One of the most studied linguistic functions that prosody assumes is hierar-chisation and segmentation of units.If there is a large consensus in literature concerning the major role of prosody in language ac-quisition and structuring of speech,authors diverge on the way prosody actually encodes information.In the framework of au-tomatic prosody generation the aim is to establish an acceptable evolution of prosodic parameters depending on the structure of the utterance.The major questions to answer are:What information is transmitted?–and:How is this information encoded? Encoding linguistic information–supposed to be discrete–by means of continuously varying prosodic parameters is described by a large variety of approaches.In most cases a phonological interface is used that aims to translate linguistic structure in a phonological structure by organising salient prosodic events into tonal and accentual structures.This step of phonological transfer is followed by the generation of the prosodic continuum thanks to a specific phonetic model.Phonological units.Automatic generation systems may be differ-entiated by means of the richness of the phonological structures they employ:Black and Hunt[3]use the ToBI-transcription[13], Di Christo et al.IntSyn[7]–whereas other authors prefer a more economic description of the phonological structure mainly in terms of accentual groups[15,9,10].This last group of studies is very heterogeneous:Malfrère et al.[9]use a crude segmenta-tion and indexing procedure concentrating on an elegant concate-nation of contours,whereas Pasdeloup[12]focusses on establish-ing a well suited segmentation into accentual groups.Phonetic Models.Differences in the phonetic models are partly induced by the differences in phonological models:If the phono-logical description allows a determination of target points,a sim-ple interpolation between these points may be sufficient[7].If the output of the phonological model consists in indexed do-mains,prosodic contours are generally obtained by concatenation and/or superposition of sub-contours living on the domains.Sub-contours maybe generated by various manners ranging from rule-based to statistical methods.Targets vs.Contours.Gating experiments seem to indicate that prosodic contours contain more information than a series of tar-get points.Our believe is that such targets(if they exist)are a secondary product of a more global and implicit process.Salient prosodic events may be used to describe specific prosodic real-isations and to compare natural and synthetic prosody,but they should not be at the basis of a model.An extreme example of such an implicit modelling is the work of Traber[15]who uses a neural network to map the information supposed to determine prosody directly to the phonetic realisation.The important con-tribution is not the use of a neural network,but the proposition of an encoding procedure on a sub-symbolic level.On the other hand,this model operates as a black box and hence provide no comprehensive inside on prosody at all.Linear vs.superpositional encoding.In order to communicate we have to be able to compose and decompose the information in the prosodic signal.If we reject the decomposition into target points for the reasons given above,we have to adopt another en-coding/decoding procedure.Since Fujisaki[5],superposition of contours has been widely used.Many models use at least two su-perposing levels:phrase and accentual group.Superposition may be very explicit as in Möbius et al.[10]or more implicit as in Black et al.[3]where accent realisations are expressed relative to a declination line.Following Thorsen[14],Aubergé[1]uses up to four levels.The main characteristic of her proposal is the pri-ority given to the functions that may be encoded by prosody and the direct process of phonetic encoding.The model we present here is inspired by Aubergé.We propose a straightened relation between functions and phonetic realisation which allows for a simple and comprehensive description of the encoding process that operates by superposing overlapping and nested contours that are coextensive to the discourse units con-cerned by the encoded function.This model is able to generate highly structured prosody since we do not impose a restriction on the number of superposed levels.An important part of this paper is the description of how to obtain from a learning corpus the con-tours to be superposed.We will show and discuss the application of the model on the enunciation of mathematical formulae(MF) and utterances carrying various attitudes–demonstrating that our model is compatible with the expansion of prosodic contours de-scribed by Morlec[11].2.ENUNCIATION OF MATHEMATICALFORMULAEOur corpus was established in order to study how prosody may encode dependency relations in an utterance.Read MF were cho-sen because they offer a deep syntactical structure and because they are–when spoken–often ambiguous,forcing thus speaker and listener to use prosodic cues.All formulae are algebraic equa-tions such as proposed in4th grade exercises.They involve classi-cal operations on2nd degree polynomials.The corpus was gener-ated automatically varying systematically the length and syntactic depth of constituents.We end up with157MF recorded by one male French speaker who was instructed not to use lexical struc-tural markers–such as"open parenthesis"–but to make use of prosody.As shown infigure1and more thoroughly analysed in[8],the prosodic structure of the spoken formulae is rich and deep.More-over,the height of a node in the performance tree(cf.Gros-jean[6])grows with the syntactic depth of the associate con-stituent which is in good correspondence with a superpositional model.(a)Syntax(b)PerformanceFigure1:Syntactic structure and performance structure of a for-mula3.DESCRIPTION OF THE MODELIn Aubergé’s[1]proposal every linguistic level generates,de-pending on its nature,function and length,a set of multipara-metric contours that are then concatenated and superposed.Mor-lec[11]proposed a modular connectionist model enabling a learn-ing of contours with less a priori assumptions and a thorough anal-ysis of movement expansion.This approach has been validated in analysis as well as synthesis.Nevertheless this morphological model suffers from two draw-backs:(a)it follows syntax too closely,i.e.contours are indexed by detailed and often redundant syntactic characteristics–and(b) even if the implementation by means of recurrent neural networks copes better with coarticulation phenomena as a simple concate-nation of contours[1,9],it looses the notion of a lexicon of con-tours indexed by linguistic functions.Our proposal aims to solve these problems by(a)establishing a real functional morphophonology–and(b)using a superposition of localised and overlapping contours.3.1.A functional morphophonologyWe suppose that prosody is part of an interacting system of lin-guistic agents that provide general functions.Some functions–such as encoding of attitudes and emotions–may be fulfilled by prosody in a more or less autonomous manner,others–such as segmentation and hierarchisation are accomplished more syner-getically.In this study we test the hypothesis that prosody is able to encode segmentation and hierarchy of adjacent discourse units by a contour that is coextensive with the two units and that is anchored at the frontier between these units.Hierarchy is en-coded by superposition of these localised contours that may over-lap and that may be nested.The number of nesting levels is not constrained.This type of encoding offers an attractive compro-mise between information spreading(needed to explain anticipa-tory phenomena)and information localisation(to that part of the utterance it is meant to act on).3.2.Learning of contoursIn order to get the model to work,the crucial problem is its inver-sion,i.e.the extraction of contours from a natural speech corpus. Inversion becomes possible if we impose several constraints:(1) a contour is determined by the function it encodes,(2)it does not depend on thehierarchical level it is applied to and(3)contour shapes depend only on their lengths(in terms of number of sylla-bles)and the position of the anchor point.For each linguistic function to be encoded there is one generation module in charge with providing the mapping from phonotactic input information to prosodic parameters(cf.fig.2).The modules are implemented as simple feed-forward neural networks–not in order to claim any neuromimetic properties but because they have proofed their ability to generate coherent contours with respect to the input information.Munit Ainput:unit B syllables:markerFigure2:Generation of a contour encoding the relation"M"be-tween two adjacent units.For each syllable the module provides based on a4-component input vector four prosodic parameters (three-targets and a lengthening factor that measures the de-viation of the syllable duration with respect to an expected dura-tion).Since each module may be used to generate contours on any hierarchical level,we cannot use a simple hierarchical learning scheme as done by Morlec.We propose an iterative analysis-by-synthesis method as follows(cf.fig.3):(1)generating synthetic contours with the modules in a preliminary state,(2)using the error of the predicted contours with respect to the observed ones in order to calculate a better set of contours for each module that (3)will be used as targets during a classical learning procedure for neural networks.–This scheme relies on two hypothesis:(a)The prediction error contains the information that is contained in nat-ural prosody but not(yet)captured by the contributing generation modules–and(b)the learning step(3)provides afilter capturing regularities within each target set,i.e.if a contribution of the pre-diction error is attributed to the"wrong"module,it should have no systematic relation to the associated input values and will thus beflattened in(3).Thisfilter property allows for a certain free-dom in the implementation of(2).The main constraint for"bet-ter"target contours is that their superposition equals the observed contour.The easiest way to do this is to divide for each syllable and for each prosodic parameter the error by the number of con-tributing contours and to add that to these contours.While this procedure provides a good approximation of the training corpus after a reasonable number of learning cycles,we can expect better generalisation properties if we impose further constraints during (2):Prototypical contours should be reasonable simple–this can be achieved byflattening the contributing contours before calcu-lating the preliminary prediction.Properties of the superposing contours may be used to weight the correction terms(reinforcing existing maxima e.g.).Knowledge about salient prosodic events associated with some function could be used to attribute a privi-lege to a contour in(2).Figure3:analysis-by-synthesis-scheme3.3.Enunciation of mathematical formulae The predominant role of prosody in the enunciation of MF is seg-mentation/hierarchisation,i.e.to signal the nesting of operators. There are two kind of operators in our corpus:unary ones(such as1see alsofigure6and explanation below of the preceding unit.A similar behaviour can be observed in the contours for the lengthening factor.RMS-errors and correlations for the-contours are given infigure4.We divided each corpus into two equally sized parts A and B.Training was performed ei-ther on the entire corpus(T)or on one of the parts.No effort has yet been put on the optimisation of the stop criterion which might explain the slight over-learning with the training set A.testT BT 2.02 2.071.85B 2.07 2.01(a)RMS-errortestT BT0.900.900.92B0.900.90(b)correlationFigure4:Top part of the plots:Predicted(full line)and origi-nal(dashed)contours(in half-tons with respect to126Hz);bot-tom part:contours contributing to the prediction–anchor points and the associated generation modules are given(M,L,R),dotted lines indicate zero for each contour.The table shows RMS-errors and correlations for different training/test-configurationsThe strength of the proposed model is its ability to exploit the recursivity of the syntactic structure by using the same genera-tion modules on all hierarchical levels which is particularly effi-cient for the enunciation of MF.Nevertheless,it provides good prosody predictions when trained on ordinary speech corpora.In figure5we show an example for a French sentence uttered in four different attitudes(assertion,evidence,incredulity and yes/no-question).The RMS-errors show–as for the maths corpus–fairly good generalisation properties(e.g.training on A–test on B).Best scores are obtained for yes/no-questions due to the fact that the contours are ratherflat.Nevertheless,results for the intonationally more structured assertions are satisfying.Figure6 shows the movement expansion of the IQ-contours.Our observa-tions are fully compatible with Morlec[11].5.CONCLUSIONS AND OUTLOOK Compared to the prior work of Aubergé/Morlec the model pre-sented here offers several advantages:(1)It is now possible to exploit naturally the deep recursivity of dependency relations in the maths corpus–the model architecture does not depend any-more on the number of nesting levels aimed to capture.(2)The relation between linguistic functions to encode and the generation of contours is straightened–one module is charged to encode one function.The model offers thus a dynamic lexicon:contours are indexed by the linguistic function and generated dynamically in order tofit phonotactic needs.(3)Contours are localised where they are meant to act i.e.on the discourse units they relate.o c a z e d c o n t o u r ss u p e r p o s t o n /o r g n a (a)assertion (AS)(b)evidence (EV)(c)incredulity (IQ)(d)yes/no-question (QS)AS T B T 1.681.691.59B 1.81 1.64EV T B T 1.761.761.68B 1.91 1.63DI T B T 1.311.291.32B1.351.20QS T B T 1.201.191.15B1.311.14Figure 5:(a–d):-contours for the sentence "Les gamins coupaient des rondins"in four different attitudes.Bottom:RMS-errors for the different corpora.Further work is needed to refine the error-distribution step of the model-inversion-algorithm and to optimise the learning of indi-vidual modules (number of hidden units,stop criterion)in order to obtain even better generalisation properties.Our main interest is to furnish a perceptual evaluation of the model.We are working on an experimental protocol aiming to compare different prosodic realisations with respect to the online processing of a listener.We will analyse the lag between natural vs synthetic speech and handwriting events in a dictation task.REFERENCES1.Aubergé,V .Developing a structured lexicon for synthesis of prosody.In Bailly,G.and Benoît,C.,editors,Talking Machines:Theories,Models and Designs ,pages 307–321.Elsevier B.V .,1992.2.Bailly,G.Integration of rhythmic and syntactic constraints in a model of generation of French prosody.Speech Commu-nication ,8:137–146,1989.3.Black,A.W.and Hunt,A.J.Generating f0contours from tobi labels using linear regression.In Proceedings of the In-ternational Conference on Speech and Language Processing ,pages 1385–1388,1996.4.Emerard, F.Synthèse par diphones et traitement de lafor sentence lengths varying from 2to 6syllables (left:,right:lengthening factor).prosodie.Thèse de troisième cycle,Universitéde Grenoble III,Grenoble,France,1977.5.Fujisaki,H.and Sudo,H.A generative model for the prosody of connected speech in Japanese.Annual Report of Engineer-ing Research Institute ,30:75–80,1971.6.Gee,J.P.and Grosjean,F.Performance structures:a psy-cholinguistic and linguistic appraisal.Cognitive Psychology ,15:411–458,1983.7.Hirst,D.J.and Di Cristo,A.Intonation systems:a survey of twenty languages .Cambridge University Press,Cambridge,1998.8.Holm,B.,Bailly,G.,and Laborde,C.Performance struc-tures of mathematical formulae.In Proceedings of the In-ternational Congress of Phonetic Sciences ,volume 2,pages 1297–1300,San Francisco,USA,1999.9.Malfrère, F.,Dutoit,T.,and Mertens,P.Automatic prosody generation using suprasegmental unit selection.In ESCA/COCOSDA Workshop on Speech Synthesis ,pages 323–328,1998.10.Möbius,B.,Pätzold,M.,and Hess,W.Analysis and synthesisof german f0contours by means of fujisaki’s model.Speech Communication ,13:53–61,1993.11.Morlec,Y .,Bailly,G.,and Aubergé,V .Synthesising attitudeswith global rhythmic and intonation contours.In Proceed-ings of the European Conference on Speech Communication and Technology ,volume 1,pages 219–222,Rhodes -Greece,1997.12.Pasdeloup,V .A prosodic model for french text-to-speechsynthesis:A psycholinguistic approach.In Bailly,G.,Benoît,C.,and Sawallis,T.,editors,Talking Machines:Theories,Models and Designs ,pages 335–348.Esevier B.V .,1992.13.Silverman,K.,Beckman,M.,Pitrelli,J.,Ostendorf,M.,Wightman,C.,Price,P.,Pierrehumbert,J.,and Hirschberg,J.Tobi:a standard for labeling english prosody.Proceedings of the International Conference on Speech and Language Pro-cessing ,2:867–870,1992.14.Thorsen,N.G.Standard Danish sentence intonation –Pho-netic data and their representation.Folia Linguistica ,17:187–220,1983.15.Traber,C.Fo generation with a database of natural fo pat-terns and with a neural network.In Bailly,G.and Benoît,C.,editors,Talking Machines:Theories,Models and Designs ,pages 287–304.Elsevier B.V .,1992.。
